Issued Superseding Dated
May 2000 BR 45(2) May 1997
BR 45(2) ADMIRALTY MANUAL OF NAVIGATION VOLUME II ASTRO NAVIGATION
By Command of the Defence Council
COMMANDER COMMANDER IN CHIEF FLEET CINCFLEET/FSAG/P45/2
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SPONSOR
This publication sponsored by the Commander in Chief Fleet. All correspondence correspondence concerning this publication is to be forwarded to the Operational Publications Authority: CINCFLEET/PFSA Fleet Staff Authors Group Pepys Building HMS COLLINGWOOD FAREHAM Hampshire PO14 1AS
Copied to the Sponsor Desk Officer: | | | | | | | | |
SO1 N7 NAV Room 170 Office of the Commander in Chief Fleet West Battery (PP 300) Whale Island HMS EXCELLENT Portsmouth Hampshire PO2 8DX
Copied to the Subject Matter Specialist: | | | | | | | |
SO(N) Navigation Section Endeavour Building Maritime Warfare School HMS COLLINGWOOD Fareham Hampshire PO14 1AS
© MOD 2000
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BR 45(2)
PREFACE The Admiralty Manual of Navigation (BR 45) consists of seven volumes:
bound book book (also (also supplied supplied in A4 loose leaf from from 2002) 2002),, covering covering General General Volume 1 is a hard bound Navigation and Pilotage (Position and Direction, Geodesy, Projections, Projections , Charts and Publications, Publicat ions, Chartwork, Fixing, Tides and Tidal Streams, Coastal Navigation, Visual and Blind Pilotage, Navigational Errors, Relative Velocity, Elementary Surveys and Bridge Bri dge Organisation). Organisation) . This book is available to the public from The Stationary Stationary Office.
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Volume 2 is a loose-lea loose-leaff A4 A4 book covering covering Astro Navigation Navigation (including (including Time). Chapters Chapters 1 to 3 cover cover the syllabus syllabus for officers officers studying studying for the the Royal Royal Navy Navy ‘Navigationa ‘Navigationall Watch Certificate’ Certificate’ (NWC) and for the Royal Royal Navy ‘n’ Course. (The NWC is equivalent to the certificate awarded by the Maritime & Coastguard Agency (MCA) to OOWs in the Merchant Service under the international inter national Standardisa Stand ardisation tion of Training, Certification and Watchkeeping Watchkeeping (STCW) (STCW) agreements. ) The remainder remainder of the the book book covers the detailed detailed theory theory of astro-nav astro-navigatio igation n for officers officers studying studying for the the Royal Royal Navy Navy Specialist Specialist ‘N’ ‘N’ Course, Course, but but may also be of interest interest to ‘n’ level level officers officers who who wish to to resear research ch the subject subject in greater greater deta detail. il. Volum Volumee 2 is not avai availab lable le to the the genera generall public, public, although it may be released for sale in the future.
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protectively ly mark marked ed loose loose-lea -leaff A4 book, book, cov coverin ering g navig navigatio ation n equipm equipment ent and and Volume 3 is a protective systems (Radio Aids, Satellite Navigation, Direction Finding, Navigational Instr uments, Logs and Echo Sounders, Gyros and Magnetic Compasses, Inertial Navigation Systems, Magnetic Compasses and De-Gausing, Automated Navigation and Radar Plotting Systems, Electronic Chart equipment). equipment). Volume 3 is not available to the general public.
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protectively ly marked marked loose-leaf loose-leaf A4 A4 book book coverin covering g conduct conduct and and operation operational al methods methods Volume 4 is a protective at sea (Navigational sea (Navigational Command and Conduct of RN ships, passage planning and routeing, and operational navigation techniques that are of particular concern to the RN). Assistance (Lifesaving) and Salvage are Salvage are also included. Volume 4 is not not available to the general general public.
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Volume 5 is a loose-leaf A4 book containing exercises in navigational calculations (Tides and Tidal Streams, Astro-Navigation, Great Circles and Rhumb Lines, Time Zones, and Relative Velocity). Velocity). It also provides provides extracts from most of the the tables necessary necessary to undertake undertake the exercise exercise calculations. calculations. Volume Volume 5 (Supplement (Supplement)) provides provides worked worked answers. answers. Volumes Volumes 5 and 5 (Supple (Supplement) ment) are not not avail availab able le to to the the gen gener eral al pub public lic,, alth althou ough gh they they may may be be rele releas ased ed for for sale sale in the the futu future re..
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Volume 6 is supplied supplied in three, three, loos loose-le e-leaf af A4 binde binders: rs: the the non-pr non-prote otectiv ctively ely mark marked ed Binder Binder 1 covering generic principles of shiphandling (Propulsion of RN ships, Handling Ships in Narrow Waters Manoeuvring and Handling Ships in Company, Replenishment, Towing, Shiphandling in Heavy Weather and Ice), Ice), and the the prote protecti ctivel vely y marke marked d Binder Binderss 2 and 3 coveri covering ng all all aspects aspects of of class-specific Shiphandling Characteristics of RN Ships / Submarines a nd RFAs). Turning data quoted in Volume 6 is approximate and intended only for overview purposes. Volume 6 is not not avai availab lable le to the the gene general ral publ public, ic, alth althou ough gh Bin Binde derr 1 may may be be releas released ed for for sal salee in the the fut futur ure. e.
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protectively marked loose-leaf loose-leaf A4 book book covering covering the management management of a chart outfit outfit Volume 7 is a protectively (Upkeep, Navigational Warnings, Chronometers and Watches, Portable and Fixed Navigational Equipment, and Guidance Guidance for the Commanding Officer / Navigating Officer). Officer) . Volume 7 is not available to the general public.
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Note.
Terms appearing in italics in newer books are are defined in the ‘Glossary’ of each book. book.
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PROPOSALS FOR CHANGES
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Protective Marking ......................................... ................................................................ ............................................. ...................... Ship/Establishment ....................................... Originating Dept .................................... .................................... Date .......................... Title of Publication Current Issue Status DETAILS OF COMMENTS Page
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Comment Continue on a separate sheet if required
Originator: (Name in Block Letters) Signature Rank/Rate
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Protective Marking ......................................................................................
Forward copies of the above form through the usual Administrati ve Channels to the addressees listed on Page ii.
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RECORD OF CHANGES Note:
The incorporation of Temporary Amendments Amendments such as Signals, AILs etc should be recorded on page vi overleaf. CHANGE NO.
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Incorporating Change 1
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RECORD OF TEMPORARY AMENDMENTS Note.
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REFERENCE NO.
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BR 45(2)
CONTENTS Chapter 1
The Celestial Sphere - Introduction Section 1 Basic Definitions and Structure The Magnitudes of Stars and Planets Section 2 Methods of Identifying Heavenly Bodies Section 3
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Chapter 2
Time Systems
Chapter 3
Practical Planning, Taking, Reduction and Plotting of Sights Introduction Section 1 Section 2 Planning Astro Sights Section 3 Description, Preparation and Use of Sextant Reducing Sights (Processing of Sextant Readings) Section 4 Plotting Sights Section 5 Annex 3A NAVPAC 2 - Extracts from HM Nautical Almanac Office NAVPAC 2 User Instructions
Chapter 4
Chapter 5
Chapter 6
Chapter 7
The Celestial Sphere - Definitions, Hour Angles and the Theory of Time Section 1 ‘Ready Reference’ List Section 2 Hour Angles Solar Time Section 3 Sidereal Time Section 4 Section 5 Lunar and Planetary Time Identification of Heavenly Bodies, Astronomical Position Lines, Observed Position and Sight Reduction Procedures Section 1 Identification of Heavenly Bodies Section 2 Astronomical Position Lines Calculating Altitude, Azimuth and True Bearing Section 3 Sight Reduction Procedures Section 4 Section 5 Very High Altitude (Tropical) Sights Section 6 High Latitude (Polar) Sights Description and Setting of the Star Globe Annex 5A
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Meridian Passage and Polaris Section 1 Meridian Passage Polaris Section 2
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The Rising and Setting of Heavenly Bodies Section 1 Requirements and Generic Definitions Sunrise, Sunset and Twilights Section 2 Moonrise and Moonset Section 3 High Latitudes Section 4
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Chapter 8
Refraction, Dip and Mirage
Chapter 9
Errors in Astronomical Position Lines
Appendix 1
The Sky at Night
Appendix 2
Extracts from the Nautical Almanac (1997)
Index Index LEP
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List of Effective Pages
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ACKNOWLEDGEMENTS AND COPYRIGHT
UK Hydrographic Office (UKHO)
Thanks are due to the UK Hydrographic Office (UKHO) for their permission and assistance in reproducing data contained in this volume. This data has been derived from material published by the UKHO and further reproduction is not permitted without the prior written permission of CINCFLEET/PFSA and UKHO. Applications for permission should be addressed to CINCFLEET/PFSA at the address shown on Page ii and also to the Copyright Manager at UK Hydrographic Office, Admiralty Way, Taunton, Somerset TA1 2DN.
HM Nautical Almanac Office (HMNAO) and the Council for the Central Laboratory of the Research Councils (CCLRC)
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Thanks are due to the HM Nautical Almanac Office (HMNAO) for their assistance in reproducing data contained in this volume. The materi al from the ‘Nautical Almanac’ and from ‘NAVPAC and Compact data 2001-2005’ (published by the Stationary Office) is reproduced by kind permission of the Council for the Central Laboratory of the Research Councils (CCLRC). ‘NAVPAC and Compact data 2001-2005’ is also published by Willmann-Bell in the US under the name ‘AstroNavPC and Compact data 2001-2005’. Further reproduction of this data is not permitted without the prior written permission of CINCFLEET/PFSA and CCLRC. Applications for permission should be addressed to CINCFLEET/PFSA at the address shown on Page ii and also to HMNAO, Space Science and Technology Department, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom.
General
Other parts of BR 45 Volume 2 not covered by the copyright notes above are MOD copyright and further reproduction is not permitted without the prior written permission of CINCFLEET/PFSA at the address shown on Page ii.
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CHAPTER 1 THE CELESTIAL SPHERE - INTRODUCTION CONTENTS SECTION 1 - BASIC DEFINITIONS AND STRUCTURE
The Celestial Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Angular Distance Between Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Apparent Path of the Sun in the Celestial Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The First Point of Aries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Declination and Parallels of Declination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hour Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sunrise and Sunset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Twilight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geographic Position of a Heavenly Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Great Circles and Small Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Meridian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Greenwich Meridian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rhumb Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Observer’s Zenith (Z) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Celestial Horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Visible Horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Azimuth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Altitude (of a Heavenly Body) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vertical Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Para 0101 0102 0103 0104 0105 0106 0107 0108 0109 0110 0111 0112 0113 0114 0115 0116 0117 0118 0119
SECTION 2 - THE MAGNITUDES OF STARS AND PLANETS
The Solar and Stellar Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stellar Magnitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0120 0121
SECTION 3 - METHODS OF IDENTIFYING HEAVENLY BODIES
The Identification of Heavenly Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Use of Computers for Identification of Heavenly Bodies . . . . . . . . . . . . . . . . . . . . . . . Description of the Star Finder and Identifier (NP 323) . . . . . . . . . . . . . . . . . . . . . . . . . The Nautical Almanac Planet Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0130 0131 0132 0133
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CHAPTER 1 THE CELESTIAL SPHERE - INTRODUCTION SECTION 1 - BASIC DEFINITIONS AND STRUCTURE 0101.
The Celestial Sphere To an observer on Earth, the sky has the appearance of an inverted bowl, so that the star s and other heavenly bodies, irrespective of their actual distance from the Earth, appear to be situated on the inside of a sphere of immense radius described about the Earth as centre. This is called the Celestial Sphere (Fig 1-1). The Earth’s axis, if produced, would cut the Celestial Sphere at the Celestial Poles (P, P’). The Earth’s equator, if produced, would cut the Celestial Sphere at the Celestial Equator (Q, Q’).
Fig 1-1. Celestial Sphere, Celestial Poles and Celestial Equator 0102.
Angular Distance Between the Stars The appearance of the stars on the Celestial Sphere conveys no idea of their actual distances from the Earth. Two stars chosen at random may actually be at vastly different distances from earth, but as both are deemed to reside on the surface of the Celestial Sphere, the only practical method of measuring their relative positions is to measure the angle between them. This angle is known as an Angular Distance. As the stars are immensely far away, the Angular Distances of stars remain virtually constant within the ordinary limits of time. The position of a heavenly body on the celestial sphere can be defined by two Angular Distances - ‘Declination’ and ‘Hour Angle’ which are explained more fully at Paras 0105-0106 and Chapter 4. 1-3 Change 1
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0103.
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Apparent Path of the Sun in the Celestial Sphere
a. The Ecliptic. The Earth describes an elliptical orbit around the Sun which takes one year to complete. The apparent path of the Sun in the Celestial Sphere is known as The Ecliptic. It is a Great Circle, and makes an angle of 23° 27' (23½°) with the Celestial Equator because the Earth’s axis of rotation is tilted by that amount from the perpendicular to the plane of the Earth’s orbit (Fig 1-2). The angle between the plane of the Celestial Equator and that of the Ecliptic is known as the Obliquity of the Ecliptic.
Fig 1-2. Celestial Equator, Plane of the Ecliptic and First Point of Aries
b. Seasons, Tropics, Solstices and Equinoxes. The existence of the Earth’s 23° 27' tilt is of fundamental importance to life on earth, as it defines the limits of the tropics, causes the seasons to change and the length of daylight to vary during the year (outside the equatorial region where very little change takes place). The extent of the Sun’s apparent movement can be established by plotting the Latitude of positions on Earth where the noon sun is directly overhead at some ti me during the year (Fig 1-3) . The Sun is directly over the Equator at the Spring Equinox (21 March), moves north to Latitude 23½° at the Summer Solstice ( 21 June), back to the Equator at the Autumn Equinox (23 September), moves south to Latitude 23½° at the Winter Solstice (22 December) and back to the Equator at the Spring Equinox (21 March). The seasonal changes caused by this apparent movement of the sun through the year have a profound effect on ocean currents, weather systems and overall climate. Many biological ecosystems in the world depend on these seasonal changes for their existence (Fig 1-4). 1-4 Change 1
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Fig 1-3. Latitude of Positions on Earth where the Noon Sun is Directly Overhead
Fig 1-4. Change of Seasons during the Year , Associated with Sun’s Movement The First Point of Aries To measure Angular Distances, a fixed point in space is needed as a datum; a star located where the Ecliptic cuts the Celestial Equator would be ideal for this. When the early Greek astronomers started to make observations, the Ecliptic cut the Celestial Equator at the Spring Equinox (21 st March) in the vicinity of the constellation of Aries; one star on the edge of the constellation, known as the First Point of Aries ( ), was perfectly aligned and so was selected as this datum (Fig 1-2). Over time, due to slow Precession of the earth’s tilt (see Para 0544f for a full explanation of Precession), there has been a backward movement of the point of intersection of the Ecliptic and the Celestial Equator . As a result, Aries has ‘apparently moved away’ from this position. However, the name ‘ First Point of Aries’(normally abbreviated to ‘ Aries or ’) for the spring intersection of the Ecliptic and the Celestial Equator has been retained as the datum for calculations and tables ever since, even though no star now occupies this position. The position of the autumn intersection of the Celestial Equator and the Ecliptic (23rd September) is known as the First Point of Libra.
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0104.
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0105.
Declination and Parallels of Declination Declination corresponds to terrestrial Latitude projected onto the Celestial Sphere and is the Angular Distance of the heavenly body north or south of the Celestial Equator (Fig 1-6). A Parallel of Declination corresponds to a terrestrial parallel of Latitude and is a Small Circle on the Celestial Sphere, with its plane parallel to the plane of the Celestial Equator . Note 1-1. Although the concept of projecting terrestrial Latitude onto the Celestial Sphere is a very good description, ‘Declination’ should never be described as ‘Celestial Latitude’ because this term is used by astronomers to measure an Angular Distance, referenced to the Ecliptic rather than the Celestial Equator. ‘Celestial Latitude’ has no use in the navigational problem. 0106.
Hour Angles Hour Angles loosely correspond to terrestrial Longitude projected onto the Celestial Sphere, but the analogy is complicated by the easterly rotation of the Earth which continually changes some Angular Distances with time. It was because of this fundamental link to time that the term Hour Angles was used to describe this measurement. There are several variants of Hour Angle which, depending upon which two bodies are to be referenced for measurement, can be added or subtracted to calculate the required Angular Distance. Further details of these are at Chapter 4 but do not concern students studying for the Royal Navy NWC (Navigational Watchkeeping Certificate) except familiarity with the titles and where to look up the data if using the Star Finder and Identifier (Paras 01312 and 0324) or The Nautical Almanac Planet Diagram (Para 0133). A brief summary of these terms is as follows:
a. Sidereal Hour Angle (SHA). The Sidereal Hour Angle (SHA) is almost static for stars and is tabulated once per 3 days for stars and planets in The Nautical Almanac. b. Right Ascension (RA). Right Ascension (RA) is the same as SHA except measured eastwards (rather than westwards as in SHA). Thus RA = 360° - SHA. c. Greenwich Hour Angles (GHA). The Greenwich Hour Angle (GHA) of the First Point Aries ( ) and the GHAs of the Sun, Moon and Planets are tabulated hour-by-hour (and can be established to the second using Increment Tables) in The Nautical Almanac. d. Local Hour Angle (LHA). The Local Hour Angle (LHA) is GHA of the body +/the observers’s Longitude. Note 1-2. Although the concept of projecting terrestrial Longitude onto the Celestial Sphere is a useful analogy, ‘Hour Angles’ should never be descri bed as ‘Celestial Longitude’ because this term is used by astronomers to measure an Angular Distance, referenced to the Ecliptic rather than the Celestial Equator. ‘Celestial Longitude’ has no use in the navigational problem. 0107.
Sunrise and Sunset
a. Visible Sunrise or Sunset . Visible Sunrise or Sunset occurs when the Sun’s Upper Limb (UL) appears on the Visible Horizon (ie. the Apparent Altitude of the Sun (UL) is 0° 00'). The times of Visible Sunrise and Sunset for Latitudes 60°S to 72°N are displayed on right hand pages of The Nautical Almanac. These times, which are given to the nearest minute, are the UT of the Sunrise / Sunset on the Greenwich Meridian for the middle day of the three days covered by each double page. b. True (Theoretical) Sunrise or Sunset . True (Theoretical) Sunrise or Sunset occurs when the Sun’s centre is on the Celestial Horizon, but due to Atmospheric Refraction the Sun’s Lower Limb appears to be one Semi-Diameter above the Visible Horizon. 1-6 Change 1
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0108.
Twilight Twilight is the period of the day when the Sun is between 0° and 18° below the Celestial Horizon. During Twilight , although the Sun is below the Celestial Horizon, the observer is still receiving light reflected and scattered by the upper atmosphere.
a. Civil Twilight (CT). The times of Morning Civil Twilight (MCT) and Evening Civil Twilight (ECT) are tabulated in The Nautical Almanac for the moment when the Sun’s centre is 6° below the Celestial Horizon. The times are shown in chronological order and the terms ‘ Morning ’ and ‘ Evening ’ are omitted. This is roughly the time at which the horizon becomes clear (morning) or becomes indistinct (evening). b. Nautical Twilight (NT). The times of Morning Nautical Twilight (MNT) and Evening Nautical Twilight (ENT) are tabulated in The Nautical Almanac for the moment when the Sun’s centre is 12° below the Celestial Horizon. The terms ‘ Morning ’ and ‘ Evening ’ are omitted as the times are in chronological order. Morning and evening stars are usually taken between the times of Civil Twilight (CT) and Nautical Twilight (NT). c. Astronomical Twilight. The time of Astronomical Twilight (AT) is the moment when the Sun’s centre is 18° below the Celestial Horizon. Whilst the Sun’s centre is 18° or greater below the Celestial Horizon, ‘Total Darkness’ (with respect to the Sun) is deemed to exist and observations by astronomers may usefully take place. The times of Astronomical Twilight (AT) have no significance in solving the astro- navigation problem and so AT times are not tabulated in The Nautical Almanac. 0109.
Geographic Position of a Heavenly Body The Geographic Position of a heavenly body is the position where a line drawn from the body to the centre of the Earth, cuts the Earth’s surface. To an observer at the Geographic Position, the heavenly body would appear to be directly overhead, ie. at the Observer’s Zenith(Z). 0110.
Great Circles and Small Circles Great Circles and Small Circles are defined and discussed in BR 45 Volume 1. For the convenience of readers their definitions are repeated here:
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Great Circle. The intersection of a spherical surface and a plane which passes through the centre of the sphere is known as a Great Circle. It is the shortest distance between two points on the surface of a sphere.
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Small Circle. The intersection of a spherical surface and a plane which does NOT pass through the centre of the sphere is known as a Small Circle.
0111.
Meridian A Meridian is a semi - Great Circle on the Earth’s surface which also passes through both Poles. 0112.
Greenwich Meridian The Greenwich Meridian is also known as the Prime Meridian, and passes through Greenwich. It is the starting point (0°) for the measurement of Longitude, East and West from this Meridian.
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0113. Rhumb Lines Rhumb Lines are defined and discussed in BR 45 (1). For the convenience of readers the Rhumb Line’s definition is repeated here: Rhumb Line. A line on the Earth’s surface which cuts Meridians (of Longitude) and Parallels (of Latitude) at the same angle is known as a Rhumb Line. It appears on Mercator Charts as a straight line and equates to the (True) compass course steered. It is NOT always the shortest distance between two points on the surface of a sphere. (See BR 45(1) for information on Meridians, Parallels and Mercator Charts.) 0114.
Observer’s Zenith (Z) The Observer’s Zenith (Z) is the point where a straight line from the Earth’s centre passing through the observer’s terrestrial position cuts the Celestial Sphere, and may be described (loosely) as the point on the Celestial Sphere directly above the observer. The Declination of this point (Z) on the Celestial Sphere is equal to the observer’s Latitude. 0115.
Celestial Horizon The Celestial Horizon is a Great Circle on the Celestial Sphere, every point of which is 90° from the Observer’s Zenith (Z). It corresponds to the projection of the terrestrial horizon onto the Celestial Sphere, but without the errors associated with atmospheric optical refraction at the Visible Horizon. 0116.
Visible Horizon The Visible Horizon is position on the Earth’s surface where a straight line drawn from an observer, at a given Height of Eye, meets the Earth’s surface as a tangent to that surface. 0117.
Azimuth Azimuth may be regarded (loosely) as the True Bearing when using tables in The Nautical Almanac. More precise definitions may be found at Paras 0535 and 0536. 0118.
Altitude (of a Heavenly Body) Altitude is (loosely) described as the angle between a ‘horizon’ and the heavenly body, but normally has to be qualified as Sextant Altitude, Apparent Altitude, Observed (True) Altitude or Calculated (Tabulated) Altitude depending which ‘horizon’ is used and which corrections are applied.
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Sextant Altitude. Sextant Altitude of a heavenly body is the angle measured by a sextant between the Visible Horizon and the body on a Vertical Circl e towards the Observer’s Zenith(Z) and must be corrected before use.
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Apparent Altitude. Apparent Altitude of a heavenly body is Sextant Altitude corrected for Index Error and Height of Eye (Dip).
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Observed (True) Altitude. Observed (True) Altitude is Apparent Altitude corrected for atmospheric refraction errors. See Para 0348d.
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Calculated (Tabulated) Altitude. See Para 0531.
1119.
Vertical Circles All Great Circles passing through the Observer’s Zenith (Z) are necessarily perpendicular to the Celestial Horizon and are known as Vertical Circles.
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SECTION 2 - THE MAGNITUDES OF STARS AND PLANETS 0120.
Solar and Stellar Systems The Earth rotates on its axis to the east, and thus the bodies in the Celestial Sphere appear to rotate westward (ie. rise in the east and set in the west).
a. Planets. The planets reflect light from the Sun and only Venus, Mars, Jupiter and Saturn are sufficiently bright for navigational use. There are at least 1,500 other small satellites and asteroids orbiting the Sun but none of these are relevant for navigational use. The ‘navigational planets’ move across the backdrop of stars in the Celestial Sphere within a band of about 5° from the Ecliptic. The speed and volatility with which they move is irregular due to their widely changing ranges from the earth and care is needed to identify them. Further details of the ‘Navigational Planets’ are at Appendix 1. b. Stars. The stars transmit their own light from an immense distance and because of this distance remain in a fixed pattern in the sky. Of the 4,850 stars visible to the naked eye, only Polaris and the 57 other stars tabulated in The Nautical Almanac are sufficiently bright for navigational use. Further details of the ‘Navigational Stars’are at Appendix 1. 0121.
Stellar Magnitudes Hipparchus (2nd century BC) and Ptolemy (2 nd century AD), arbitrarily graded stars and planets into six magnitudes according to their brightness. Heavenly bodies of the first magnitude were among the brightest in the sky and sixth magnitude were those just visible to the naked eye. The discovery by Sir John Herschel in 1830 that a first-magnitude star was about one hundred times brighter than a sixth-magnitude star, and that the brightness each magnitude of star varied to the next magnitude by a factor of about 2.5 (the fifth root of 100) caused the Ptolemaic grading to be modified slightly. Stars are now classified by brightness according to the definition that: A first-magnitude star is one from which the earth receives exactly one hundred times as much light as it received from a sixth-magnitude star.
By this definition, the intervening magnitudes between 1 and 6 are found from a logarithmic scale, so that, if a is the numerical index of the quantity of light received: ‘
’
a6 : a 100 : 1 5 ie. a = 100 a = 2.51
With numerically small magnitudes indicating the brightest objects, any object 2.51 times brighter than a first-magnitude star must have a magnitude of 0 and any object brighter than this must have a negative magnitude. Sirius is of magnitude -1.46, Venus at its brightest can be -4.4, the Sun’s magnitude (as seen from earth) is 26.7, and the Moon when full is 12.5. With brightness varying by a factor of 2.51 between each magnitude, it is simple to calculate the relative brightness of heavenly bodies from the magnitude information given in The Nautical Almanac: simply multiply 2.51 by power of the difference between magnitudes. Egs.
Vega (0.1), Aldebaran (1.1) Canopus (-0.9), Aldebaran (1.1) Sirius (-1.6), Regulus (1.3)
Vega: 2.51(1.1-0.1) = 2.51(1) = 2.51 times brighter Canopus: 2.51 (1.1-(-0.9)) = 2.51(2) = 6.3 times brighter Sirius: 2.51(1.1-(-1-6)) = 2.51 (2.9) = 14.4 times brighter
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SECTION 3 - METHODS OF IDENTIFYING HEAVENLY BODIES 0130.
The Identification of Heavenly Bodies In the practice of astro-navigation, ‘star’ sights are usually taken at Morning Twilight and Evening Twilight when the Visible Horizon and only a few bright stars/planets are visible at the same time. This means that the background of constellations are not visible to assist the navigator in star/planet identification, although an ear ly start for ‘morning stars’ can overcome this difficulty. However, in the main, other methods of identification must be used. 0131.
Use of Computers for Identification of Heavenly Bodies
a. History. A variety of computer programs for star and planet identification became available from 1980, and they also carried out rhumb line / great circle passage planning and astro-navigation calculations. Between 1980 and 1996 the Hewlett Packard HP41CV Hand-held Calculator was used in the Royal Navy for this purpose but was replaced i n 1996 by a PC program produced by The Nautical Almanac Office called ‘Compact Data for Navigation and Astronomy 1996-2000' (short title NAVPAC 1), for star/planet identification, rhumb line / great circle passage planning and astro-navigation calculations. b. NAVPAC 1. This program was effective and accurate, but the user interface was labour intensive and rather awkward to use. The program ran under MSDOS and could be operated on the simplest of PCs (minimum IBM 286 or equivalent). The ephemeral data in the program expires on 31 December 2000 and it may not be used after this date. It is to be replaced for Royal Navy use by NAVPAC 2 in mid-2000. c. NAVPAC 2. NAVPAC 2 replaces the earlier (NAVPAC 1) version for the post2000 epoch. The program is Windows-based and needs a PC operating on a minimum of Windows 95 and may also be used under later Windows systems (98, NT etc). NAVPAC 2 incorporates a much improved user interface and has an extended functionality. It is also capable of making calculations for dates prior to the year 2001 and so may be used for the worked exercises contained in BR 45(5). Operating instructions for NAVPAC 2 are contained at Annex A to Chapter 3. d. Command Support System. The inclusion of NAVPAC 2 into the Command Support System in major warships is under consideration. 0132.
Description of the Star Finder and Identifier (NP 323) The Star Finder is carried by all warships and affords a simple and speedy means of identifying stars and planets. It is also independent of power supplies and the availability of NAVPAC / computer facilities. It consists of a double-sided 30cm x 30cm cardboard star-chart (Fig 1-5a) and eight transparent templates for Latitudes 10°, 20°, 30°, 40°, 50°, 60° and 75° (Fig 1-5b) respectively. One side of the star-chart is for use in the northern hemisphere and the other for use in the southern hemisphere, although both have an overlap to allow equatorial stars to be identified. The 57 navigational stars are printed on the sta r-chart, and on the templates show rings of Altitude and curves of Azimuth. The edge of the star-chart is marked in LHA Aries for alignment with the Meridian of the grids. Full instructions for use are printed on the star-chart and are designed to allow a user with no prior experience of the Star Finder to obtain immediate results. 1-10 Original
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Fig 1-5a.
Fig 1-5b.
Star Finder and Identifier - Star Chart (Underlay)
Star Finder and Identifier - Example Template (Overlay) 1-11 Original
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0133.
The Nautical Almanac Planet Diagram The Nautical Almanac Planet Diagram shows the local mean time of Meridian Passage (see Para 0325 for explanation of Meridian Passage) of the Sun and the five planets Mercury, Venus, Mars, Jupiter and Saturn in graphical form, together with lines showing the Local Mean Time (LMT) (see Para 0435a for explanation of LMT ) of Meridian Passage of even-hour circles of Right Ascension (for every 30° of SHA). The horizontal argument on the page is date, and the vertical argument is LMT . A band on either side of the time of transit of the Sun is shaded to indicate the bodies within this area on a particular date which are too close to the Sun for observation. The lines joining the times of transit of the five planets are drawn in a distincti ve manner to avoid confusion. The diagram is mainly intended for planning purposes when a star globe is not available and by entering with the date alone gives the following information:
a. Observable. The diagram shows whether a planet is observable on that day or whether it is too close to the Sun (within the shaded area). b. Meridian Passage. The diagram shows the local mean time of Meridian Passage for each planet. The time of Meridian Passage of a star may be found by inspection if its SHA is known. Users may also plot an SHA / date line corresponding to any particular star if desired. c. Morning and Evening Stars. The diagram shows that when Meridian Passage is at about 24h the planet is observable from Evening Twilight (in the east ), through the night until Morning Twilight (in the west). When Meridian Passage falls just below the shaded area (ie before 11h) , it is visible low in the east during Morning Twilight . When Meridian Passage falls just above the shaded area (ie after 13 h), it is visible low in the west during Evening Twilight . In broad terms, a body in the bottom half of the diagram is a morning star, and one in the top half is an evening star. d. Confusion with Other Planets. The diagram shows whether other planets are in the immediate vicinity, when care must be taken to avoid confusion.
1-12 Original
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CHAPTER 2 TIME SYSTEMS CONTENTS
Uniform Time System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Standard Legal Time and Summer Time/Daylight Saving Time (DST) . . . . . . . . . . . . . Standard Legal Time - Regional Designators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Use of Standard Time and Zone Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conversion between UT and LMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . International Date Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Clock Zone Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zone Times of RVs and ETAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Universal Time (UT1 or abbreviated to UT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Greenwich Mean Time (GMT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Co-ordinated Universal Time (UTC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Para 0201 0202 0203 0204 0205 0206 0207 0208 0209 0210 0211
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CHAPTER 2 TIME SYSTEMS 0201.
Uniform Time System The world is divided into 24 Standard Time Zones. ‘Standard Time Zone’ is the generic term for all Time Zones within the Uniform Time System, both on land and sea. Each zone is 15° wide and each zone is numbered and lettered. The Greenwich Meridian is the centre of Zone 0 and also the centre of the system. Zones to the east of Zone 0 are numbered 1, 2 etc., and those to the west +1, +2 etc. The 12th zone is divided by the International Date Line ( IDL), the part to the west being 12 and that to the east +12. The zone number indicates the number of hours by which Standard (or Zone) Time must be decreased or increased to obtain Universal Time UT (previously known as GMT - see Para 0210). Time Zones may also be indicated by letters; UT is Z (zero) and the zones to the east are lettered A to M (omitting J) and those to the west N to Y. The Standard (or Zone )Time appropriate to Longitude (see Fig 2-1 and Fig 2-2) is usually referred to as ‘Zone Time’ and is the Time Zone normally kept at sea.
| |
0202.
Standard Legal Time and Summer Time / Daylight Saving Time (DST) On land, countries may modify the Standard (or Zone)Time to suit local needs. The Time Zone kept on land is decided by national laws and is known as Standard Legal Time (or ‘ Legal Time’). The ALRS Vol 2 (NP 282) gives the Standard Legal Time in each territory (see Fig 2-1 and Fig 2-2). Within NP 282 a negative prefix denotes that Legal Time is ahead of UT and positive behind it; details are given if there is a seasonal change from the Standard Legal Time to Daylight Saving Time (DST) (Summer Time); an asterisk indicates that a territory is not expected to observe DST in the current year; DST dates followed by the letter ‘E’ are estimates. The change from Standard Legal Time to DST is normally effected before 0300 (Local Time) and the change from DST to Standard Legal Time after 2200 (Local Time). Certain Islamic countries that observe DST may revert to their Standard Legal Time during the 29 days of Ramadan. The list is corrected in Section VI of the Weekly Edition of Admiralty Notices to Mariners. Standard Legal Time (sometimes abbreviated to ‘ Legal Time’) is the Time Zone kept on land. 0203.
Standard Legal Time - Regional Designators In countries extending over large east-west distances (eg USA), different Standard Legal Times may be kept in separate geographical areas within a country. Such variations may have their own regional designators. Regional designators may also be used to describe collectively a common Standard Time adopted by a number of countries. The table below lists the regional designators for Standard Time with their abbreviations and relationship to Universal Time UT . A negative prefix denotes Standard Times in advance of UT ; a positive prefix those behind UT , as shown at Table 2-1. Table 2-1. Standard Time Designators Designator
Abbreviation
Standard Time
Atlantic Standard Time (Canada) Central European Time Central Standard Time (Canada and USA) Eastern Standard Time (Canada and USA) Mountain Standard Time (Canada and USA) Newfoundland Standard Time (Canada) Pacific Standard Time (Canada and USA) Yukon Standard Time (USA)
AST
+04 01 +06 +05 +07 +03½ +08 +09
CST EST MST NST PST YST
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2-3 Change 1
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Fig 2-1. Standard Time Zone Chart of the World
2-4 Change 1
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Fig 2-2. Standard Time Zone Chart of Europe and North Africa
2-5 Change 1
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0204.
Use of Standard Time and Zone Time UT is used as the standard Time Zone for worldwide reference books such as The Nautical Almanac, is the Time Zone in which Ship’s Chronometers and Deck Watches are kept and is also used for signal message Date-Time-Groups (DTGs). UT was previously known as GMT (see Para 0210). It should be noted that Tides Tables, which are specific to local areas, normally provide information in Standard Legal Time (See Para 0202) but care must be exercised when any Daylight Saving Time (DST) is in force. 0205.
Conversion between UT and LMT Applying the Uniform Time System (Para 0201), the following rules may be established: If a Longitude is West, ADD the time equivalent of the Longitude when changing from Local Mean Time to UT (and vice versa - SUBTRACT if changing from UT to LMT ). If a Longitude is East, SUBTRACT the time equivalent of the Longitude when changing from Local Mean Time to UT (and vice versa - ADD if changing from UT to LMT ).
Examples 2-1 and 2-2. What are the LMT equivalents if UT is 23 hours 31 minutes 25 seconds on 14 September, (1) at 48° West, and (2) at 22½° East. Note that this is changing from UT to LMT. Example 2-1: At 48° West Date
Example 2-2: At 22½° East
Hrs Mins Secs
14 Sep UT
23
31
25
03
12
00
14 Sep LMT (48°W) 20
19
25
Long W. (-)
Date
Hrs Mins Secs
14 Sep UT Long E. (+) 15 Sep LMT (22½°E)
23
31
25
01
30
00
01
01
25
Examples 2-1 and 2-2. Converting UT (previously known as GMT ) to LMT ( Note that the date has also changed in Example 2-2 at 22½° East ) 0206.
International Date Line
a. Reason for the International Date Line. Inspection of Fig 2-1 will show that a traveller leaving UK and heading east to make a trip around the world would advance clocks by 1 hour on passing each successive Meridian 15° further east from Greenwich, in accordance with the Standard (or Zone)Time arrangements of the Uniform Time System (Para 0201). If this process were to continue until the traveller circumnavigated the world and reached UK again, 24 hours would have been added to the traveller’s clock and calendar, and thus the traveller would believe it to be the same time as kept in UK but 1 day later (this fact was the key to the plot in Jules Verne’s famous book, ‘Around the World in 80 Days’ which was later made into a classic film). To avoid this difficulty, it has been agreed worldwide that at approximately 180° East, on crossing the International Date Line, travellers would advance or retard calenders by 1 day (retard when eastbound, advance when westbound) and simultaneously apply the new Time Zone (-12hr to +12hr or vice-versa) to the new date.
2-6 Change 1
BR 45(2)
b. Co-ordinates of the International Date Line. To avoid populated areas, the International Date Line does not follow the Meridian of 180° East exactly. The precise co-ordinates of the International Date Line may be found from appropriate British Admiralty charts and are also tabulated in the ‘Standard Times’ section of the Admiralty List of Radio Signals Volume 2 (NP 282). c. Calculation of Dates and Times when Crossing the International Date Line. When calculating dates and times involving any crossing the International Date Line: (1) Convert all dates and times (eg ETDs and ETAs) on both sides of the International Date Line to UT . See Para 0205 for conversion procedure. (2) Make all passage calculations in UT , including the total of days/hours available, the Speed Over All (SOA) and associated fuel requirements. (3) Re-convert the dates / times at (2) above to the new Standard (or Zone)Times and dates required. The International Date Line will be incorporated. Note that the sign of the Time Zone has to be applied in reverse when converting from UT . Note 2-1: The correct application of this procedure is essential t o avoid confusion and error, particularly when planning passages across the Pacific Ocean when time and fuel constraints will often leave no room for mistakes. Example 2-3. On 15th September at 0800( 12), a ship in position 30°N, 178°E travelling on a course of 090° speed 16, crosses the International Date Line. What is the local time and date, in Standard (or Zone)Time, 8 hours later?
Zone Date & Time Zone (-12)
150800M Sep 12
UT Passage Interval
142000Z Sep +0800
UT Zone (+12)
150400Z Sep -12
Zone Date & Time
141600Y Sep
Example 2-3. Summary of the International Dateline Conversion Calculation 0207.
Clock Zone Changes At sea, within the Royal Navy, it is normal to advance clocks (when travelling east) at 2330 local time and retard clocks (when travelling west) at 1830 local time, assuming a normal cruising watch system. 0208.
Zone Times of RVs and ETAs Care should be taken when arranging any Rendezvous (RV) with other ships to ensure correct Time Zones are applied by all participants. It is often more sensible to specify UT to preclude the possibility of mistakes being made. Similarly, when making a port visit to a foreign country, the ‘Legal Times’ section of Admiralty List of Radio Signals Volume 2 (NP 282) should be checked for the correct Time Zone, making sure that any DST (Para 0202) is taken into account and any amendments to NP 282 have been correctly inserted. To prevent any possible embarrassment, the visit letter (where applicable) should also be checked to confirm that this agrees with the information in NP 282.
2-7 Original
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0209.
Universal Time (UT1 or abbreviated to UT) Universal Time (UT1 or UT) is the Mean Solar Time (MST) (see Chapter 4 for definition of MST ) of the Prime Meridian obtained from direct astronomical observation and corrected for the effects of small movements of the Earth relative to the axis of rotation (polar variation). Since these time scales correspond directly with the angular position of the Earth around its axis of diurnal rotation, they are used for astronomical navigation and form the time argument in The Nautical Almanac. 0210.
Greenwich Mean Time (GMT) GMT may be regarded as the general equivalent of UT / UT1.
0211.
Co-ordinated Universal Time (UTC)
a. Requirement. Co-ordinated Universal Time (UTC) has been developed to meet the needs of scientific users for a precise scale of time interval, and those of navigators, surveyors and others who require a timescale directly related to the Earth’s rotation (like UT1). b. UTC - TAI - UT1 Linkage. UTC corresponds exactly in rate with International Atomic Time (TAI). TAI is based on atomic clocks and is independent of the Earth’s rotation and UTC differs from it by an integral number of seconds. The UTC scale is adjusted by the insertion or deletion of seconds (positive or negative leap seconds) to ensure that the departure of UTC from UT1 does not exceed +/- 0.9 seconds. Further details of these time systems may be found in Radio Time Signals section of the Admiralty List of Radio Signals Volume 2 (NP 282). c. Time Signal Broadcasting Stations. Operational details of stations broadcasting time signals are listed in Radio Time Signals section of the Admiralty List of Radio Signals Volume 2 (NP 282) and they broadcast in the UTC time scale unless otherwise indicated. Leap seconds are notified in advance as corrections in a Table in the Radio Time Signals section of NP 282. Changes to this Table are notified in Section VI of the Weekly Edition of Notices to Mariners. d. GPS Time-Transfer. GPS provides a very accurate source for time-transfer and may be the most convenient source of UT for time checks (see Paras 0326c.2 and 0340), and to establish any error in the chronometer time and any Deck Watch Error (DWE).
2-8 Original
BR 45(2) CHAPTER 3 PRACTICAL PLANNING, TAKING, REDUCTION AND PLOTTING OF SIGHTS CONTENTS SECTION 1 - INTRODUCTION
Assumptions Made and Scope of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Para 0301
SECTION 2 - PLANNING ASTRO-SIGHTS
Ship’s DR / EP Position for Sights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NAVPAC 2: Calculating SS / SR, CT, NT (RiseSet Pages) . . . . . . . . . . . . . . . . . . . . The Nautical Almanac - Calculating SS / SR, CT, NT . . . . . . . . . . . . . . . . . . . . . . . NAVPAC 2: Prediction of a Body’s Azimuth (Bearing) and Altitude (FindIt Page) . The Star Finder - Prediction of a Heavenly Body’s Altitude and Azimuth (Bearing) . The Nautical Almanac - Calculating Time of Sun’s Meridian Passage . . . . . . . . . . . NAVPAC 2: Calculating Time of Sun’s Meridian Passage (FindIt Page) . . . . . . . . . . Other Organisational and Material Preparations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0320 0321 0322 0323 0324 0325 0326 0327
SECTION 3 - DESCRIPTION, PREPARATION AND USE OF SEXTANT
Sextant - Principle of Operation and Origin of Name . . . . . . . . . . . . . . . . . . . . . . . . . . Description of Sextant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurements ‘On’ and ‘Off’ the Arc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Positioning and Marking of the Index Bar and Arc . . . . . . . . . . . . . . . . . . . . . . . . . . . . Viewing and Collar / Telescope Adjustments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Sextant Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sextant Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sextant Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Care of a Sextant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using a Sextant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0330 0331 0332 0333 0334 0335 0336 0337 0338 0339
SECTION 4 - REDUCING SIGHTS (PROCESSING OF SEXTANT READINGS) NAVPAC 2: Assumptions and Overall Arrangement of ‘Sights’ Sub-Programs. . . . . NAVPAC 2: Options Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NAVPAC 2: Sights-Fix Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NAVPAC 2: Sights-Legs Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NAVPAC 2: Sights-Astronomical Observations Page (using Stars / Planets) . . . . . . . NAVPAC 2: Sights-Astronomical Observations Page (using Sun / Moon Planets) . . NAVPAC 2: Sights-Results, Sights-Log and Sights-Position Line Plot Pages . . . . . . NAVPAC 2: Summary of Printing, Saving and Loading Facilities . . . . . . . . . . . . . . The Nautical Almanac - Meridian Passage, Polaris and Altitude Corrections . . . . . . NAVPAC 2: Almanac Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0340 0341 0342 0343 0344 0345 0346 0347 0348 0349
SECTION 5 - PLOTTING SIGHTS NAVPAC 2: Plotting of Astronomical Position Lines . . . . . . . . . . . . . . . . . . . . . . . . . Manual Plotting Astronomical Position Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0350 0351
ANNEXES Annex A:
Extract of HM Nautical Almanac Office NAVPAC 2 User Instructions 3-1 Original
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3-2 Original
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CHAPTER 3 PRACTICAL PLANNING, TAKING, REDUCING AND PLOTTING OF SIGHTS SECTION 1 - INTRODUCTION INTRODUCTION 0301. 0301.
Assum Assumpti ptions ons Made Made and Scope Scope of the Chapte Chapterr
a. Navigational Watchkeeping Certificate (NWC). This chapter provides a practical guide for planning, taking, reducing and plotting of astro-sights for readers studying for the (Navigational Watchkeeping Certificate (NWC). b.
c.
Assumptions. •
Chap Chapte terr 3 ass assum umes es tha thatt NAVP NAVPAC AC 2 is ava availa ilabl blee on-s on-scr cree een n and and can can be worked through, step by step, with the instructions in the chapter; it is not intended that the NAVPAC 2 elements of Chapter 3 should be read in isolation.
•
It is assu assumed med that that NAV NAVPA PAC C 2 will will be used used to carr carry y out out the the majo majorit rity y of of calculations.
Scope.
•
Althou Although gh NAV NAVPA PAC C 2 is the the pri prima mary ry meth method od for for sol solvi ving ng calc calcul ulati ation ons, s, som somee simple procedures using The Nautical Almanac are Almanac are also covered.
•
Although solutions of Great Circle and Circle and Rhumb Rhumb Line sailings Line sailings are contained in NAVPAC 2 they they are not included in Chapter 3; explanation of of these sailings are at BR 45 Volume 1 Chapters 2 and 5 and the NAVPAC 2 user’s manual at Annex 3A includes instructions for making these calculations.
•
Astr Astroo-th theo eory ry is cove covere red d at Chap Chapte ters rs 4-9. 4-9.
0302 0302-0 -031 319. 9. Sp Spar aree SECTION 2 - PLANNING PLANNING ASTRO-SIGHTS ASTRO-SIGHTS 0320. 0320.
Ship’s Ship’s DR / EP Posit Position ion for Sights Sights
a. Star Sights. The starting point for all astro-sights is to establish an approximate DR / EP position from the Bridge chart for the time of the planned observation. It is only possible to take star sights sights between Civil and Nautical Twilight , when both the horizon and the brightest stars/planets are visible. This will require the calculation of Morning of Morning Nautical Twilight Twil ight (MNT), Morning Civil Twilight (MCT) and Sunrise (SR) or Sunset Sunset (SS), Evening Civil Twilight (ECT) and Evening Nautical Twilight (ENT) as appropriate. b. Sun Sights. The Sun’s position in the sky is normally self evident and calculation to predict this is not required except for its Meridian its Meridian Passage ( Passage ( Mer Mer Pass). Pass). NAVPAC 2 does not specifically calculate the time of Mer of Mer Pass Pass but an iterative process in the FindIt page will allow the user to predict precisely when the Sun will cross the Observer’s the Observer’s Meridian (ie Meridian (ie due North or South of the observer). The Nautical Almanac may Almanac may also be used to calculate for the time of Mer of Mer Pass. Pass. If the ship’s Longitude ship’s Longitude is is changing rapidly both of these calculations may involve involve extensive iterative processes. 3-3 Original
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0321. 0321.
NAVPAC NAVPAC 2: Calculatin Calculating g SS SS / SR, CT, NT (RiseSet (RiseSet Pages) Pages)
a. NAVPAC Home Page. On starting NAVPAC 2, 2, the user is taken to a top-level Home’ page. To calculate SS / SR, CT or NT times, menu page referred hereafter as the ‘ Home click on the button on the Home page (see Fig 3.1) or key in ‘ Alt ‘ Alt T ’. ’. This brings NAVPAC 2 to the ‘ RiseSet ’ page. Note 3-1 3-1 . NAVPAC 2 provides provides keyboard shortcuts throughout throughout the the program by the use of ‘Alt’ and the key for letter underlined on the menu buttons (Eg. See Fig 3-1 below).
Home’ Page. Fig 3-1. NAVPAC 2 ‘ Home’
b. RiseSet Page. A RiseSet page, page, with a variety of dialogue boxes (Fig 3-2 opposite) , or for data input allows the user to select a DR / EP position , , , , , the observer’s or ), of eye above sea level, the required, the predictions required and the heavenly for which rising and setting data is needed. The should be set to 1 (unless the ship will remain in the same position for more than 1 day), and only the ‘Sun’, ‘Civil Twilight’ and ‘Nautical Twilight’ should be sel ected in the option. When all details are complete, click the button and the RiseSet - Results page will be displayed. c. RiseSet-Results Page. The RiseSet-Results page (Fig 3-3) may be printed or saved (see Paras 0323e/f and 0347). The line showing MNT showing MNT for morning stars or ECT or ECT for evening stars should be clicked and the or buttons should be clicked in order to save the time calculated for use in later. Irrespective of any set, if saved, the appropriate UT will be transferred to subsequent NAVPAC 2 menus. Click the button to return to the Home page.
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Fig 3-2.
Fig 3-3.
NAVPAC 2 ‘ RiseSet’ RiseSet’ Page.
NAVPAC 2 ‘ RiseSet-Results’ RiseSet-Results’ Page.
3-5 Original
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0322. 0322.
The Naut Nautica icall Almana Almanacc - Calcul Calculati ating ng SS / SR, SR, CT, CT, NT
a. Latitude Time. Using the ship’s DR / EP position position from the Bridge Bridge chart, from The Nautical Almanac obtain Almanac obtain the ‘Latitude Time’ for for the nearest Latitude nearest Latitude on on the mid-date for the page in question for ENT for ENT / ECT / SS or or SR / MCT / MNT . Note that The Nautical Almanac displays Almanac displays this information in chronological order and so does not display the prefix ‘ Evening Evening ’ or ‘ Morning Morning ’ with CT or NT or NT . Because the tables only only provide provide times at intervals of 5° of Latitude of Latitude,, interpolation may have to take place. This is undertaken undertaken either by mental arithmetic or by using ‘TABLE 1 - FOR LATITUDE ’ at the end of the yellow pages at the back of The Nautical Almanac. Almanac . b. Date Interpolation. Should the date not be the central date on the on The Nautical Almanac Almanac double page, then interpolation by mental arithmetic will require to be undertaken between the pages before or after the required date. c. Longitude. The result of the data extraction and interpolation at Paras 0322a and 0322b above is the UT of ENT of ENT / ECT / SS or SS or SR / MCT / MNT on on the Greenwich Meridian. Meridian. If the ship's position is not on the Greenwich Meridian, Meridian, ie either East or West of the 0o line of Longi of Longitude tude,, a correction must be subtracted or added. added. Converting Longi Converting Longitude tude to to Time is undertaken either by mental arithmetic arit hmetic or by using the the ‘CONVERSION ‘CONVERSION OF ARC TO TIME ’ table at the start of the yellow pages in The Nautical Almanac Almanac.. A useful way way to remember whether to add or subtract is given by the rhymes: East is Least - MINUS West is Best - PLUS Note 3-2. The Nautical Nautical Almanac Table II (at end of yellow pages) is for additional additional Moon corrections, and is NOT for SR/SS corrections.
d. UT (GMT). If the data from The Nautical Almanac Almanac has has been extracted / interpolated correctly and the observer’s Longi observer’s Longitude tude applied, applied, the result will be the UT of ENT of ENT / ECT / SS or or SR / MCT / MNT as as appropriate at the observer’s DR DR / EP position. If desired the Time Zone may Zone may be applied to obtain Local obtain Local Mean Time (LMT) (LMT) (see (see Para 0205). 0205). e. Summary and Example 3-1. The calculation is summarised below with an example ex ample of SS (interpolated from The Nautical Almanac Almanac)) at 1800, 1800, at 25° East, East, in Time Zone B(-2). Zone B(-2). Worked examples of rising and setting set ting calculations, and answers are contained in BR 45 (5), pages 1B-2 to 1B-3. Interpolated SS (or (or SR SR/CT/NT) fr from NA
1800
Longitude (W+ or E-) (2 (25°E)
-0140
Local Mean Time UT(GMT)
1620Z
Zone(-2) (+ ( + = subtract) (- = add)
+0200
Zone Time
1820B
Example 3-1. 3-1. Summary of SS/SR/CT/NT Calculations
f. Further Iterations. If the time of the DR / EP position from the Bridge Chart was not close to the time subsequently calculated for MNT for MNT (for (for morning stars) or or ECT ECT (for (for evening stars), a further iteration of the calculation may be required to refine the answer. 3-6 Original
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0323. 0323.
NAVPAC NAVPAC 2: Predictio Prediction n of a Body’s Body’s Azimuth Azimuth (Bearing) (Bearing) and Altitu Altitude de (FindI (FindItt Page) Page)
a. Use. The prediction of a heavenly body’s bearing and altitude is usually associated with taking morning or evening stars, as the position of the sun s un (and sometimes the moon) in the sky during the day is self evident. Note that NAVPAC 2 uses the astronomical term ‘navigational body’ ‘heavenly body’. body’ throughout, instead of the traditional maritime usage ‘heavenly body’. b. Transfer of Times and Positions. Assuming that the times of ENT of ENT / ECT / SS or SS or SR have been calculated in NAVPAC 2 and the appropriate time saved ( MNT / MCT / MNT have for morning stars or ECT or ECT for for evening stars), then NAVPAC 2 will transfer that information to the next NAVPAC 2 menu (Para 0321). Otherwise it must be entered manually into the new menu in the next part of the program. c.
FindIt Page. From the Home page of NAVPAC 2, click or key ‘ Alt Alt F’ ; this brings the screen to the FindIt page page (Fig 3-4). Confirm that , (U (UT), ( / ) and ( / ) have transferred correctly into the dialogue dialogue boxes, or if not, correct them. Then:
•
In the the dialo alogue box, select lect an shown set to the default default in Fig 3-4 below) and an if they have not already been set.
•
In the
dial ialogue box, sele elect
•
Chec Check k all all data data is corr correc ectt and and clic click k on the the page will then then be displayed. displayed.
Fig 3-4.
of
to
of
(not as to ,
. butt button on;; the the FindIt-Results
NAVPAC 2 ‘FindIt’ Page.
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d. FindIt-Results. The heavenly bodies visible on the date and time within the parameters parameters selected selected will now now be be display displayed ed on on the the FindIt-Results page as a 360° plot and a list (Fig 3-5). By clicking on or and then double-clicking any star on the plot, the appropriate item will be identified on the list (and vice-versa). Bodies which have been identified (double-clicked) will have their details transferred through to the Sights-Astro page. Sights-Astronomica nomicall Observa Observations tions page.
Fig 3-5.
NAVPAC 2 ‘FindIt-Results’ Page.
e.
Printing FindIt-Results. The FindIt-Results page may be printed by clicking the button or on the direct-print button (see Para 0347a for a general explanation of printing). A printout of both the plot and list will be needed for taking stars. When printed, printed, unlike the screen (Fig 3-5) , the plot will include include the name of each body (Fig 3-6a). The list of heavenly body details is provided on a separate sheet (Fig 3-6b).
f.
Saving FindIt-Results. The FindIt-Results page may be saved to a file using the Saving button. Clicking on the button brings up the standard NAVPAC Saving Loading Loading page page (see Fig 3-18). 3-18). See Paras Paras 0347b/c 0347b/c for for general general explanations explanations of of saving and loading. 0324.
The Star Finder - Prediction Prediction of Heavenly Body’s Body’s Altitude and Azimuth (Bearing) (Bearing) The ‘Star Finder and Identifier’ is is described in full at Para 0132. Full instructions for use are printed on the star-chart (shown at Figs 1-5a and 1-5b) and are designed to allow a user with no prior experience experience of the Star Finder Finder to obtain immediate immediate results. In summary, summary, by placing one of the 8 transparent templates over the star-chart underlay the Altitud the Altitudee and Azimuth and Azimuth (Bearing) of the heavenly bodies may be read of the template. The ‘Star Finder and Identifier’ provides provides a quick, cheap method of identifying heavenly bodies and is independent of power supplies. However, it is less accurate than NAVPAC 2.
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Fig 3-6a. Printout of NAVPAC 2 ‘FindIt-Results’ Page (Plot) FindIt Altitudes and Azimuths Lat N32 45.0 Long W015 30.0 Date 2001/02/09 Time 06:56:00 UT Mag. Name +2.1 +2.5 +2.4 >+1.3 >+0.1 >+0.9 +2.1 +2.1 +2.3 +2.0 +2.6 +1.7 >+1.2
Altitude o ' 32 03.5 05 02.3 54 49.3 27 34.6 48 29.8 21 48.4 51 35.2 10 38.4 82 10.3 09 10.9 33 51.6 12 46.4 28 01.7 38 21.3 40 58.2 19 16.4 39 16.9 71 31.5 24 29.7 40 43.1 23 05.6 18 19.4 67 13.5 56 48.3 41 35.3 48 32.0
Azimuth o ' 000 08.8 019 49.5 045 23.8 051 52.4 < 066 36.7 < 093 24.5 < 113 15.3 130 58.2 138 59.6 141 31.3 145 00.0 151 40.5 160 17.3 < 171 24.8 * 186 37.7 193 48.4 214 36.0 < 226 10.2 226 39.4 260 51.6 < 270 59.4 * 272 42.0 322 48.2 324 42.2 326 02.3 < 357 50.0
Polaris Schedar Eltanin Deneb * Vega * Altair * Rasalhague Nunki Alphecca Kaus Australis Sabik Shaula Antares * *Mars +2.9 Zubenelgenubi +2.3 Menkent >+1.2 Spica * +0.2 Arcturus +2.8 Gienah >+2.2 Denebola * *Moon +1.3 Regulus +1.9 Alkaid +1.7 Alioth >+2.0 Dubhe * +2.2 Kochab --------------------------------------------------------------------Printed on 2000 January 27 at 11:48:23 (Computer Clock Time). Produced by HM Nautical Almanac Office's NavPac v 2.0-2. Copyright Council for the Central Laboratory of the Research Councils
Fig 3-6b. Printout of NAVPAC 2 ‘FindIt-Results’ Page (List)
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0325.
The Nautical Almanac - Calculating Time of Sun’s Meridian Passage
a. Background. By taking the altitude of the Sun at ‘ Meridian Passage’( Mer Pass), when it crosses the Observer’s Meridian (ie due North or South of the observer) and is near to its highest point in the sky (see Para 0348b), a simple manual calculation will provide the observer’s Latitude. However, it is necessary to know what time this phenomenon will occur and recourse to The Nautical Almanac may be necessary. b. Method. The Local Mean Time of the Sun’s Mer Pass on the Greenwich Meridian is tabulated for each day at the bottom of the right hand daily pages of The Nautical Almanac. No interpolation is necessary, but the observer’s Longitude and Time Zone in use need to be applied in the same way as in SR / SS calculations (see Para 0322), in order to calculate the Local Mean Time of Mer Pass on the Observer’s Meridian. If the time of the DR / EP was not close to the time subsequently calculated for Mer Pass, a further iteration of the calculation may be required to refine the answer. The calculation is summarised below at Example 3-2 with Mer Pass at 1210, at 25° W, in Time Zone O(+2). Worked examples with answers are at BR 45(5) pages 1B-7 and 1B-8. Mer Pass Time from Nautical Almanac
1210
Longitude (W+ or E-) 25°W
+0140
Local Mean Time UT(GMT)
1340Z
Zone(+2) (+ = subtract) (- = add)
-0200
Zone Time
1140(O)
Example 3-2. Summary of Mer Pass Calculations 0326.
NAVPAC 2: Calculating Time of Sun’s Meridian Passage (FindIt Page) The exact time of the Sun’s Meridian Passage may be established to the nearest second by using the dialogue box in NAVPAC 2's FindIt page in an iterative manner to obtain a bearing of 180° or 000° for the Sun on the FindIt - Results page (see Para 0323, Figs 3-4 and 3-5). Given the errors that may be induced (see Para 0348b) by taking the Mer Pass sight at the moment of highest altitude rather than at the time when the heavenly body is in the Observer’s Meridian (ie bearing 180° or 000°) using NAVPAC 2 is the preferred method of calculating the time of Mer Pass. Its limiting accuracy is the Longitude component of the ship’s DR / EP, which in turn affects the calculation. However, this potential error is common to both the tabular method from The Nautical Almanac (see Para 0325) and NAVPAC2. Leaving aside this possible source of error, of the two methods, NAVPAC 2 provides a more precise output for the remainder of the calculation. 0327.
Other Organisational and Material Preparations
a.
Sextant. Guidance on the care and use of the Sextant is at Paras 0338-0339.
b. NO’s Assistant. Before taking morning or evening stars and also for most sunsights, a carefully briefed assistant is needed, who can take the Deck Watch Time at the instant of observation and write down the Sextant reading, as well as to hold the star plot / list and assist with the spotting of stars. In extremis, an experienced NO can manage alone, but care is needed to avoid Deck Watch Time errors.
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c.
Deck Watch Time, Deck Watch Error and Mistakes .
(1)
GMT. The Deck Watch Time (DWT) should always be UT .
(2) Deck Watch Error (DWE). The difference between DWT and UT is the Deck Watch Error (DWE) and must be known precisely. DWT must be manually corrected for DWE before inputting the resultant time (UT ) into NAVPAC 2. (3) Analogue Clocks. Deck Watches are 12-hour analogue clocks and care must be taken not to confuse 0600 with 1800 and thus inject a 12 hour error into the NAVPAC 2 calculation. If this is done it should become evident by the excessive size of the intercepts and/or a refusal by NAVPAC 2 to compute a sensible observed position. (4) Errors in Recording Time. The second and minute hands of the Deck Watch should be aligned precisely, so that there can be no possibility of an error when the reading the minute hand. If times are being taken by an assistant, it is advisable for the minute hand to be checked by the NO as well. Times should be read to the nearest second. It is useful to be able to count in seconds so that, if there is no one else available to take times, the NO can count the seconds until it is possible to read the Deck Watch. d. Mustering in Good Time. Both the NO and the NO’s Assistant should be up on the Bridge in plenty of time for stars, particularly in the morning. For morning stars there should be time to adjust to night vision to help spot the best stars while they are really bright against a dark sky. As a general rule, the astro team should be on the Bridge ready to go for taking stars just after Sunset for evening stars and by Nautical Twilight for morning stars. In the tropics the periods of twilight are much shorter than in temperate Latitudes and an even earlier start is often prudent. e. Rough Weather. Taking star shots on a stormy morning or evening from a lively Bridge Roof, with spray flying and patches of cloud skudding past the stars giving only a few seconds for a snatched observation can be a challenging experience. The NO and the NO’s Assistant need to be correctly dressed as wet clothes and cold hands make accurate Sextant work much harder. Similarly, the Sextant mirrors and lenses need to be protected from spray; if they become wet the Sextant rapidly becomes impossible to use accurately and any clumsy attempts to wipe the mirrors clean will probably introduce unknown errors into an otherwise ‘zeroed’ Sextant . Having a suitably sized towel ready and keeping the Sextant covered with it until immediately before raising it to the eye often solves the problem in such conditions. If the Sextant does get wet, a damp chamois leather or a small, clean, dry, soft, absorbent, lintless cloth should be immediately available to dry it quickly and carefully before the next sight. Afterwards the Sextant will need careful cleaning and oiling.
0328-0329. Spare
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SECTION 3 - DESCRIPTION, PREPARATION AND USE OF SEXTANT 0330.
Sextant - Principle of Operation and Origin of Name If a ray of light is reflected twice in the same plane by two plane mirrors, the angle between the first and the last ray is twice the angle between the mirrors. Thus the Sextant has a graduated Arc of about 1/6th of a circle’s circumference (60°- hence the name), but the arc is graduated to 120°. 0331.
Description of Sextant The micrometer Sextant in Royal Navy service is illustrated at Fig 3-7 and consists of elements built around the Main Frame. The bottom edge of the Main Frame is the Arc, which has its geometric centre at the top of the Main Frame. An adjustable Collar is fitted on the rear edge of the Main Frame into which a removable Telescope is fitted. The Index Bar, which can rotate about the geometric centre of the Arc, is hinged at the top of the Main Frame and has a Clamp at the bottom; an Index Mark and Micrometer Drum are fitted at the Clamp end. The Horizon Glass, which is half-silvered and half-clear, is mounted on the front of the Main Frame. Various Shades are fitted to filter the Sun’s rays and a Reading Lamp for observing the scales is also fitted.
Fig 3-7. The Marine Sextant
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0332.
Measurements ‘On’ and ‘Off’ the Arc The Arc is graduated in degrees of observed altitude, and so arranged that when the Index Glass is parallel to the Horizon Glass, the Index Mark on the Index Bar should point to the zero on the Arc scale. Angles read on the main part of the scale part are said to be ‘On’ the Arc. The graduations are continued over a small arc on the other side of the zero; this is called the ‘ Arc of Excess’ and angles read on this part are said to be ‘Off ’’ the Arc. When establishing the Index Error of the Sextant (see Para 0336), if the Micrometer Drum reads ‘Off ’’ the Arc, this error must be added to subsequent Sextant readings and if ‘On’ the Arc the error must be subtracted. The sign of the correction can easily be remembered by the rhyme: “When its ‘Off’ its on (+), and when its ‘On’ its off (-)” 0333.
Positioning and Marking of the Index Bar and Arc The Index Bar can be set to any position on the Arc by means of the Clamp; this releases or engages a worm thread in the teeth of a rack that extends along the entire periphery of the Arc. When clamped, the Index Bar’s motion along the Arc can be controlled in either direction by turning the Micrometer Drum which rotates the worm in the rack. With this arrangement it is the worm and the rack that govern the accuracy of the setting. One rotation of the Micrometer Drum moves the Index Bar one degree along the Arc. When reading the Sextant , the engravings on the Arc are read against the Index Bar to the nearest whole degree, while the Micrometer Drum provides the intermediate reading for minutes. In Fig 3-7 the Sextant may be seen to read 34° 58.1'. 0334.
Viewing and Collar / Telescope Adjustments
a. Telescope and Mirror Alignment. The Telescope is fitted in the Collar so that its axis makes the same angle with the plane of the Horizon Glass as the latter makes with the line joining the centres of the Index Glass and Horizon Glass, thus ensuring the Sextant is capable of accurate altitude readings of heavenly bodies. b. Telescope Adjustment Facility. The Collar can be moved nearer or further from the Main Frame by means of a Milled Head beneath the frame. In the normal (mid) position of the Collar , the optical centre of the Telescope is aligned with the silvered/unsilvered boundary of the Horizon Glass and equal parts of the silvered and unsilvered halves of the horizon glass should be visible; the Telescope should normally be aligned to this position.
c. Telescope Adjustment Effect. The action of moving the Collar and Telescope nearer or further from the Main Frame regulates the brilliance of the reflected image, which will greatest when the Telescope is nearest to the Main Frame. As the Telescope is moved away from the Main Frame, less of the silvered part of the Horizon Glass appears in the field and the reflected image is less bright. This action can be useful when an experienced user wishes to regulate the relative brilliance of the horizon and the reflected heavenly body but is not recommended for inexperienced users who will find the Sextant very difficult to handle when configured away from the mid-setting.
d. Shades and Reading Lamp. Sets of neutral density Shades are mounted in front of both the Index Glass and Horizon Glass for use when observing the Sun. Three legs and a handle are fitted on the other side of the Main Frame to that shown in Fig 3-7. The handle contains a battery and switch for operating the swivel-mounted Reading Lamp.
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0335.
The Sextant Telescopes The Sextant is provided with two telescopes: a ‘Star Telescope’ and a ‘Sun Telescope’.
a. Star Telescope. The (short, fat) Star Telescope (shown in Fig 3-7) is an ‘erecting’ telescope which shows objects the right way up; it has a large object lens with a low magnification. The ‘ Star Telescope’ is designed for taking star-sights and for observing terrestrial objects (ie. vertical and horizontal Sextant angles) but should also be used by inexperienced Sextant users for taking sun-sights. b. Sun Telescope. The (long, thin) Sun Telescope is an ‘inverting’ telescope which shows objects upside down; it has a small object lens with a high magnification. It is designed for taking sun-sights in good conditions only, as it is hard to hold steady. It has two eyepieces, one of which has higher magnification than the other. Each eyepiece is fitted with cross-wires at its focus (to define the line of ‘collimation’, which is the line joining the focus to the centre of the object-glass). The eyepiece of higher power has two cross-wires and the lower power eyepiece has four. These cross-wires are fragile and can be destroyed by careless cleaning. The high-power eyepiece is designed for use when the horizon is bright and the ship is very steady. Experienced Sextant users can achieve a higher degree of accuracy with the Sun Telescope than with the Star Telescope. However, inexperienced Sextant users will find great difficulty in using the Sun Telescope at first and should wait until manual dexterity has been achieved with the Star Telescope before graduating to the Sun Telescope. 0336.
Sextant Errors Apart from a lack of manual dexterity in using the Sextant (which is overcome by practice), the greatest single cause of inaccurate sights is the presence of unknown errors in the Sextant . There are 3 adjustable errors which must be corrected or determined by the user and also 2 non-adjustable errors which if significant will require the Sextant to be returned for workshop repair. The adjustable errors must be adjusted or established for each sight in the following order:
a. Perpendicularity. This is the perpendicular (90°) alignment of the Index Glass to the plane of the Arc and thus to the Sextant . To check Perpendicularity, remove the Telescope and set the Index Bar to about 60° (roughly the middle of the Arc). Hold the instrument horizontal at arm’s length with the Index Glass nearest to oneself and look into the Index Glass as nearly as possible along the plane of the Arc in order to see the reflected image of the Arc at the edge of the Index Glass mirror, in line with the actual Arc observed directly. The Index Bar may need to be moved slightly to allow this to be seen. If the reflected image of the Arc is not absolutely aligned with the directly observed part of the Arc, bring the two in line by adjusting the small screw in the centre of the Index Glass frame. This adjustment is critical and must be carried out before any others. b. Side Error. Side Error is a variation from the perpendicular alignment of the Horizon Glass to the plane of the Arc and thus to the Sextant . Side Error adjustment cannot be carried out successfully unless Perpendicularity of the Index Glass (see Para 0336a above) has already been correctly set. Once the presence of Side Error has been established (see sub-paras below), it can be removed by turning one of the two adjusting screws on the Horizon Glass. Side Error may be established as shown below and the screw used to correct it may be remembered by the linkage of the word ‘ side’: Side Error may be removed by adjusting the screw on the side of the Horizon Glass.
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(1) To check for Side Error , fit a Telescope (the Sun Telescope provides the most accurate results but the Star Telescope may be preferred by inexperienced Sextant users due to the difficulty of holding the Sun Telescope sufficiently steady). (2) With the chosen Telescope fitted, hold the Sextant in the vertical plane ( ie as normal) and look at a well-defined distant object such as a medium-bright star and move the Index Bar across the zero of the Arc. (3) As the Index Bar passes the zero of the Arc (+/- any Index Error), the reflected image should be exactly superimposed over the direct image of the star. (Very bright objects such as Venus or Saturn should be avoided, as it will be found their very size and extreme brightness make them awkward to use for this purpose ). (4) If two images sit level, but to the left and right of each other, Side Error is present and adjustment can be made (as above) until the images are superimposed. c. Index error. Index Error is a variation from the parallel alignment of the plane of the Horizon Glass to the plane of the Index Glass when the Index Bar is set to the zero position on the Arc. If Index Error is zero, when the Sextant is pointed at a well-defined distant object (such as a medium-bright star) it should show exactly 0° 00.0' on the Arc scale when the direct and reflected images of a distant heavenly body are coincident. This seldom occurs in practice because the two glasses are rarely adjusted so well that they are exactly parallel at this point. When this difference occurs, the zero on the scale is therefore not the true zero of the instrument and a small correction has to be made (see Para 0332). Index Error can be determined by 4 methods, and once its presence has been established (see sub-paras below), it can be removed by turning one of the two adjusting screws on the Horizon Glass. If the Index Error is less than 3.0' of arc it may be left and allowed for mathematically (see Para 0332). If the Index Error is larger than 3.0' of arc it should be removed or reduced by turning the adjustment screw at the bottom of the Horizon Glass. If the method of recalling the correct adjustment screw for Side Error is remembered (see Para 0336b), it is simple to ensure the other screw is used for Index Error . (1) By Observing the Diameter of the Sun On and Off the Arc. To check for Index Error set the Sextant to about 0° 30', fit shades and adjust the Micrometer Drum to make the edges of the two images of the Sun touch (Fig 3-8a). Note the ‘On’ the Arc reading. Reverse the images (Fig 3-8b) and note the ‘Off’ the Arc reading. To obtain the Index Error halve the difference in readings and note the resultant sign from the larger reading. If Index Error exists either correct it (see Para 0336c above) or make a note its amount and whether it is ‘On’ or ‘Off’ the Arc (see Para 0332).
Fig 3-8a. Index Error ‘On’ the Arc
Fig 3-8b. Index Error ‘Off’ the Arc
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(2) Difficulties in Observing the Diameter of the Sun On and Off the Arc. To check Index Error by the Sun On and Off the Arc method (Para 0336c(1) above) is a particularly awkward procedure. For accurate results the adjacent images have to be sighted exactly under each other (ie At the maximum tangential reading). The slightest error in this vertical alignment will induce an additional accidental error as shown by Fig 3-8c and Fig 3-8d.
Fig 3-8c. Correct Alignment of Images
Fig 3-8d. Incorrect Alignment of Images
Note 3-3. The Sun’s semi-diameter given for the day in The Nautical Almanac will provide a check on accuracy - the Sextant readings On and Off the Arc added together should equal four times the semi-diameter of the Sun.
WARNING NEVER OBSERVE THE SUN WITHOUT FIRST FITTING SEXTANT / TELESCOPE SHADES.
(3) By Observing a Star . The best method of checking for Index Error is to set the Index Bar a few minutes of arc to one side of zero, then bring the two images of a star together so that they are coincident. If any error exists either correct it (see Para 0336c above) or make a note of its amount and whether it is ‘On’ or ‘Off’ the Arc (see Para 0332). The choice of telescope is similar to Side Error procedure (see Para 0336b(1)). (4) By observing the horizon (or other distant terrestrial object). This is a variation on the ‘star’ method but is the least reliable method of checking for Index Error. The reflected horizon (or distant object) is brought in line with the directly observed horizon (or distant object). The accuracy of this method depends on having a clearly defined, sharp horizon or a sharply defined distant object; it is much preferable to observe a heavenly body if one is available. Having aligned horizons/objects as carefully as possible, if any error exists either correct it (see Para 0336c above) and or make a note its amount and whether it is ‘On’ or ‘Off’ the Arc (see Para 0332). d. Collimation Error. Collimation Error is an variation from the parallel alignment of the axis of the Telescope to the plane of the instrument. Collimation Error should be checked periodically but cannot normally be corrected outside a specialist workshop and correction should not be attempted by users. It is a difficult error to establish (see Para 0336e below) and should only be attempted in good conditions and with the utmost care.
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BR 45(2)
e. Collimation Error Check. After having corrected the Sextant for Perpendicularity, Side Error and Index Error, check the Sextant for Collimation Error as follows: (1) To check for Collimation Error , ship the inverting telescope with the wires parallel to the plane of the instrument. Then choose two heavenly bodies not less than 90 apart, and bring them into accurate contact on one wire of the telescope. (2) Then move the telescope until the bodies are on the other wire. If they are not still in contact, there is Collimation Error and the Sextant should be returned. f. Backlash in a Micrometer Sextant. The Micrometer Drum might wear over time and develop an error due to backlash. The amount of backlash may be determined by setting the Index Bar a few minutes of arc to one side of zero (as for Index Error checks on a star), rotating the Micrometer Drum clockwise to bring a star into coincidence and then repeating this, but turning anti-clockwise. The difference in the two readings will reveal any backlash. It should be negligible in operational Sextant s in ships but may exist in those used regularly by students for training. If there is sufficient backlash to justify making a correction, either make two observations by bringing the drum from opposite directions and mean the result, or habitually turn the Micrometer Drum from one direction and apply any backlash established as a ± correction to the Sextant Altitude. g. Micrometer Drum Friction Clutch. In a micrometer Sextant , if the Index Error adjustment screw on the Horizon Glass (see Para 0336c) has reached the extent of its travel, the index setting may also be adjusted by releasing the friction clutch of the Micrometer Drum. The friction clutch should then be reset lightly in conjunction with the Index Error adjustment screw, and by trial and error, the index setting reduced and set close to zero. The clutch should then be tightened again carefully and firmly. The need to carry out this procedure is very rare and it must be done with particular care. 0337.
Sextant Calibration Marine Sextant s are calibrated when first supplied and on completion of repair or refurbishment, either by a MoD Agency or a contractor. A calibration certificate (or certificates), located in the Sextant box list any small residual errors due to prismatic errors in the mirrors and shade glasses, and aberrations in the lenses of the telescopes. These corrections do not normally exceed a maximum if 0.8' of arc on any part of the Arc, and may be applied to Sextant readings for absolute accuracy. However, in most Royal Navy Sextant s these errors are so small as to be almost negligible. Once calibrated, these characteristics should not change if the Sextant is stored. When in regular use for astronomical observations, the Sextant ’s general performance ( Perpendicularity, Side Error, Index Error ) can be checked and corrected by the navigator. Sextant s should therefore only be returned for re-calibration or repair if:
a. They have been badly knocked, dropped, otherwise physically damaged or have a significant Collimation Error . b.
The mirrors lose their reflective coating.
c. There is a strong reason to suspect their accuracy (eg Worm and racks errors in the Micrometer Drum which change with wear, and other mechanical defects).
3-17 Original
BR 45(2)
d.
Parts of the equipment are missing.
e.
The calibration certificate is in excess of ten years old.
0338.
Care of a Sextant Handle a Sextant with care as any slight blow is liable to upset the adjustments. Always lift a Sextant by the centre of the Frame, and, once lifted, hold it by the handle and never by the Arc or Index Bar . Micrometer Sextant s need care to avoid damage to the worm and rack; press the Clamp in fully to disengage the worm and never grind the worm on the rack. Keep the rack free of dirt and corrosion by applying a little light oil from time to time, brushing it off gently afterwards to ensure that it is evenly and thinly distributed. It is recommended that a safety neck lanyard should be secured to the central handle of the instrument; this will enable altitude information to be written down without placing it on the deck. Bear in mind the following points when using a Sextant :
a. Telescope. When screwing a Telescope into the Collar , take care not to burr the threads. b. Lanyard. Always use a safety lanyard around one’s neck in c ase the Sextant slips from one’s grasp. c. Care. Never leave the Sextant lying unattended out of its box. It is a valuable and fragile instrument. d. Exposure to Sun. Never leave the Sextant exposed to the Sun unnecessarily, as the expansion caused by the Sun’s rays will alter the Sextant ’s errors. e. Preservation. If the Sextant is to be stowed away for a long period, put a thin c oat of vaseline on the Arc to preserve it. f. Stowage. When putting a Sextant away, see that the Shades are closed and the Index Bar set in a position that allows the instrument to be put in the case. Secure the Sextant with the rotating clip in the box and close the lid gently. Keep the box in a safe place. If possible do not allow a Sextant to travel in the care of anyone except its custodian. 0339.
Using a Sextant
a. Errors. Always test the Sextant for Perpendicularity, Side Error and Index Error before taking sights (see Para 0336). The first two errors should always be removed. If the Index Error is under 3, it may be left in and allowed for arithmetically. When possible, take the Index Error both after sights as well as before them. b. Glasses. After adjusting the Index Glass or Horizon Glass, see that they are firm in their mountings and that no adjusting screws are loose. It is a good plan to flick the Glasses with a finger nail and then note if this produces any change in the errors. c. Telescope. For convenience, mark the position of the infinity of the telescope eyepieces for the personal focus of the observer. Take observations in the centre of the field of view so that light rays from the object are parallel to the plane of the instrument.
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BR 45(2)
d. Shades. Unless there are other considerations, it is preferable to use a Telescope Shade rather Shade rather than the Sextant Shades. Shades. Dazzle from the Sun can cause permanent damage to the eyes and must be avoided. WARNING NEVER OBSERVE THE SUN WITHOUT FIRST FITTING SEXTANT / TELESCOPE SHADES.
e.
the Reading Lamp should Lamp should be fully charged and checked. Batteries. Batteries for the Reading
f. Time of Sights. In daylight it is sometimes possible to obtain observations of the Sun, Moon and Venus. Sights should be taken between Civil and Nautical Twilight when the horizon and heavenly bodies are visible. The horizon is visible earlier in the east in the morning and later in the west at evening twilight. However, the best observations are usually taken late at morning twilight and early at evening twilight when the horizon is best. g. Visibility. Take observations from the highest highest convenient position in clear weather as this will give the best view from the ship. Take observations from the lowest convenient position in fog, haze or mist as the visible horizon will be closest. h. Records. Record the name of the heavenly body (if known), the Deck the Deck Watch Watch Time (DWT), (DWT), Sextant Altitude and Altitude and the approximate bearing of the body for each observation. i. Temperature Errors. If a cold Sextant is is taken from an air conditioned ship into hot tropical temperatures all the previously zeroed errors will change rapidly as the Sextant components components start to expand. In hot climates, either take sun-sights very quickly indeed, or allow the Sextant to to warm up thoroughly and zero it when ‘hot’. During starsights in i n hot damp climates, in addition to expansion errors, bringing a ‘cold’ Sextant out out into a balmy but very damp tropical morning can cause condensation to form instantly on the optical surfaces of the Sextant . In polar conditions condensation will also form on a warm Sextant and and then freeze, making the Sextant unusable. unusable. To prevent this, place the Sextant in in an airtight plastic bag while it cools (see Para 0560 for details). Choice of Heavenly Bodies. When choosing stars, note the weather and the j. direction in which the horizon is likely to be clearest. After obtaining a list and plot of bearings and elevations of stars and planets from NAVPAC 2 or the Star Identifier, choose three or more stars and planets to give the best cuts. The best combination is four stars at 90° apart in azimuth az imuth (grouped in pairs, in opposition) because any Abnormal any Abnormal Refraction error Refraction error will be eliminated by using opposite opposite horizons. Stars should be selected between 30° and 60° and where possible with approximately the same altitude. At least four additional stars (and preferably all the available NAVPAC 2 / Nautical Almanac selected stars) should also be selected as standbys, sta ndbys, in case the sky is partly clouded and the preferred stars are obscured.
k. Spray. When there is spray s pray or after using the Sextant in in damp or rough weather, use a chamois leather or an absorbent, clean lint free cloth to wipe away all moisture, particularly on the Arc the Arc and and Glasses (see also Para 0326e). 3-19 Original
BR 45(2)
l. Swinging the Sextant. When taking the altitude of any heavenly body, the Sextant should be swung in an arc, in a plane perpendicular to the line of sight to the heavenly body. When carried out correctly, correctly, this will cause the heavenly body to appear to swing in an arc in the field f ield of view. The Micrometer The Micrometer Drum should Drum should be rotated at the same time until the heavenly body touches the horizon at bottom-dead-centre of the arc ( Star ( Sun Telescope). Telescope) Telescope) or top-dead-centre of the arc (Sun Telescope). Taking the altitude at the instant of contact at either of these dead-centre positions will ensure that the correct vertical angle has been taken. If this ‘swinging’ procedure is not carried out correctly, significant errors will result which may negate the entire sight. m. Sextant - Normal Method. Set the elevation of the chosen star on the Sextant (for (for Polaris see Para 0623). Look through the Star Telescope on Telescope on the approximate bearing and sweep the horizon at this point. The star will frequently be found before before it is visible to the naked eye while the horizon is still good (ie. take the brightest star early at Evening Stars). This is the best way of finding dim stars. Familiarity with this method is invaluable if there is broken cloud when a star may be visible for only a few seconds. n. Sextant - Inverting Method. In broken cloud conditions it can also be helpful to invert the Sextant and and point the clear part of the Horizon the Horizon Glass at the star, and bring the horizon to the star instead of the normal method (see Para 0339.m above). Once an approximate angle has been set on the Sextant with with the star in the field of view, the Sextant can can be turned the right way up and normal sighting procedures resumed. o. Rising and Falling onto the Horizon. An alternative method of sighting a heavenly body is to bring it down to the horizon and then note whether it is rising or setting - if the body is west of the meridian it will be setting, if e ast of the Meridian the Meridian it it will be rising. If it is setting, move the Micrometer the Micrometer Drum Drum until the object is slightly s lightly above the horizon: then, leaving the Sextant set, set, swing it gently from sided to side (see Para 0339.l above) until the star or limb just touches the horizon. If it is rising, move the Micrometer the Micrometer Drum until the object is slightly below the horizon, and carry out the same procedure. p. Sets of Observations. Observations. When possible, take observations of a heavenly body in sets of three or five at equal time or altitude intervals, which should provide evenly changing results. This will provide a confidence check on the accuracy of the sights, particularly if the horizon is poor. An uneven pattern of results will indicate whether one or more of the sights are inaccurate (rogue) sights. q. Unknown Body. Having taken a set of observations of a star or planet, the identity is uncertain, take a bearing of it. r. Rolling. When the ship is i s rolling heavily, errors due to rapidly changing Dip changing Dip (see (see Chapter 8) may be reduced and more accurate observations obtained by observing from a position close to the centre line of the ship. s. Sights by Moonlight. On a clear night within about two days of Full Moon, Moon, star sights can be taken by experienced Sextant users users to a reasonable degree of accuracy with a horizon illuminated by moonlight. This should only be attempted when the Moon is high. The horizon on the bearing of the moon appears to dip dip and is therefore suspect. The Moon itself and stars near it should not be used.
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BR 45(2)
SECTION 4 - REDUCING SIGHTS (PROCESSING OF SEXTANT READINGS) 0340 0340..
NAVP NAVPAC AC 2: 2: Assu Assump mpti tion onss and Overall Arrangement of ‘Sights’ Sub-Programs
a. Assumptions. Full instructions for NAVPAC 2 are at Annex Annex 3A. In the procedures for reducing sights in this Section, the following assumptions have been made: •
The DR/EP DR/EP positio position n for for the fix time time is known known (see Para Para 03200320-032 0322 2 and and 0325 0325). ).
•
The Deck Watch Error (DWE) is known (see Paras 0212.d and 0326.c.2). (DWE) is
•
The Sextant errors have been checked, adjusted where necessary and any residual Index residual Index Error recorded recorded (see Para 0336).
•
The The iden identi tity ty of the the heav heaven enly ly bodi bodies es obs observ erved ed are are kno known wn,, and and the the Deck Watch Watch Time (DWT), (DWT), the Sextant Altitude and Altitude and the approximate bearing of the body have been recorded for each observation (see Paras 0323-0324 and 0326c.4). 0326c.4).
•
The The other other org organ anisa isatio tiona nall and and mater material ial prep prepara arati tion onss at Para Para 032 0326 6 and and the the precautions when using the Sextant at at Para 0339 have been observed.
•
NAVP NAVPAC AC 2 is is avail availab able le on on a sui suita tabl blee PC and and a pri print nter er is is avai availab lable. le.
•
For For Morn Mornin ing g and and Eve Eveni ning ng Star Stars, s, NAV NAVPAC PAC 2 has has been been use used d to find find the the tim timee of twilight, for the prediction of the approximate bearings and altitudes of the heavenly bodies, and that the data from these predictions has been transferred across to other parts of the program (see Para 0321.c and 0323.b).
•
If NAVPAC NAVPAC 2 is is used used for sun sights sights or star star sights sights withou withoutt havi having ng transfer transferred red data across to other parts of the program, the body observed will be selected manually from the menu within the ‘Astro’ ‘Astro’ sub-program (see Para 0323.b).
b. Overall Arrangement of NAVPAC 2 ‘Sights’ Sub-Programs. An understanding of the relationships between the various Sight s sub-programs of NAVPAC 2 is important, and this is best summarised in a diagram, shown at Fig 3-9 below.
Fig 3-9. Overall Arrangement of NAVPAC 2 ‘ Sights’ Sub-Programs Sub-Programs
3-21 Original
BR 45(2)
0341 0341..
NAVP NAVPAC AC 2: Op Opti tion onss Page Page
a. Options Page. The Options page (see Fig 3-10 opposite), which may be selec ted by clicking the button on the Home page (or key in ‘Alt O’ ), ), can be altered at any time and the configuration saved. While the Options settings are not critical when doing preparatory work in the FindIt page, before using the Sights pages (ie Fix, Legs, Astronomical Observations, Log, Results, Position Line Plot ), it will be found helpful to save convenient settings for: • • •
Units of
an and and
, Time and
• •
. and
of eye.
(Bearing). .
for saving files.
b. Saving Options. To save chosen settings, click on button (or key in ‘Alt S’ ). ). When the Saving-Loading page (Fig 3-17) appears, click the button (or ‘Alt ‘Alt S’ ) and then complete the file name in the dialogue box. See the general explanation and instructions for saving at Para 0347b). c. Saving Default Settings. To change the default settings, carry out the procedures in ‘Saving Options’ Options ’ above but re-save file as ‘ Navpac2.ini’. Navpac2.ini’. It is strongly strongly recommended that a copy of the original ‘ Navpac2.ini’ Navpac2.ini ’ is kept in another folder/disc in case any problems develop. d. Loading Options. To load chosen settings on starting NAVPAC 2, open the (‘Alt L’ ), ), then from the Saving Options page and click Loading page presented (see Fig 3-17), click (‘Alt L’ ), ), then click the chosen file. 0342 0342..
NAVP NAVPAC AC 2: Sigh Sights ts-F -Fix ix Page Page
a. From the NAVPAC PAC 2 Home page, click on in ‘Alt in ‘Alt P’) to open the Sights-Fix page page (see Fig 3-11 opposite).
(or key
b.
On the Sights-Fix page page (see Fig 3-11opposite), carry out the following: f ollowing:
•
Then Then chec check k that that the the , (in (in UT), UT), and and / EP for the time of fix are correct; if they are not, correct them.
•
IF REQU REQUIR IRED ED to purge purge othe otherr (previ (previou ous) s) data data and calculatio calculations ns from from the the progra program m (see Para 0343), THEN click button.
of the the DR
Note 3-4. The space bar acts as a separator for each element of the data data fields, irrespective of the punctuation displayed. displayed. After inputting the changes for each complete data field, click the ‘Return’ / ‘Enter’ key. The punctuation will then appear in the data field and helps check what has been entered at each stage. Note 3-5. Care should be taken to ensure dates are input in the format YYYY/MM/DD. 3-22 Original
BR 45(2)
Fig 3-10. NAVPAC 2 ‘Options’ Page Page
Fig 3-11. NAVPAC 2 ‘Sights-Fix’ Page Page
3-23 Original
BR 45(2)
0343 0343..
NAVP NAVPAC AC 2: Sigh Sights ts-L -Leg egss Page Page When data displayed in the Sights-Fix page page has been checked correct or amended (see Para 0342), click on button on the Sights-Fix page page (or key in ‘Alt L’ ). ). This will bring up the Sights-Legs page (see Fig 3-12 below). and carry out the following procedure:
•
Firs Firstt chec check k that that the the and and (in (in UT) UT) disp displa lay yed on the the Sights-Legs page are correct (ie have been correctly transferred); if not, not, correct them. In some cases, particularly where classroom examples with widely differing positions have been used immediately before, it may be necessary to use the facility on the Sights-Fix page page (see Para 0342b) before proceeding further. If If the and (in UT) are not not correct correct on the Sights Legs page, significant errors will occur in subsequent calculations.
•
Usin Using g the the whit whitee dial dialog ogue ue boxes boxes and and the the yello ellow w butto button, n, enter enter the the s and s for the period during which NAVPAC 2 will have to make calculations. The ‘Leg No’ may No’ may be selected using the or buttons.
•
Once Once cou cours rsee and and spee speed d data data for for the the leg leg has has bee been n inpu input, t, clic click k the the yel yello low w button. Repeat the procedure for for each leg.
•
‘Leg’ inputs may be changed retrospectively if the ship manoeuvres after initial inputs have been made.
•
To move to the Sights-Astronomical Observations page, click the yellow button (Alt A). A).
Fig 3-12. NAVPAC 2 ‘Sights-Legs’ Page Page
3-24 Original
BR 45(2)
0344.
NAVPAC 2: Sights-Astronomical Observations Page (using Stars / Planets) The Sights-Astronomical Observations page (see Fig 3-13) is normally entered by clicking on the button in the Sights-Legs page (see Para 0343 opposite), but can also be accessed directly from the Home or other pages in the program by clicking on the appropriate button. Once in the Sights-Astronomical Observations page, carry out the following procedure:
•
Check that
is correct (note that the format is YYYY/MM/DD).
•
Select the body observed by clicking on the using the buttons for the previous or next observation.
•
Input
•
Check that (Index Error Correction), / , ( Height of Eye), (Temperature) and are correctly input; if they are not, then correct them.
•
When content with all inputs, click on the yellow button (all data in the large window in Sights-Astronomical Observations page displayed in red).
•
Set button to (tick displayed, and all data in the large window in the Sights-Astronomical Observations page displayed in blue).
•
Repeat this process for subsequent sights. When all sights are input, double check that the in Sights-Fix page menu is correct (see Para 0342) and return to the Sights-Astronomical Observations page.
•
Click
UT ( DWT corrected for DWE ), and
with
button, or by selected.
. This brings up the Sights-Results page.
Note 3-6. The space bar acts as a separator for each element of the data fields, irrespective of the punctuation displayed. After inputting the changes for each complete data field, click the ‘Return’ / ‘Enter’ key. The punctuation will then appear in the data field and helps check what has been entered at each stage.
Fig 3-13. NAVPAC 2 ‘Sights-Astronomical Observations’ Page
3-25 Original
BR 45(2)
0345.
NAVPAC 2: Sights-Astronomical Observations Page (using Sun / Moon Planets) The procedure for Sun and Moon sights is as for Stars /Planets (see Para 0344), exc ept: •
Upper and Lower Limbs. In the Sights-Astronomical Observations page , defaults to - for the Sun and Moon. Care must be taken to select the button when inputting Sun and Moon altitudes if the ‘Upper Limb’ has been observed.
•
Single Sun Sights. With single/running Sun-sights, NAVPAC 2 will NOT work out an observed position or display the Sights-Plot page. When data has been input in the Sights-Astronomical Observations page, button clicked, and button set to , the large dialogue window on that page will show sufficient information to plot the sights manually (see Para 0351). The information supplied in the large dialogue window is as follows (see Fig 3-13 on previous page):
‘Estimated Position of Sight at (Time) UT’ at the top of the dialogue window is the ‘Run’ position allowing for course and speed between the Observation Time and the ‘Initial’ time set on the Sights-Fix page (see Para 0342).
‘Azimuth’ , ‘Calculated (Tabulated) Altitude’ & ‘Observed (True) Altitude’ are displayed on the next three lines of the dialogue window and the difference between the last two items is the ‘Intercept’ , which is also displayed near the bottom of the window. This may be plotted manually from the ‘Run’ position displayed a few lines above.
The procedure for manual plotting of the ‘Position Line’ is at Para 0351
•
Fix Time. With ‘running’ astro-fixes (eg Sun-run-Sun, or Sun-run-Mer Pass), update the for the later sight on the Sights-Fix page. If this is not done, NAVPAC 2 will run the second sight back to the initial (first sight) time.
•
Plotting Lines Symbology. NAVPAC 2 displays ‘ Position Lines’ as solid black lines if they have been run on or back less than 15 minutes, and as dashed black lines if they have been run on or back more than 15 minutes
0346.
NAVPAC 2: Sights-Results, Sights-Log and Sights-Position Line Plot Pages After inputting sights in the Sights-Astronomical Observations page and clicking on the ‘Calculate’ button (see Para 0344), the Sights-Results page is displayed and provides information in a large window with other facilities via yellow buttons, as follows (see Fig 3-14):
a.
b.
3-26 Original
Sights-Results Page Data. The dialogue window contains the following data:
•
A summary of the DR / EP position (top right of dialogue window).
•
Calculated Position at the Time of Fix (bottom of dialogue window and equating to Observed Position).
•
Intercepts for each observation and associated confidence data.
Sights-Log Page. On clicking the button in the Sights-Results page, the Sights-Log page is displayed (see Fig 3-15 opposite) and gives full details of each sight. This may be printed or saved, and Sights-Fix, Sights-Astronomical Observations, Sights-Legs or Home pages may displayed as required by clicking the appropriate buttons. To return to the Sights-Results page, go to Sightsbutton. Astronomical Observations page and click on the
BR 45(2)
Fig 3-14. NAVPAC 2 ‘Sights-Results’ Page
Fig 3-15. NAVPAC 2 ‘Sights-Log’ Page
3-27 Original
BR 45(2)
c. Sights-Position Line Plot Page. When the button in the Sights-Results page (see Fig 3-14) is clicked, the Sights-Position Line Plot page is displayed, usually showing a 20 mile diameter colour plot of the sight (see Fig 3-16 below). The initial DR / EP position is marked with a red cross, the ‘Confidence Ellipse’ (equivalent to an ‘ Error Ellipse’ - see Para 0902) in magenta, Star lines in blue, Sun and Moon lines in black, and Venus/Mars/Jupiter/Saturn lines in magenta/red/cyan/green respectively. To avoid confusion when viewing Sun-run-Sun sights, Position Lines that have been Run (Transferred ) for more than 15 minutes are shown as hatched lines. This plot can be zoomed, re-scaled and printed by using the appropriate buttons. Once the plot has been examined and/or printed, the display can be returned to the Sights-Results page by clicking on the button at the bottom right corner of the screen.
Fig 3-16. NAVPAC 2 ‘Sights-Position Line Plot ’ Page
d. Sights-Results Page: Adopt Fix Button. If the user is happy with the sight, having carefully examined the Sights-Results, Sight-Log and Position Line Plot pages and taken any prints necessary ( see Note below) , the button on the Sights-Results page (see Fig 3-14 on previous page) may be clicked. On clicking button, the (calculated) Observed Position will replace the original DR / EP position input in the ‘ Reduction of Sights’ page and the Intercepts will change from being relative to the DR /EP, to being relative to the (calculated) Observed Position. Note 3-7. If it is desired to record the original intercepts from the DR / EP position (eg for use with BR 45(5) worked examples and answers), take a print the Sights-Results, Sight-Log and Position Line Plot pages as required, before clicking on the ‘Adopt Fix’ button on the Sights-Results page.
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BR 45(2)
0347.
NAVPAC 2: Summary of Printing, Saving and Loading Facilities
a. Printing. Throughout NAVPAC 2, prints can be obtained by the direct-print button or via the button. If the direct-print is clicked, the page will be printed using the default printer. If the button is used, a standard Windows printer box (see Fig 3-17 below) is displayed and the user can customise arrangements for the print including printing to a file. Prints can be obtained from the following pages: •
RiseSet Results Page. The print command(s) on this page cause the contents of the RiseSet Results page window (Fig 3-3) to be printed.
•
FindIt-Results Page: This 2-sheet print contains a polar diagram of the visible heavenly (navigational) bodies for the selected time, date a nd position, together with a list of those bodies detailing their name, magnitude, altitude and azimuth (see Fig 3-5 and Figs 3-6a / 3-6b).
•
Sights-Results Page. The print command(s) on this page cause both the Sights-Results page window (Fig 3-15) and the Position Line Plot page (Fig 3-16) to be printed. This double print is sufficient for general navigation use.
•
Sights-Log Page. The print command(s) on this page cause the Sights-Log page (Fig 3-15) and all the data from the Sights-Astronomical Observations page (Fig 3-13) to be printed. This gives a comprehensive record of the sight on one sheet of paper and is a most useful facility for detailed analysis of the sight (eg for training purposes), especially when used in conjunction with the Sights-Position Line Plot print.
•
Sights-Position Line Plot Page. The print command(s) on this page cause the Sights-Position Line Plot page (Fig 3-16) to be printed. This gives a visual appreciation of the sight and is a most useful facility for general navigation. It is also useful for detailed analysis of the sight (eg for training purposes) especially when used in conjunction with the Sights Log page print.
Fig 3-17. NAVPAC 2 Standard Windows Printer Dialogue Box 3-29 Original
BR 45(2)
b. Saving. Saving facilities are provided so that all or part of the work in progress may be saved to a file on disc for future use via a combined Saving-Loading page (see Fig 3-18) . By default this data (except Options - see below) is saved to the NAVPAC 2 \ Examples folder. This facility has particular value in the training situation where students may wish to record their work, either for later use or for discussion with their instructors. It also has a use in ships where the computer used for NAVPAC 2 is not dedicated to this task and may have to be restarted and the data reloaded during the day’s run. Data may be saved from the following pages: •
FindIt Results Page: This file saves all the FindIt results data.
•
Options. Saving a new Options file allows it to be reloaded at any time, but NAVPAC 2 will always restart to the default settings. A new file saves the chosen settings. Options has a slightly modified Saving-Loading page (see Fig 3-19)
•
Default Options Setting. The default Options file (navpac2.ini) contains the ‘home’ parameters and paths for the ephemerides and examples and must be kept in the top level folder with the execution program. Care must be taken with this file; it contains non-printing characters. If it is desired to change the Options default settings, it is essential to make a copy/copies of the original “navpac2.ini” in case of any subsequent problems in the modified Options default file, so that the original can be restored.
•
Sights-Fix / Sights-Legs / Sight-Astronomical Observations / Sight-Results / Sight-Log. Saving is possible at all these points in the program. The dialogue boxes are identical except for the button in the bottom right corner. This button is context sensitive. The arrangement of dialogue boxes at Fig 3-18 shows the user was on one of the Sights pages.
Fig 3-18. NAVPAC 2 ‘Saving-Loading’ Page (From Sights Page) 3-30 Original
BR 45(2)
Fig 3-19. NAVPAC 2 ‘Saving-Loading’ Page (From Options Page)
c. Loading. Loading facilities are provided so that all or part of the work in progress previously saved may be re-loaded from a file on disc with the minimum of fuss. The button is on the same shared page as the button and both are shown for general use at Fig 3-18 and for use with Options only at Fig 3-19). The ‘Loading’ process is the mirror image of the ‘Saving’ process (see Para 0347b opposite).
3-31 Original
BR 45(2)
0348.
The Nautical Almanac - Meridian Passage, Polaris and Altitude Corrections
a. Time for Observing the Sun’s Meridian Passage (Mer Pass). By taking the altitude of the Sun at ‘ Meridian Passage’( Mer Pass), a very simple manual calculation will provide the observer’s Latitude. The Mer Pass observation should be at the moment when the Sun is in the Observer’s Meridian (ie. bearing 180° or 000°) as calculated at Para 0325. For a stationary observer, Mer Pass will also be the Sun’s highest altitude. b. Mer Pass - Potential Errors of Timing. Although Mer Pass equates to the Sun’s highest observed altitude for a stationary observer, if the observer is moving with any appreciable north-south component, taking the altitude of the Sun at its highest altitude rather than at the calculated time will induce an error (see Chapter 6). This error may of up to 5' of altitude (which equates to 5' of Latitude) for a fast moving ship on a northsouth course. Thus it is important that the observation be made at the time, to the nearest minute, as calculated at Para 0325, rather than at the Sun’s highest altitude. c. Mer Pass - Requirement for Deck Watch Time. If NAVPAC 2 is used to calculate the intercept and plot the sight as a normal Sun-sight, the precise Deck Watch Time (DWT) will also be needed. If a manual Latitude calculation (of which there are 3 variants) is made, provided the observation has been taken at the time (to the nearest minute) calculated at Para 0325, the precise DWT is not needed. d. Correcting Sextant Altitude to Observed (True) Altitude. Before applying it to the Mer Pass formulae at Paras 0348f-h, or the Polaris formula at Para 0348j, the Sextant Altitude must be corrected for Index Error (IE), Height of Eye (Dip) and Refraction to obtain the Observed (True) Altitude, as follows: •
Index Error(IE) is added or subtracted as described in Para 0332.
•
The Dip correction (obtained from a Table in the inside front cover of The Nautical Almanac at Page A2) is always subtracted. The resultant (Sext. Alt ± IE - Dip) is known as the ‘Apparent Altitude’ .
•
Altitude correction ( Refraction) tables for stars and the Sun are in the front of The Nautical Almanac (Pages A2 / A3) and those for the Moon are inside the back cover of The Nautical Almanac (Pages xxxiv / xxxv). They are entered with arguments of Apparent Altitude, Time of Year, HP (see Note 3-8) , and UL or LL as appropriate.
Note 3- 8. HP (Horizontal Parallax) is not significant except in the case of the Moon, where a separate correction is needed which may be taken from the HP tables at the back of The Nautical Almanac. A similar, very small correction is listed for Venus and Mars as an ‘Additional Correction’ at the front of The Nautical Almanac. See Para 0401 ‘Horizontal Parallax’ for a more detailed explanation.
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•
Additional ( Refraction) corrections tables for unusual temperature and pressure conditions are found in the front of The Nautical Almanac (Page A4) but these are very small and are only significant at very low Apparent Altitudes.
•
The total Refraction corrections are added to subtracted from Apparent Altitude as indicated in the tables to obtain Observed (True) Altitude.
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e. Correcting Sextant Altitude to Observed (True) Altitude. An example of this calculation for an observation in extreme conditions, thus including every possible correction, is at Example 3-3 below: Example 3-3. What is the Observed (True) Altitude for an observation with a Sextant Altitude of 10° 00.0' for the Sun (LL) in March, a temperature of -10°C, an atmospheric press ure of 1010 millibars, a Height of Eye of 6.2 metres and Index Error Correction of -1.6'? Sextant Altitude
10° 00.0'
IE
- 01.6'
Dip (-)
- 04.4'
Sub-Total
- 0° 06.0'
Apparent Altitude
09° 54.0'
Altitude Corrections.
+0° 10.9'
Sub-Total
10° 04.9'
Temperature/Pressure
- 0° 00.5'
Observed (True) Altitude
10° 04.4'
- 06.0'
Example 3-3. Correcting Sextant Altitude to Observed (True) Altitude
f. Mer Pass - Latitude Greater than Declination with ‘Same’ Names (N or S). If observing Mer Pass when the observer’s Latitude and the Sun’s (or other heavenly body’s) Declination have the SAME (ie. N or S) names and the Latitude is greater than the Declination (Lat > Dec), then the observer’s Latitude may be calculated by applying the following formula (the proof of which is at Para 0612): Latitude = Declination - Observed (True) Altitude + 90°
g. Mer Pass - Declination Greater than Latitude with ‘Same’ Names (N or S) . If observing Mer Pass when the observer’s Latitude and the Sun’s (or other heavenly body’s) Declination have the SAME (ie. N or S) names and the Declination is greater than the Latitude (Dec > Lat, ie. the opposite of Para 0348f above), then the observer’s Latitude may be calculated by applying the following formula (the proof of which is a t Para 0612): Latitude = Declination + Observed (True) Altitude - 90°
h. Mer Pass - Latitude and Declination with ‘Opposite’ Names (N or S) . If observing Mer Pass when the observer’s Latitude and the Sun’s (or other heavenly body’s) Declination have CONTRARY (ie. N or S) names, then the observer’s Latitude may be calculated by applying the following formula (proof of which is at Para 0612): Latitude = 90° - Observed (True) Altitude - Declination 3-33 Original
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i. Mer Pass - ‘Lower’ Transit. There is a further Mer Pass case in which the heavenly body makes a Lower Meridian Passage, some 12 hours before or after the Upper Meridian Passage for which the formulas are given at Paras 0348f-h above. In the case of the Sun, this Lower Meridian Passage would take place at around midnight; the Sun is not visible at that time except in very high Latitudes at certain times of the year. However, certain stars do make Lower Meridian Passages in moderate Latitudes at times when they are visible and if observed, it is possible to derive the observer’s Latitude by a simple calculation. In practice, Lower Meridian Passage sights are not normally observed as such and so the appropriate formula is not provided here. However, the formula and a full explanation of the calculation are at Para 0612e. j. Polaris. NAVPAC 2 (Astronomical Observations Sights sub-program) can be used in the conventional way with an observation of Polaris (the Pole Star) to produce the observer’s Latitude and the direction of true North. However, with a very simple manual calculation from Nautical Almanac data, observation of Polaris (the Pole Star) will provide the same information even more simply. The ability to obtain the direction of true North at any time of the night (without needing a horizon) is particularly useful. The Polaris Tables are found in The Nautical Almanac after the Daily Tabulated Pages and their Explanation Section, but before the Sight Reduction Tables; they are usually on or around page 274/275. The procedure is as follows: •
Correct Sextant Altitude to Observed (True) Altitude (see Para 0348d).
•
The upper Polaris Table is entered with LHA Aries ( ) (see Paras 0106d and 0324b) to determine the column of the Table to use; each column refers to a range of 10° of LHA Aries ( ). With mental interpolation, correction a0 is taken from this upper Polaris Table with units of LHA Aries ( ) in degrees as the argument.
•
Corrections a1 and a2 are taken, without interpolation, from the second and third Tables with arguments Latitude and month respectively.
•
Corrections a0, a1 and a2 are always +ve and are applied in the formula: Latitude = Observed (True) Altitude -1° + a 0 + a1 + a1
•
The final table gives the Azimuth (true bearing) of Polaris.
Example 3-4 (Polaris). On 9 December 1997 in DR position 62° 17.0'N 030° 47.0'W Polaris was observed. The Observed (True) Altitude (Sextant Altitude, corrected for Index Error, Height of Eye and Refraction) was 62° 19.6' and the LHA of Aries at the moment of observation was 314° 43.0'. What was the observed Latitude and true bearing of Polaris? (See extract of 1997 Nautical Almanac at Appendix 2.)
Observed (True) Altitude From Polaris Tables
Sub-Total Constant Latitude
a0 a1 a2
62° 19.6' + 00° 53.4' + 00° 00.8' + 00° 00.9' 63° 14.7' - 1° 00.0' 62° 14.7'
Bearing (by inspection) = 001½°
Example 3-4. Summary of Polaris Calculations 3-34 Original
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0349.
NAVPAC 2: Almanac Facilities.
a. Summary of NAVPAC 2: Almanac . In addition to its wide ranging computation facilities, NAVPAC 2 also provides basic Nautical Almanac data, which may also be printed, for all navigational heavenly bodies. The Almanac page (see Fig 3-20) is accessed by clicking on the button (or keying Alt A) from the NAVPAC 2 Home page. When displayed, the Almanac page tabulates the GHA and Declination for all navigational bodies to a precision of 0.1'. It also tabulates the semi-diameter (S) of the Sun, the Horizontal Parallax (HP) of the Moon, Venus and Mars, and the magnitudes of all the stars. Almanac also introduces an additional (imaginary) body called Aries for which the GHA only is tabulated. b. Almanac Inputs and Outputs. To obtain Almanac data, input and (UT) into the appropriate dialogue boxes and click on the list heavenly bodies as appropriate. The required data will be shown in the large dialogue box window. If selecting heavenly bodies, note that Aries does not appear in alphabetical order, but at the very end of the output list, after the Sun, Planets and Moon. c. Printing. The Almanac data output may be printed by clicking on the button or on the direct-print button (see Para 0347a for a general explanation of printing).
Fig 3-20. NAVPAC 2 ‘Almanac’ Page with Almanac Data Displayed
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SECTION 5 - PLOTTING SIGHTS 0350.
NAVPAC 2: Plotting of Astronomical Position Lines
a. General. Full instructions for NAVPAC 2 are at Annex 3A. NAVPAC 2 has a sophisticated calculation and plotting system which will normally preclude the requirement to carry out manual plotting. Provided that the calculation procedures at Paras 0340-0347 are carried out correctly, NAVPAC 2 will display and print the appropriate fix on demand. Especially when conducting Sun-run-Sun calculations or a full ‘Day’s Run’, it is important to be meticulous in updating each page correctly, otherwise serious errors may result (see Paras 0351d / 0346d). b. Display of Position Lines. To avoid confusion, Sun-run-Sun sights, Position Lines that have been Run (Transferred) for more than 15 minutes are shown as hatched lines. c. Saving of Data. If conducting a Day’s Run in NAVPAC 2 it is valuable to save each element as a file, which can be reloaded and updated for the next calculation. See Paras 0347b/c for general explanations of saving and loading. d. NAVPAC 2 Recording and Plotting Form. A convenient ‘NAVPAC 2 Recording and Plotting Form’ is at Fig 3-21 (overleaf) and may be reproduced locally. See Para 0351e opposite for guidance on its use. The use of the form is optional but it does provide a place to make the important manual DWT / DWE / UT (GMT) calculation prior to inputting UT (GMT ) to NAVPAC 2 for each sight (see Para 0344). 0351.
Manual Plotting of Astronomical Position Lines
a. Concept. An Astronomical Position Line is actually a small element of the circumference of a Small Circle (see Para 0110) centred on the Geographic Position (see Para 0109) of the star with a radius equivalent to ‘90° - Altitude’, converted into nautical miles. This radius is usually between 1200 n. miles ( Altitude 70°) and 4200 n. miles ( Altitude 20°) in length, and is impossible to plot on any chart of a reasonable scale. However, if the Calculated (Tabulated) Altitude for the DR position is subtracted from the Observed (True) Altitude and the result (converted into nautical miles and known as the ‘Intercept’ ) is plotted from the DR / EP position either ‘To’ or ‘From’ the bearing of the star, then plotting at a reasonable scale on a normal chart is possible. Given the large radius of the Small Circle, it is accepted that for short distances the Astronomical Position Line may be considered to be a straight line. b. Runs. Astro-sights for a fix cannot all be taken at the same instant; typically, star sights may take place over a 10 or 15 minute period. To plot an accurate fix, the DR / EP position for each sight must be ‘Run-on’ or ‘Run-back’ (Transferred ) along the ship’s course and speed (allowing for any tidal stream or current), to a common time. In the case of Sun-run-Sun sights or other similar running fixes, the earlier sight is normally ‘Run-on’ (Transferred ) to the time of the latter. Astronomical Position Lines are displayed on paper charts with a single open arrowhead at each end and Transferred Astronomical Position Lines with a double open arrowhead at each end.
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c. Procedure. The following procedure is used to plot Astronomical Position Lines manually from NAVPAC 2 data: •
Select the ‘ Fix Time’ required (usually the nearest convenient quarter hour).
•
NAVPAC 2 automatically produces a DR position for each sight, which is already ‘run-on’ or ‘run-back’ along the ship’s course and speed as set in the Sights-Legs page (Fig 3-12), to the time set in the Sights-Fix page (Fig 3-11).
•
Select a suitable Mercator Plotting Sheet or draw up a D6018 (Plotting Sheet for Astro Fixing) (see Para 0526).
•
Plot each Astronomical Position Line from the NAVPAC 2 Latitude and Longitude which is set in the Sights-Fix page (Fig 3-11) as a straight line at right angles to the heavenly body’s Azimuth (bearing), at an ‘Intercept’ distance, either ‘To’ or ‘From’ from the direction of the heavenly body’s Azimuth (bearing).
Note 3-9. NAVPAC 2 includes the ‘run’ in the DR position from which each sight is plotted; it is important NOT to apply the run manually when plotting, as this will induce an error rather than correct it.
•
To establish whether to plot the Intercept ‘To’ or ‘From’ from the direction of the heavenly body’s Azimuth (bearing), check the NAVPAC 2 printout for the sign of the ‘Intercept’ : NAVPAC 2 displays ‘To’ intercepts as + ve and ‘From’ intercepts as -ve.
•
Another method of establishing whether to plot the Intercept ‘To’ or ‘From’ is to inspect the two altitudes (Calculated (Tabulated) Altitude and Observed (True) Altitude) on the NAVPAC 2 printout, using the rule: ‘TABULATED (Calculated) TINIER TOWARDS’
d. Potential Errors when Plotting Intercepts from NAVPAC 2. If it is intended to plot sights manually (eg if presenting a Day’s Run or when using BR 45(5) worked examples and answers), it is essential to take a print ( or record details manually) from the Sights-Results, Sight-Log and Position Line Plot pages as required, before clicking on the button on the Sights-Results page, for the reasons given at Para 0346d. e. NAVPAC 2 Recording and Plotting Form. A convenient ‘NAVPAC 2 Recording and Plotting Form’ is at Fig 3-21 (overleaf) and may be reproduced locally. This form is intended for manual completion and may be used instead of, or in addition to, the NAVPAC 2 printouts and plot. The form itself contains comprehensive instructions for the plotting procedure required. The use of the form is optional. See Para 0350d opposite concerning calculation of UT from DWT and DWE.
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Fig 3-21. NAVPAC 2 Recording and Plotting Form (May be reproduced locally)
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CHAPTER 4 THE CELESTIAL SPHERE - DEFINITIONS, HOUR ANGLES & THEORY OF TIME CONTENTS SECTION 1 - ‘READY REFERENCE’ LIST
Celestial Sphere and Associated Terms - Definitions and References . . . . . . . . . . . . .
Para 0401
SECTION 2 - HOUR ANGLES
Hour Angles - Explanation and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hour Angles and Declination - Pictorial Representation & Standard Nomenclature . . Greenwich Hour Angle (GHA) and Local Hour Angle (LHA) of a Heavenly Body . . .
0420 0421 0422
SECTION 3 - SOLAR TIME
Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Solar Day and Solar Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Apparent Solar Day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The True Sun and the Mean Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Mean Solar Day / Time and UT, the Civil Day and the Astronomical Day . . . . . . . Local Mean Time (LMT) and Universal Time (UT) / Greenwich Mean Time (GMT) . . Longitude and Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conversion between UT / GMT and LMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Use of Standard Time and Zone Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Equation of Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Para 0430 0431 0432 0433 0434 0435 0436 0437 0438 0439
SECTION 4 - SIDEREAL TIME
Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Sidereal Day and Sidereal Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Length of the Sidereal Day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Local Sidereal Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relationship between UT / GMT and GHA Aries ( ) . . . . . . . . . . . . . . . . . . . . . . . . .
0440 0441 0442 0443 0444
SECTION 5 - LUNAR AND PLANETARY TIME
The Hour Angle of the Moon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Lunation or Lunar Month . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Phases of the Moon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Hour Angle of the Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0450 0451 0452 0453
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CHAPTER 4 THE CELESTIAL SPHERE - DEFINITIONS, HOUR ANGLES & THEORY OF TIME SECTION 1 - ‘READY REFERENCE’ LIST 0401.
Celestial Sphere and Associated Terms - Definitions and References Some elements of the Celestial Sphere have already been introduced at Chapter 1. For a full understanding of astro-navigation theory, precise definitions of all elements of the Celestial Sphere and some associated terms are needed at the outset. A convenient ‘ready reference’ list of terms with their definitions or a brief explanation to support more detailed study, is included below (positioned at the start of the main ‘theory chapters’) and is primarily intended for RN Specialist N Course students. The main reference(s) are included in this list, but comprehensive cross-referencing is available via the Index. •
Abnormal Refraction. The atmosphere contains many irregularities which are erratic in their influence upon Atmospheric Refraction; where these irregularities exceed the corrections contained in The Nautical Almanac, conditions of Abnormal Refraction are deemed to exist. See Paras 0339j, 0804, 0807.
•
Altitude (of a heavenly body). The Altitude (of a heavenly body) is (loosely) described as the angle between a ‘horizon’ and the heavenly body, but normally has to be qualified as Apparent Altitude, Sextant Altitude, etc, depending which ‘horizon’ is used and which corrections are applied. See Para 0118 and separate entries (at Para 0401) for: Apparent Altitude Calculated (Tabulated) Altitude ‘d’ (Altitude Difference (d) from NP 401) Observed (True) Altitude Sextant Altitude Tabulated Altitude Very High Altitude (Tropical) Sights
•
Altitude Difference (d). See separate entry (at Para 0401) for ‘d’ (Altitude Difference (d) from NP 401).
•
Angle of Incidence (). The Angle of Incidence () is the angle at which a ray of light travelling in one medium meets the boundary of another medium. See Para 0802.
•
Angle of Refraction (θ). The Angle of Refraction ( θ ) is the angle through which a ray of light is bent when passing from one medium to another of different density. See Para 0802.
•
Angular Distance. Heavenly bodies are deemed to reside on the surface of the Celestial Sphere and the only method of measuring their relative positions is to measure the angle between them, known as an Angular Distance. See Para 0102.
•
Apparent Altitude. The Apparent Altitude of a heavenly body is Sextant Altitude corrected for Index Error and Height of Eye (Dip). See Para 0118.
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Apparent Solar Day / Time. The interval that elapses between two successive transits of the Sun across the same Meridian is an Apparent Solar Day. See Para 0432.
•
Aries ( ). The name ‘ First Point of Aries’(often abbreviated to ‘ Aries’ or ‘ ’) is given to the spring intersection of the Ecliptic and the Celestial Equator and is used as the datum for calculations and tables. See Paras 0104, 0421 / Fig 4-1 .
•
Astronomical Day. The Astronomical Day (which uses 24 hour notation) and the Civil Day (which uses the am / pm notation) both contain 24 Mean Solar Hours. See Para 0434.
•
Astronomical Position Line / Position Line. An Astronomical Position Line (often abbreviated to ‘ Position Line’) is a small element of the circumference of a Small Circle centred on the Geographic Position of the star with a radius equivalent to ‘90° - Altitude’, converted into nautical miles. See Paras 0350, 0351, 0521.
•
Astronomical Twilight (AT). The time of Astronomical Twilight (AT) is the moment when the Sun’s centre is 18° below the Celestial Horizon. See Paras 0108, 0724, 0725, 0726.
•
Atmospheric Refraction. The Earth’s atmosphere generally decreases in density with increased height and so has a gradually changing Refractive Index. When a ray of light from a star approaching the Earth enters the Earth’s atmosphere, this causes it to be bent progressively and thus to follow a curved path; this gradual change of direction which occurs is called Atmospheric Refraction. See Paras 0802, 0803, 0804.
•
Autumn Equinox. See separate entry (at Para 0401) for Equinoxes - Spring & Autumn.
•
Axis (of the Earth). The Earth’s Axis is its shortest diameter, about which it rotates in space.
•
Azimuth (of a heavenly body). The Azimuth (Z) of a heavenly body is the angle between the observer’s Meridian and the Vertical Circle through the heavenly body. Azimuth is measured and expressed in different ways by different authorities. See Paras 0117, 0535, 0536 & also separate entries (at Para 0401) for: Azimuth Angle (of a heavenly body) Calculated (Tabulated) Azimuth Supplementary Azimuth True Bearing (of a heavenly body)
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Azimuth Angle (of a heavenly body). The Azimuth Angle (Z) is the Azimuth of a heavenly body when measured and named East or West from the Observer’s Meridian ( if LHA of Body <180° Azimuth is West, if LHA of Body > 180° Azimuth is East). Azimuth is named ‘N’ or ‘S’ from the Elevated Pole. See Paras 0536 and 0543.
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Bearing. See separate entry (at Para 0401) for True Bearing (heavenly body).
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BR 45(2)
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Calculated (Tabulated) Altitude. The Calculated (Tabulated) Altitude is the Altitude of a heavenly body calculated from the Chosen Position at the exact time of observation, based on ephemeral data (from The Nautical Almanac or computer information). It is also known as Calculated Altitude or Tabulated Altitude and is thus expressed in BR 45(2) as Calculated (Tabulated) Altitude. See Paras 0118, 0531.
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Calculated (Tabulated) Azimuth. The Calculated (Tabulated) Azimuth is the Azimuth (or Azimuth Angle) of a heavenly body calculated from the Chosen Position at the exact time of observation, based on ephemeral data (from The Nautical Almanac or computer information). It is also known as Calculated Azimuth or Tabulated Azimuth and is thus expressed in BR 45(2) as Calculated (Tabulated) Azimuth. See Paras 0530, 0531.
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Calculated (Tabulated) Co-Declination. The Calculated (Tabulated) Co Declination is the Angular Distance of a heavenly body from the Elevated Pole calculated from the Chosen Position at the exact time of observation, based on ephemeral data (from The Nautical Almanac or computer information). See Para 0531 and also separate entry (at Para 0401) for Co-Declination (also known as ‘Polar Distance’).
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Calculated (Tabulated) LHA. The Calculated (Tabulated) LHA is the LHA of a heavenly body calculated from the Chosen Position at the exact time of observation, based on ephemeral data (from The Nautical Almanac or computer information). It is also known as Calculated LHA or Tabulated LHA and is thus expressed in BR 45(2) as Calculated (Tabulated) LHA. See Para 0531.
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Calculated (Tabulated) Position Circle. The Calculated (Tabulated) Position Circle is the Position Circle of a heavenly body calculated from the Chosen Position at the exact time of observation, based on ephemeral data (from The Nautical Almanac or computer information). It is also known as Calculated Position Circle or Tabulated Position Circle and is thus expressed in BR 45(2) as Calculated (Tabulated) Position Circle. See Paras 0522, 0524 and also separate entry (at Para 0401) for Position Circl e.
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Calculated (Tabulated) Zenith Distance (CZD). The Calculated (Tabulated) Zenith Distance is the Zenith Distance of a heavenly body calculated from the Chosen Position at the exact time of observation, based on ephemeral data (from The Nautical Almanac or computer data). It is also known as Calculated Zenith Distance or Tabulated Zenith Distance. To avoid confusion between abbreviations for True Zenith Distance (TZD) and Tabulated Zenith Distance, the latter title is not used in BR 45(2), where for clarity it is expressed either as Calculated (Tabulated) Zenith Distance (CZD) or Calculated Zenith Distance (CZD). See Para 0524 and also separate entry (at Para 0401) for Zenith Distance.
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Calculated Zenith Distance (CZD) . See separate entry (at Para 0401) for Calculated (Tabulated) Zenith Distance (CZD).
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Celestial Equator. The Earth’s Equator , if produced, would cut the Celestial Sphere at the Celestial Equator . See Paras 0101, 0421 / Fig 4-1.
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BR 45(2)
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Celestial Horizon. The Celestial Horizon is a Great Circle on the Celestial Sphere, every point of which is 90° from the Observer’s Zenith (Z). It corresponds to the projection of the terrestrial horizon onto the Celestial Sphere, but without the errors associated with atmospheric optical refraction at the Visible Horizon. See Para 0115.
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Celestial Latitude. ‘Celestial Latitude’ is a term used by astronomers to measure an Angular Distance referenced to the Ecliptic rather than the Celestial Equator. ‘Celestial Latitude’ as used by astronomers has no use in solving the navigational problem and should not be confused with ‘Declination’. See Para 0105 (Note 1-1).
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Celestial Longitude. ‘Celestial Longitude’ is a term used by astronomers to measure an Angular Distance referenced to the Ecliptic rather than the Celestial Equator. ‘Celestial Longitude’ as used by astronomers has no use in solving the navigational problem and should not be confused with ‘Hour Angle’. See Para 0106 (Note 1-2).
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Celestial Meridian. A Celestial Meridian is a Semi-Great Circle joining the north and south Celestial Poles and corresponds exactly to a terrestrial Meridian. See Para 0421 / Fig 4-1.
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Celestial Poles. The Earth’s axis, if produced, would cut the Celestial Sphere at the Celestial Poles. See Paras 0101, 0421 / Fig 4-1.
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Celestial Sphere. To an observer on Earth, the sky has the appearance of an inverted bowl, so that the stars and other heavenly bodies, irrespective of their actual distance from the Earth, appear to be situated on the inside of a sphere of immense radius described about the Earth as centre. This is called the Celestial Sphere. See Paras 0101, 0421 / Fig 4-1.
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Chosen Declination. To avoid enormously bulky and expensive tables, NP 401 uses the method of entering its main tables with an integer ‘Chosen Declination’ rather than the exact value of Declination. Tabular interpolation for the actual Declination is then required to compensate for this initial approximation. See Para 0542g.
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Chosen Latitude. See separate entry (at Para 0401) for Chosen Position .
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Chosen Longitude. See separate entry (at Para 0401) for Chosen Position .
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Chosen Position. The Chosen Position is a position, usually close to or at the DR / EP position, and consisting of a Chosen Latitude and Chosen Longitude, selected by the Navigator for mathematical convenience in reducing the sight. It will vary for each sight, and can be adjusted for time difference of observations by running it ‘on’ or ‘back’ along the ships course or course made good (allowing for tidal stream/ ocean current). See Paras 0524, 0542f, 0544.
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Circumpolar. Although every heavenly body is circumpolar (in that to an observer on Earth it describes a circle about the Celestial Pole) the term ‘Circumpolar’ is normally used to denote that a heavenly body never sets and is always above the observer’s Visible Horizon. See Para 0727.
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BR 45(2)
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Civil Day. The Civil Day (which uses am / pm notation) and the Astronomical Day (which uses 24 hour notation) both contain 24 Mean Solar Hours. See Para 0434.
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Civil Twilight (CT). See separate entries (at Para 0401) for: Evening Civil Twilight (ECT) Morning Civil Twilight (MCT)
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Cocked Hat. Astronomical Position Lines obtained from three observations (which, for simplicity are considered as being taken simultaneously) are unlikely to pass through a common point. With Astronomical Position Lines, the most likely reason for a Cocked Hat being formed is that the Zenith Distances are incorrect. See Paras 0906, 0907.
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Co-Declination (also known as Polar Distance). The Co-Declination is the Angular Distance of a heavenly body from the Elevated Pole. The Co-Declination is also the Polar Distance (PX) and can be calculated from the Declination of the body, depending on whether the Elevated Pole and Declination have SAME or OPPOSITE names (north/south), as follows: Elevated Pol e and Declination have SAME names: PX = (90° - Declination) Elevated Pole and Declination have OPPOSITE names:PX = (90° + Declination) See Para 0534b and also separate entry for Calculated (Tabulated) Co Declination at Para 0401.
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Co-Latitude. The Co-Latitude is (90° - Latitude). See Para 0531.
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Collimation Error. See separate entry (at Para 0401) for Sextant-Collimation Error.
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Common Equal Error (corrections). If it is believed that there is a Common Equal Error in magnitude and sign for each Sextant sight (as in an incorrect Index Error), then simple constructions or iterations will allow the true Observed Position to be plotted. The most common use of this technique is among experienced and skilled Sextant users who consistently have a small ‘personal error’ caused by always ‘cutting’ the heavenly body deep (or shallow) on the horizon. See Para 0906 and CAUTIONS at Para 0907.
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Confidence Ellipse. ‘Confidence Ellipse’ is the name given within NAVPAC 2 for what is otherwise known as an ‘ Error Ellipse’. See Para 0346c and also separate entry for Error Ellipse at Para 0401.
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CONTRARY (name). Term used with NP 401 and NP 303 to indicate that Declination and Latitude within the calculation have opposite (North / South) names. See Para 0542b and also separate entry (at Para 0401) for SAME (name).
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BR 45(2)
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Co-ordinated Universal Time (UTC). UTC corresponds exactly in rate with International Atomic Time (TA1) but differs from it by an integral number of seconds. The UTC scale is adjusted by the insertion or deletion of seconds (positive or negative leap seconds) to ensure that the departure of UTC from Universal Time (UT1 or UT) does not exceed +/- 0.9 seconds. See Para 0211.
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Corrected Tabulated Altitude (Corr Tab Alt). Corrected Tabulated Altitude (Corr Tab Alt) is the result of applying First Difference Corrections (FDC) (±) to Tabulated Altitude in NP 401 calculations to solve the PZX triangle. See Paras 0542g, 0543.
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‘d’ (Altitude Difference (d) from NP 401). Altitude Difference (d) or ‘d’ is the difference of Altitude in minutes of arc of one Declination entry and that for the next higher degree, and is used with the interpolation table to establish the exact calculated Altitude. See Paras 0542d, 0542g, 0543a.
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“d” / “d corrn” (Declination correction from The Nautical Almanac). The “d” / “d corrn” is the hourly difference in Declination, tabulated in The Nautical Almanac and is used with the (yellow) ‘Increments and Corrections’ tables at the back of The Nautical Almanac to calculate the precise Declination of the Sun, Moon or Planets with NP 400 (Sight Form) and NP 401 method of solving the PZX triangle. See Para 0543b.
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Daily Difference (suffixed with MP, MR or MS as appropriate). The LMT of the Moon’s Mer Pass and Visible Moonrise / Moonset is not constant for all Longitudes and must be corrected for the Daily Difference between consecutive Moon’s Mer Pass, Visible Moonrises or Visible Moonsets at the Latitude considered. See Paras 0607c (Note 6-1), 0731 (Note 7-1).
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Day. A ‘ Day’ is the interval that elapses between two successive transits of a heavenly body across the same Meridian. See Para 0431 and also separate entries (at Para 0401) for: Apparent Solar Day / Time Astronomical Day Civil Day Lunar Day / Month Mean Solar Day Sidereal Day / Time Solar Day
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Daylight Saving Time. Daylight Saving Time (DST) is a seasonal change from the Standard Legal Time to make the best use of the available light, usually in summer. See Para 0202.
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Deck Watch. An accurate timepiece (now issued as a quartz wristwatch), normally kept in Time Zone 0 (UT ), and used to take the precise times of astro observations. See Para 0903 and also separate entries (at Para 0401) for: Deck Watch Time Deck Watch Error
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BR 45(2)
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Deck Watch Error (DWE). This is the exact difference between the Deck Watch Time of an individual ‘Deck Watch’ and UT . It must be applied to Deck Watch Time (DWT) before the latter is used for sight reduction purposes. See Para 0327, 0903 and also separate entry for Deck Watch Time (DWT) at Para 0401.
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Deck Watch Time (DWT). This is the time kept on individual Deck Watches and used to record the exact time of astronomical observations. See Para 0327 and also separate entry for Deck Watch Error (DWE) at Para 0401.
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Declination. Declination corresponds to terrestrial Latitude projected onto the Celestial Sphere and is the Angular Distance of the heavenly body north or south of the Celestial Equator. It should NOT be confused with ‘Celestial Latitude’ . See Paras 0105, 0421 /Fig 4-1 and also separate entries (at Para 0401) for: Chosen Declination Parallels of Declination Tabulated Declination.
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Declination Increment (Dec Inc). The Declination Increment ’ ( Dec. Inc.) is the excess minutes of actual Declination over the integer Declination used to enter the main NP 401 tables. This ranges from 0.0' to 59.9'. See Para 0542g.
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Depressed Pole. The Depressed Pole is the Pole located in the Lower Hemisphere. See Para 0741.
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Diamond of Error. When a position is decided by the result of two Position Lines or Astronomical Position Lines, and they are given an ‘Assessed Possible Error’, the ship may or may not lie within a parallelogram ( Diamond of Error ) with sides parallel to the Position Lines and spaced at the ‘Assessed Possible Error’ distance from them. See Para 0902 and also separate entry for Error Ellipse at Para 0401.
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Difference“d”. See separate entry (at Para 0401) for “d”(Altitude Difference from NP 401).
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Difference of Time for Longitude (suffixed MP, MR or MS as appropriate). The Difference of Time for Longitude (suffixed MP (Mer Pass), MR (Moonrise) or MS (Moonset ) as appropriate) is the proportion of the relevant Daily Difference which is applied to the tabulated time for the Greenwich Meridian. See Paras 0607d, 0731c.
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Dip. Dip is the angle by which the line of sight to the Visible Horizon differs from the horizontal at an observer who is some ‘Height of Eye’ above the Earth’s surface. See Para 0806.
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Double Second Difference Correction. The ‘Double Second-Difference (DSD) correction is an additional tabular interpolation correction used in NP 401 on the occasions when the rate of change of Altitude is large relative to a 1° change in Declination. See Paras 0542g, 0543.
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Earth’s Axis. See separate entry at Para 0401 “Axis (of the Earth)”.
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BR 45(2)
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Ecliptic. The apparent path of the Sun in the Celestial Sphere is known as The Ecliptic. It is a Great Circle, and makes an angle of 23° 27' with the Celestial Equator because the Earth’s axis of rotation is tilted by that amount from the perpendicular to the plane of the Earth’s orbit. See Para 0103a.
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Elevated Pole. The Elevated Pole is the Celestial Pole above the observer’s horizon ( ie located in the Visible Hemisphere). See Para 0741.
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EP (Estimated Position). This is the most accurate position that can be obtained by calculation and estimation alone. It is derived from the DR position (course and speed steered) adjusted for the effects of leeway, tidal stream, current sand surface drift. An EP symbol may also be used to update a DR/EP if only one Position Line is available. See Para 0905 and also BR 45(1) Chapters 8 and 16.
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Epoch. Epoch is the term given to a period (usually a specific year ± 5 years) for which the positions of heavenly bodies have been calculated taking the Precession and Nutation of the Earth into account. It applies specifically to NP 303, the Star Globe and some other star charts. The use of these tables / aids outside the (usually 10 year) Epoch will result in some errors. See Paras 0544e, 0544f. Equation of Time. The Equation of Time is the difference between Mean Solar Time and Apparent Solar Time and is represented by the equation: Equation of Time = LHA Mean Sun - LHA True Sun See Para 0439.
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Equator. The Equator is the line traced out on the Earth’s surface by the mid points of the Meridians. See Para 0903 and also BR 45(1) Chapter 1.
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Equinoxes - Spring and Autumn. The Equinox is the moment when the position of the Sun is directly over the Equator (ie when the Ecliptic crosses the Celestial Equator). This event occurs twice per year, at the Spring Equinox (21 March), and the Autumn Equinox (23 September). The word ‘ Equinox’ is derived from Latin, meaning ‘equal periods of day and night’; at the Equinoxes the time difference between Sunrise and Sunset is 12 hours and the Sun rises due east and sets due west. See Para 0103b.
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Error Ellipse. An Error Ellipse is formed when Position Lines or Astronomical Position Lines cross and Standard Deviation calculations are used to provide a more useful measurement of probable error than a simple Diamond of Error . NAVPAC 2 produces an Error Ellipse (which is referred to within the program as a Confidence Ellipse), when three or more observations are made. See Para 0902 and BR 45(1) Chapters 8 and16.
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Estimated Position (EP). See separate entry (at Para 0401) for EP (Estimated Position).
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Evening Civil Twilight (ECT). The times of Evening Civil Twilight (ECT) are tabulated in The Nautical Almanac for the moment when the Sun’s centre is 6° below the Celestial Horizon. The times of Morning and Evening Civil Twilights are shown in chronological order and thus the term ‘ Evening ’ is omitted. This is roughly the time at which the horizon becomes clear (morning) or becomes indistinct (evening). See Paras 0108, 0724, 0725.
4-10 Original
BR 45(2)
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Evening Nautical Twilight (ENT). The times of Evening Nautical Twilight (ENT) are tabulated in The Nautical Almanac for the moment when the Sun’s centre is 12° below the Celestial Horizon. The times of Morning and Evening Nautical Twilights are shown in chronological order and thus the term ‘ Evening ’ is omitted. Star sight observations are normally taken between Civil Twilight and Nautical Twilight . See Paras 0108, 0724, 0725.
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First Difference Correction (FDC). The First Difference Correction is a tabular interpolation correction used in NP 401 to obtain the Corrected Tabulated Altitude (Corr Tab Alt) from Tabulated Altitude. See Paras 0542g, 0543.
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First Point of Aries ( ). See separate entry at Para 0401 “Aries ( )”.
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First Point of Libra. See separate entry at Para 0401 “ Libra”.
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First Quarter (of the Moon). The First Quarter (of the Moon) is the description given to the Moon when it is one quarter of the way round its orbit of the Earth, starting from a New Moon. It appears as a ‘D’ shape to an observer on Earth with only the westerly side of the Moon being illuminated. This occurs about 7 days after a New Moon and about 7 days before a Full Moon. See Para 0452.
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Full Moon. The Full Moon is the description given to the Moon when it is half way round its orbit of the Earth, starting from a New Moon. It appears fully illuminated as a ‘O’ shape to an observer on Earth. This occurs about 14 days after and before a New Moon. See Para 0452.
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Geographic Position. The Geographic Position of a heavenly body is the position where a line drawn from the body to the centre of the Earth, cuts the Earth’s surface. To an observer at the Geographic Position, the heavenly body would appear to be directly overhead, ie. at the Observer’s Zenith(Z). See Para 0109.
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Great Circle. A Great Circle is the intersection of a spherical surface and a plane which points on the surface of a sphere. See Para 0110.
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Greenwich passes through the centre of the sphere. It is the shortest distance between two Celestial Meridian. The Greenwich Celestial Meridian is the projection of the terrestrial Greenwich Meridian onto the Celestial Sphere. See Para 0421 / Fig 4-1.
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Greenwich Hour Angle (GHA). The Greenwich Hour Angle (GHA) is the Angular Distance, measured westwards from the projection of the Greenwich Meridian on the Celestial Sphere and the Meridian of the heavenly body. See Paras 0106, 0420c, 0421 / Fig 4-1.
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Greenwich Hour Angle Increment (GHA Increment). In The Nautical Almanac, GHAs are only tabulated for whole hours, and the additional amount of GHA corresponding to the minutes and seconds after the whole hour are obtained by looking in the yellow ‘Increment and Correction’ pages at the back of The Nautical Almanac. This additional GHA is known as the GHA Increment . See Para 0543b.
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BR 45(2)
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Greenwich Mean Time (GMT). Greenwich Mean Time (GMT) may be regarded as the general equivalent of UT / UT1. See Paras 0210, 0435, and also separate entry for Universal Time (UT) at Para 0401.
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Greenwich Meridian. The Greenwich Meridian is also known as the Prime Meridian, and passes through Greenwich. It is the starting point (0°) for the measurement of Longitude, East and West from this Meridian. See Para 0112.
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Height of Eye. The height of an observer’s eye above the Earth’s surface. See Para 0806 and also separate entry (at Para 0401) for Dip.
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High Latitude (Polar) Sights. High Latitude (Polar) Sights may be reduced by NAVPAC 2 or the normal use of NP 401, but when in Latitudes above 87½° an abbreviated method of reduction and plotting is possible using the Pole as the Chosen Position. This latter method is only likely to be taken by submariners, unless overland expeditions are anticipated. See Paras 0560, 0561, 0562.
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High Altitude (Tropical) Sights. See separate entry (at Para 0401) for Very High Altitude (Tropical) Sights.
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Horizon. See separate entries (at Para 0401) for: Celestial Horizon Plane of the Celestial Horizon Visible Horizon
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Horizontal Parallax. The value of Parallax is greatest when the heavenly body is close to the horizon when it is known as Horizontal Parallax (HP). It is not significant except for the Moon (due to its close proximity to Earth) and to a much lesser extent, Venus and Mars. Most Parallax corrections are incorporated in the main Altitude Correction Tables of The Nautical Almanac but in the case of the Moon, a separate HP correction is needed and may be taken from the HP tables at the back of The Nautical Almanac. A similar, very small correction is listed for Venus and Mars as an ‘Additional Correction’ at the front of The Nautical Almanac. See Para 0348d and separate entry for Horizontal Parallax (HP) at Para 0401.
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Hour Angles. See separate entries (at Para 0401) for: Greenwich Hour Angle (GHA) Local Hour Angle (LHA) Right Ascension (RA)
Sidereal Hour Angle (SHA) •
Index Error (IE). See separate entry (at Para 0401) for Sextant: Index Error.
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Index of Refraction (µ). See separate entry (at Para 0401) for Refractive Index .
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Intercept. An Intercept is the angular difference, converted into nautical miles, between the Calculated (Tabulated) Altitude of a heavenly body for the DR / EP position at the exact time of observation and the Observed (True) Altitude of that body. See Paras 0351, 0521, 0524 / Fig 5-3, Fig 5-4, 0543.
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BR 45(2)
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International Atomic Time. International Atomic Time is determined by the comparison of very accurate (better than 1 microsecond a day) atomic clocks located at national observatories throughout the world. Unlike UT / UT1, TAI does not change with variations in the rate of the Earth’s rotation. TAI provides the most accurate and uniform unit of time interval for scientific purposes. See Para 0211b.
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International Date Line. The International Date Line is an internationally agreed line on the Earth’s surface at approximately 180° East (but varying from this Longitude to avoid populated areas). On crossing the International Date Line travellers advance or retard calenders by 1 day (retard when eastbound, advance when westbound) and simultaneously apply the new Time Zone (-12hr to +12hr or vice-versa) to the new date. See Para 0201, 0206.
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Last Quarter (of the Moon). The Last Quarter (of the Moon) is the description given to the Moon when it is three quarters of the way round its orbit of the Earth, starting from a New Moon. It appears as a ‘D’ shape to an observer on Earth with only the easterly side of the Moon being illuminated. This occurs about 7 days after a Full Moon and about 7 days before a New Moon. See Para 0452.
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Latitude. The Latitude of a place on the Earth’s surface (also called the Geodetic, Geographical or True Latitude) is the angle that the perpendicular at that place makes with the plane of the Equator and is measured from 0° to 90° North or South of the Equator . See BR 45(1) Chapter 1.
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Least Square (method of calculation). The Least Square method of calculation is used to derive the Most Probable Position from three or more Position Lines.See Paras 0904, 0906 and also BR 45(1) Annex 16A (pages 494-496).
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Legal Time. See separate entry (at Para 0401) for Standard Legal Time.
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Libra. The name ‘ First Point of Libra’( abbreviated to ‘ Libra’) is the point on the Celestial Sphere where the Ecliptic and Celestial Equator intersect at the Autumn Equinox. See Para 0104.
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Local Hour Angle (LHA). The Local Hour Angle (LHA) is the Angular Distance, measured westwards, of the projection of the observer’s Meridian onto the Celestial Sphere and the Meridian of the heavenly body. It equates to the GHA of the body +/- the observers’s Longitude. See Paras 0106, 0420d, 0421 / Fig 4-1.
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Local Mean Time (LMT). Local Mean Time ( LMT ) is the mean time kept at any place when the Local Hour Angle of the Mean Sun is measured from Meridian of that place. However, as the Local Hour Angle of the Mean Sun is measured from the Greenwich Meridian and the Civil/Astronomical Day are both measured from 180° (12 hours) from the Greenwich Meridian, LMT is defined as follows: LMT at any instant is the Local Hour Angle of the Mean Sun at that instant, measured westwards from the Meridian of that place, +/- 12 hours. See Paras 0325, 0435.
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Local Sidereal Time (LST). Local Sidereal Time (LST) is equivalent to the LHA of First Point of Aries ( ). See Para 0443.
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BR 45(2)
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Longitude. The Longitude of a place on the Earth’s surface is the angle between the Greenwich (Prime) Meridian and the Meridian of that place measured from 0° to 180° East or West of Greenwich. See BR 45(1) Chapter 1.
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Looming (Mirage). When a Mirage is experienced, if the object appears elevated and the Visible Horizon farther away, it is termed Looming . See Para 0808b.
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Lower Hemisphere. The Celestial Horizon divides the Celestial Sphere into hemispheres, the upper (containing the Observer’s Zenith ‘Z’ ) is the known as the Visible Hemisphere, and the other as the Lower Hemisphere. Subject to atmospheric refraction, all heavenly bodies in Visible Hemisphere are visible to the observer but bodies in the Lower Hemisphere cannot be seen. See Para 0502 (Note 5-1).
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Lower Limb (LL). The Lower Limb of the Sun or Moon is the portion of its circumference nearest to the Visible Horizon, as seen from an observer on the Earth’s surface. See Para 0704.
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Lower Mer Pass / Lower Meridian Passage (of a heavenly body). Lower Meridian Passage occurs when the heavenly body is on the Meridian that differs in Local Hour Angle from the Observer’s Meridian by 180°. See Paras 0348i, 0603, 0610, 0612e and separate entry (at Para 0401) for Mer Pass / Meridian Passage (of a heavenly body).
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Lunar Day. A Lunar Day is 29½ divided by 28½ Mean Solar Days which equates to approximately 24 hours 50 minutes ( Mean Solar Time). This is the reason why tides generally advance at about 50 minutes per day. See Para 0451.
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Lunar Month. The Lunation or Lunar Month is the interval between two successive New Moons (when the Moon lies in a straight line between the Earth and the Sun and therefore not visible) and is important in tidal prediction. A Lunation or Lunar Month is equivalent to29½ Mean Solar Days. See Para 0451.
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Lunar Units. The units derived from Lunar Days are Lunar Units. See Para 0450.
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Lunation. See separate entry (at Para 0401) for Lunar Month.
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Mean Refraction. Mean Refraction is average condition of Atmospheric Refraction for which ‘Altitude Correction Tables’ (which also include Semi Diameters for the Sun and Moon) are given at the front and back of The Nautical Almanac respectively. See Paras 0803, 0805.
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Mean Solar Day. The interval between two successive transits of the Mean Sun across the same Meridian is called the Mean Solar Day. See Para 0434.
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Mean Solar Hour / Mean Solar Time. Mean Solar Time is based on the Mean Solar Day. The Mean Solar Day is divided into 24 Mean Solar Hours. See Para 0434.
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Mean Sun. The Mean Sun is an imaginary body which is assumed to move in the Celestial Equator at a uniform speed around the Earth and to complete one (360°) revolution in the time taken by the True Sun to complete one (360°) revolution in the Ecliptic. See Para 0433.
BR 45(2)
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Meridian. A Meridian is a semi - Great Circle on the Earth’s surface which also passes through both Poles. See Para 0111 and separate entries (at Para 0401) for: Celestial Meridian Greenwich Meridian Greenwich Celestial Meridian Lower Mer Pass / Lower Meridian Passage (of a heavenly body), (also known as ‘Meridian Passage below the Pole’) Mer Pass / Meridian Passage (of a heavenly body), (also known as ‘Upper Mer Pass / Upper Meridian Passage’) Observer’s Meridian Prime Meridian
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Meridian Passage Below the Pole. ‘Meridian Passage Below the Pole’ is another name for Lower Meridian Passage, but the usage is rare. See separate entry (at Para 0401) for Lower Mer Pass / Lower Meridian Passage (of a heavenly body) .
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Mer Pass / Meridian Passage (of a heavenly body). Meridian Passage (Mer Pass) occurs when a heavenly body is in the observer’s Meridian or in the Meridian 180° from the observer’s Meridian. Mer Pass can occur as ‘Upper’ or ‘Lower’ Meridian Passage’ , but common usage of ‘Meridian Passage / Mer Pass’ normally refers to Upper Meridian Passage. See Paras 0325, 0348f-g, 0601, 0602, 0606, 0607, 0608, 0609,0611, 0612 and separate entry (at Para 0401) for Lower Mer Pass / Lower Meridian Passage (of a heavenly body).
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Midnight Sun. If the Sun’s Declination remains above the Celestial Horizon, the Sun can never set and this effect is known colloquially as the ‘Midnight Sun’. In the Northern Hemisphere, the limiting Latitude for the ‘Midnight Sun’ to occur is: 90° minus the Sun’s greatest northerly Declination (90°23½°)N = 66½° N. See Para 0726 / Figs 7-2 and 7-4.
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Mirage. A Mirage is an optical phenomenon in which objects appear displaced, distorted, magnified, multiplied or inverted, owing to varying Atmospheric Refraction in layers close to the surface of the Earth due to large air density differences. This may occur when there is an erratic or irregular change of temperature or humidity in the Earth’s atmosphere with changes in height. See Para 0808 and separate entries (at Para 0401) for: Looming Stooping Sinking Towering
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Month. See separate entry (at Para 0401) for Lunar Day / Month.
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Moonrise, Moonset. See separate entries (at Para 0401), which co-ordinate all variants, for: True (Theoretical) Rising and Setting (Sun and Moon) Visible Rising and Setting (Sun and Moon)
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BR 45(2)
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Morning Civil Twilight (MCT). The times of Morning Civil Twilight (MCT) are tabulated in The Nautical Almanac for the moment when the Sun’s centre is 6° below the Celestial Horizon. The times of Morning and Evening Civil Twilights are shown in chronological order and thus the term ‘ Evening ’ is omitted. This is roughly the time at which the horizon becomes clear (morning) or becomes indistinct (evening). See Paras 0108, 0724, 0725.
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Morning Nautical Twilight (MNT). The times of Morning Nautical Twilight (MNT) are tabulated in The Nautical Almanac for the moment when the Sun’s centre is 12° below the Celestial Horizon. The times of Morning and Evening Nautical Twilights are shown in chronological order and thus the term ‘ Evening ’ is omitted. Star sight observations are normally taken between Civil Twilight and Nautical Twilight . See Paras 0108, 0724, 0725.
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Most Probable Position (MPP). The Most Probable Position may be derived mathematically from 3 or more Position Lines by the Least Square method of calculation. The MPP lies within the Probable Position Area (PPA). See Paras 0904-0906 and also BR 45(1) Chapters 8, 16 / Annex 16 (pages 494-496).
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Nautical Twilight (NT). See separate entries (at Para 0401) for: Evening Nautical Twilight (ENT) Morning Nautical Twilight (MNT)
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NAVPAC 2 / NAVPAC 1. NAVPAC 2 superseded NAVPAC 1 in 2000 and both are PC-based computer programs for navigational use. They calculate: very accurate sight reductions; rising, setting and twilight times; the location of all heavenly (navigational) bodies; Great Circle and Rhumb Line problems. See Chapter 3.
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New Moon. The New Moon is the description given to the Moon when it lies in a straight line between the Earth and the Sun during its orbit of the Earth. At this time the Moon is not visible to an observer on Earth. The time of a New Moon is the starting point for lunar calculations. See Para 0451.
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Nutation. Nutation is the small, continuous but slightly erratic sinusoidal oscillation of the Earth’s rotational axis superimposed about the larger Precession motion. Nutation is caused by the varying positions of the bodies (especially the Moon) within the solar system. See Para 0544f.
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Obliquity of the Ecliptic. The Obliquity of the Ecliptic is the angle between the plane of the Celestial Equator and that of the Ecliptic. See Para 0103a.
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Observed Position (Obs. Pos). The Observed Position (Obs. Pos) is the point on the Earth’s surface at which two or more Astronomical Position Lines cross, after adjustments have been made for the differing times of observations and errors . See Para 0346d and also separate entry (at Para 0401) for Observed (True) Position.
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Observed (True) Altitude. The Observed (True) Altitude of a heavenly body is its Sextant Altitude, corrected for Index Error , Dip (Height of Eye), and Refraction Corrections. It is also known as Observed Altitude or True Altitude and is thus expressed in BR 45(2) as Observed (True) Altitude. See Paras 0118, 0348d.
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BR 45(2)
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Observed (True) Position. The Observed (True) Position is a point through which an Observed (True) Position Circle passes. See Para 0524 and separate entries (at Para 0401) for: Observed Position (Obs. Pos) Observed Position Observed (True) Position Circle Position Circle
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Observed (True) Position Circle. The Observed (True) Position Circle is the Position Circle based on the Observed (True) Altitude of a heavenly body.
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See Paras 0524a, 0524b and also separate entry (at Para 0401) for Position Circl e.
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Observed (True) Zenith Distance (TZD). The Observed (True) Zenith Distance (TZD) is also known as the Observed Zenith Distance or the True Zenith Distance (TZD), and is thus expressed in BR 45(2) as Observed (True) Zenith Distance (TZD). See Para 0524 and separate entry (at Para 0401) for Zenith Distance.
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Observed Zenith Distance. See separate entry (at Para 0401) for Observed (True) Zenith Distance(TZD).
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Observer’s Meridian. The Observer’s Meridian is the Celestial Meridian which passes through the Observer’s Zenith (Z). See Para 0421 / Fig 4-1.
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Observer’s Zenith (Z). The Observer’s Zenith (Z) is the point where a straight line from the Earth’s centre passing through the observer’s terrestrial position (O) cuts the Celestial Sphere, and may be described (loosely) as the point on the Celestial Sphere directly above the observer. The Declination of this point (Z) on the Celestial Sphere is equal to the observer’s Latitude. See Para 0114.
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Parallax. The angular difference between the True Altitude of a heavenly body (taken from the centre of the Earth) and its altitude above the horizontal plane (taken from a position on the Earth’s surface) is known as the ‘Parallax in Altitude’ or usually just ‘ Parallax’, and is a correction that must be added to the Sextant Altitude. Most Parallax corrections are incorporated in the main Altitude Correction Tables of The Nautical Almanac and need not concern the user for most heavenly bodies. However for the Moon, substantial ‘ Horizontal Parallax (HP)’ corrections (and for Venus and Mars very small ‘Additional Corrections’) from The Nautical Almanac are needed.
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See separate entry (at Para 0401) for Horizontal Parallax . Parallel of Declination. A Parallel of Declination corresponds to a terrestrial parallel of Latitude and is a Small Circle on the Celestial Sphere. The plane of this Small Circle is parallel to the plane of the Celestial Equator . See Para 0105.
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Parallels of Latitude. See BR 45(1) Chapter 1.
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Perpendicularity (error). See separate entry (at Para 0401) for Sextant: Perpendicularity (error).
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BR 45(2)
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Plane of the Celestial Horizon. Where it is convenient to show the whole visible sky, it must be drawn on the Plane of the Celestial Horizon, as if the Celestial Sphere was seen from a position directly above the Observer’s Zenith (Z). Z appears in the centre of a circle which is the Visible Horizon. The Celestial Equator appears as a curve offset from the centre by an amount equal to the observer’s Latitude. See Para 0503 (Note 5-2).
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Polar Distance (PX). See separate entry (at Para 0401) for alternative title of ‘Co-Declination’ .
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Polaris. Polaris is the ‘ Pole Star’ and is very nearly located at the Celestial Pole. Observation of the star provides Latitude and a bearing of True North after very simple calculations. See Paras 0348j, 0620, 0621, 0622, 0623, 0624.
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Polar Variation. Polar Variation is a small movement of the Earth relative to the Axis of rotation. Its effects are corrected within UT / UT1 and it is does not directly concern the solution of the astro-navigation problem.
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Poles (of the Earth). The Earth’s Poles are the extremities of the Axis of the Earth.
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Position Circle. A Position Circle is a Small Circle on the Celestial Sphere projected onto the Earth’s surface about a centre of the Geographical Position of a heavenly body. The radius of the Position Circle is 90°- Altitude of the heavenly body, converted to nautical miles (1° = 60 n. miles). See Para 0522, 0524 and also separate entries (at Para 0401) for: Observed (True) Position Circle Calculated (Tabulated) Position Circle
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Position Line. A Position Line may be based on observation or detection of some terrestrial or astronomical information and represents a line on the Earth’s surface on which the observer is believed to lie. Within the context of Astro-Navigation the term ‘Position Line’ is frequently used as an abbreviation for ‘Astronomical Position Line’ , and this abbreviation is used in BR 45(2) where confusion is not likely to occur. See separate entry (at Para 0401) for Astronomical Position Line.
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Precession. Precession is the conical motion of the Earth’s rotational axis about the vertical to the plane of the Ecliptic. The result of Precession is a slow westward movement of the intersection between the plane of the Celestial Equator and the plane of the Ecliptic, and thus the Equinox. For this reason Precession is sometimes called Precession of the Equinoxes. The time for one complete rotation of Precession is 25,800 years. See Paras 0104, 0544f.
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Precession of Equinoxes. See separate entries (at Para 0401) for: Precession Equinoxes - Spring and Autumn
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Prime Meridian. The Greenwich Meridian (0° Longitude) is also called the Prime Meridian. See Para 0112.
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BR 45(2)
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Probable Position Area (PPA). The Probable Position Area (PPA) is the area derived from a combination of appropriate Position Lines obtained from available navaids or astronomical observations, after applying the relevant statistical error correction to each Position Line in turn. The PPA may be shown on the chart as an ellipse and within the PPA a Most Probable Position (MPP) may be determined. See Para 0905 and also BR 45(1) Chapters 8 & 16 / Annex 16A, & BR 45(4).
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PZX Triangle. The ‘PZX’ triangle is the abbreviation commonly used for the spherical triangle on the Celestial Sphere bounded by the Elevated Pole (P), the Observer’s Zenith (Z) and the heavenly body (X). See Paras 0501, 0531.
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P'Z'X Triangle. The P’Z’X Triangle is the mirror image of the PZX Triangle, lying completely below the Celestial Horizon (ie in the Lower Hemisphere) and is thus geared to the Depressed Pole. See Para 0741.
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Refraction. Refraction is the bending of light (or any other wave energy) when it passes from a less dense to a more dense medium, or vice versa. See Para 0801 and also separate entries (at Para 0401) for: Abnormal Refraction Angle of Incidence Angle of Refraction Atmospheric Refraction Mean Refraction Refractive Index (also known as Index of Refraction) Terrestrial Refraction
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Refractive Index (µ). The Refractive Index (µ) of a substance is a mathematical constant which allows calculation of the amount by which light will be bent when it passes from that medium to another medium. See Para 0802.
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Rhumb Line. A Rhumb Line is a line on the Earth’s surface which cuts Meridians (of Longitude) and Parallels (of Latitude) at the same angle. It appears on Mercator Charts as a straight line and equates to the (True) compass course steered. It is NOT always the shortest distance between two points on the surface of a sphere. See Para 0113.
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Right Ascension (RA). Right Ascension (RA) is the Angular Distance, measured eastwards (rather than westwards as in SHA), from the Meridian of the First Point of Aries ( ) to the Meridian of the heavenly body. ie. RA = 360° - SHA. See Paras 0106 and 0420a/b.
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Run / Run-on, Run-back. Astro-sights for a fix cannot all be taken at the same instant; typically, star sights may take place over a 10 or 15 minute period. To plot an accurate fix, the DR/EP position for each sight must be ‘Run-on’ or ‘Run-back’ (Transferred ) along the ship’s course and speed (allowing for any tidal stream or current), to a common time. In the case of Sun-run-Sun sights or other similar running fixes, the earlier sight is normally ‘run-on’ (Transferred ) to the time of the latter. Astronomical Position Lines are displayed on paper charts with a single open arrowhead at each end and Transferred Astronomical Position Lines with a double open arrowhead at each end. See Para 0351 and Note 3-9 .
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SAME (name). Term used with NP 401 and NP 303 to indicate that Declination and Latitude within the calculation have the same (North / South) names. See Para 0542b and also separate entry for CONTRARY (name) at Para 0401.
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Semi-Diameter. The Semi-Diameter of a heavenly body is half its angular diameter as viewed from the Earth. See Paras 0704, 0723.
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Sextant. A Sextant is used for measuring the angle between a heavenly body and the Visible Horizon, from the viewpoint of an observer . See Paras 0330-0339 . The following specific terms which define parts of the Sextant are explained at Paras 0331- 0334 as indicated below and are displayed at Fig 3-7: Sextant: Arc. See Para 0331. Sextant: Arc of Excess. See Para 0332. Sextant: Clamp (Index Bar). See Para 0331. Sextant: Collar. See Para 0331. Sextant: Horizon Glass. See Para 0331. Sextant: Index Bar. See Para 0331. Sextant: Index Glass. See Paras 0332, 0334d. Sextant: Index Mark. See Para 0331. Sextant: Main Frame. See Para 0331. Sextant: Micrometer Drum. See Paras 0331, 0336f. Sextant: Milled Head . See Para 0334b. Sextant: On the Arc. See Para 0332. Sextant: Off the Arc. See Para 0332. Sextant: Reading Lamp. See Para 0331. Sextant: Shades. See Para 0331. Sextant: Star Telescope. See Para 0335. Sextant: Sun Telescope. See Para 0335. Sextant: Telescope. See Para 0331.
Note: Sextant Altitude and Sextant: Errors (various) are under separate entries at Para 0401. •
Sextant Altitude. Sextant Altitude of a heavenly body is the angle measured by a Sextant between the Visible Horizon and the body, on a Vertical Circl e towards the Observer’s Zenith(Z) and must be corrected before use. See Para 0118 and separate entries (at Para 0401) for: Apparent Altitude Observed (True) Altitude
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Sextant: Collimation Error. Sextant: Collimation Error is the variation from the parallel alignment of the axis of a Sextant Telescope to the plane of the instrument. See Paras 0336d/e.
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Sextant: Index Error. Sextant: Index Error is a variation from the parallel alignment of the plane of the Horizon Glass to the plane of the Index Glass when the Index Bar is set to the zero position on the Arc of a Sextant. See Paras 0336c, 0336g.
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Sextant: Side Error. Sextant: Side Error is a variation from the perpendicular alignment of the Horizon Glass to the plane of the Arc of a Sextant. See Para 0336b.
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BR 45(2)
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Sextant: Perpendicularity (error). Sextant: Perpendicularity is the perpendicular (90°) alignment of the Index Glass to the plane of the Arc of a Sextant and the ‘error’ is any variation from this. See Para 0336a.
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Side Error. See separate entry (at Para 0401)for Sextant: Side Error.
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Sidereal Day / Time. A Sidereal Day is the interval between two successive transits of the First Point of Aries across the same Meridian. The Sidereal Day is sub-divided into hours, minutes and seconds. See Para 0441.
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Sidereal Hour Angle (SHA). The Sidereal Hour Angle (SHA) is the Angular Distance, measured westwards, from Meridian of the First Point of Aries ( ) to the Meridian of the heavenly body. It is almost completely static for stars and is tabulated once per 3 days for each star and planet in The Nautical Almanac. See Paras 0106, 0420a/b, 0421 / Fig 4-1.
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Sidereal Hours / Minutes. Sidereal Hours / Minutes are units derived directly from a Sidereal Day, using the same divisions (24 hrs / 60 minutes ) as in normal time. See Para 0443.
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Sinking (Mirage). When a Mirage is experienced, if the objects appears lower and the Visible Horizon seems closer to the observer, it is termed Sinking . See Para 0808c.
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Small Circle. A Small Circle is the intersection of a spherical surface and a plane which does NOT pass through the centre of the sphere. See Para 0110.
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Solar Day. See separate entries (at Para 0401) for: Apparent Solar Day Mean Solar Day Day
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Solar Time. See separate entry (at Para 0401) for: Mean Solar Hour / Mean Solar Time.
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Solstice. The Summer Solstice ( 21 June) and the Winter Solstice (22 December) are the names given to the dates/times when the Sun’s position in the Celestial Sphere is directly over the Tropic of Cancer ( Latitude 23½°N) and the Tropic of Capricorn ( Latitude 23½°S) respectively. At Mer Pass, an observer on the appropriate Tropic would see the Sun directly overhead and these dates correspond to the shortest and longest days in the appropriate hemispheres. See Para 0103b.
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Spring Equinox. See separate entry (at Para 0401)for Equinoxes - Spring and Autumn.
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Standard Deviation is a Standard Deviation (method of calculation). mathematical treatment which is particularly useful in processing error data. It uses ‘Root Mean Square’ techniques to obtain a more useful output of errors. See Para 0902 and also BR 45(1) Chapter 16 and Annex 16A.
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BR 45(2)
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Standard Legal Time. Standard Legal Time (sometimes abbreviated to ‘ Legal Time’) is the Time Zone kept on land and is decided by national laws. In countries extending over large east-west distances (eg USA), different Standard Legal Times may be kept in separate geographical areas within a country. Such variations may have their own regional designators. See Paras 0201, 0202 / Figs 2-1, 2-2 and separate entries (at Para 0401) for: Time Zones Zone Time.
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Standard (or Zone) Time. The Standard (or Zone )Time appropriate to Longitude is usually referred to as ‘Zone Time’ and is the Time Zone normally kept at sea. It should NOT be confused with Standard Legal Time / ‘Legal Time’ . See Para 0201, 0202, 0204, 0206 , and separate entries (at Para 0401) for: Standard Legal Time (sometimes abbreviated to ‘ Legal Time’) Standard Time Zones (sometimes abbreviated to ‘Time Zones’) Zone Time
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Standard Time Zones / Time Zones. ‘Standard Time Zone’ is the generic term given to all Time Zones within the Uniform Time System, both on land and sea. A chart showing these zones is published by the UK Hydrographic Organisation (UKHO) and is reproduced at Figs 2-1 and 2-2. See Paras 0201, 0202 / Fig 2-1, Fig 2-2, 0206, 0208.
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Stooping (Mirage). When a Mirage is experienced, if the lower part of a object observed is raised more than the top and the object appears shorter overall, it is termed Stooping. See Para 0808b.
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Summer Solstice. See separate entry (at Para 0401)for Solstice.
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Sun. See separate entries (at Para 0401) for: Mean Sun True Sun
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Sunrise, Sunset. See separate entries (at Para 0401), which co-ordinate all variants, for: True (Theoretical) Rising and Setting (Sun and Moon). Visible Rising and Setting (Sun and Moon).
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Supplementary Azimuth. Supplementary Azimuth is the geometric ‘supplement’ of Azimuth, (ie Azimuth + Supplementary Azimuth = 180° ) See Para 0742.
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Tabulated Altitude (from NP 401 / NP 303) . On entering NP 401 / NP 303, the table provides Tabulated Altitude (Hc). Tabulated Altitude (Hc) results from using ‘round-figure’ integer arguments of LHA, Latitude and Declination. Although the differences from the exact LHA and the exact DR/EP Latitude can be resolved by plotting, interpolation for Declination is required to establish the exact calculated Altitude. See Paras 0542d, 0543 and separate entries (at Para 0401) for: Calculated (Tabulated) Altitude Corrected Tabulated Altitude (Corr Tab Alt)
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BR 45(2)
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Tabulated Declination (used with NP 401 / NP 303). The Tabulated Declination is the Declination figure for the whole number of hours of the observation and must be corrected by the “d” / “d corrn” (Declination correction from The Nautical Almanac) for the outstanding minutes and seconds . See Paras 0543b and also separate entry (at Para 0401) for “d” / “d corrn” (Declination correction from The Nautical Almanac) .
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Tabulated Zenith Distance. See separate entry (at Para 0401) for Calculated (Tabulated) Zenith Distance (CZD).
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Terrestrial Refraction. The bending of the light which is approaching the observer on or near the surface of the Earth, is called Terrestrial Refraction and affects the Dip of the Visible Horizon. See Para 0802.
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Time. See separate entries for: Apparent Solar Day / Time Astronomical Day Civil Day Coordinated Universal Time (UTC) Daylight Saving Time (DST) Deck Watch Time Equation of Time Greenwich Mean Time (GMT) International Atomic Time (TAI) International Date Line (IDL) Legal Time - see separate entry for Standard Legal Time Local Mean Time (LMT) Local Sidereal Time (LST) Lunar Day Mean Solar Day Mean Solar Hour / Minute / Time Sidereal Day / Time Sidereal Hour / Minute Solar Day Solar Time Standard Legal Time Standard (or Zone) Time Standard Time Zones Summer Time - see separate entry for Daylight Saving Time (DST) Time Errors Time Zones - see separate entry for Standard Time Zones Uniform Time System ‘Universal Coordinated Time’ - see Coordinated Universal Time (UTC) Universal Time (UT or UT1) Zone Time - see separate entry for Standard (or Zone) Time
Note: All variations of ‘Hour Angle’ will be found listed separately under ‘Hour Angles’ .
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BR 45(2)
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Time Errors. Time Errors in calculating Astronomical Position Lines are infrequent, given the current generation of digital Deck Watches and time standard equipment embarked in most naval ships. The most likely errors are to misread the Deck Watch by a full minute at the time of observation (particularly if the analogue minute and second hands are not perfectly aligned), or to apply any known Deck Watch Error with the incorrect sign.
Any error in time will give rise to an error in the Calculated (Tabulated) Altitude, equivalent to a displacement in Longitude by an amount equal to the error in Hour Angle expressed in minutes of arc. When the Azimuth of the body observed is 0° or 180° this error is zero (ie Position Line is East-West), and is a maximum when the Azimuth of the body observed is 90° (ie Position Line is North-South). When converting the Longitude error to nautical miles, the same error in time will have a greater effect in distance at the Equator than in high Latitudes due to the compression of Meridians with Latitude. This error distance may be plotted or calculated. See Para 0903. •
Time Zones. See separate entry (at Para 0401) for Standard Time Zones.
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Total Darkness. Total Darkness occurs when the centre of the Sun is more than 18° below the Celestial Horizon (ie beyond Astronomical Twilight ). See Paras 0108, 0725.
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Towering (Mirage). When a Mirage is experienced, if the object appears taller than usual, it is termed Towering . See Para 0808b.
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Transferred Position Lines. See separate entry (at Para 0401) for Run / Run-on, Run-back .
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True Altitude. See separate entry (at Para 0401) for Observed (True) Altitude.
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True Bearing (of a heavenly body) . The True Bearing of a heavenly body is its direction seen from an observer and this is measured conventionally as the angle from the Meridian of True North measured clockwise, ie. 0° to 360°. See Paras 0117, 0535, 0536.
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True Sun. The True Sun is the body which gives light and heat to the Earth. However, variations in the apparent speed of the True Sun along the Ecliptic make the Hour Angle of the True Sun an impractical unit of measurement. To overcome this and yet retain a link to the True Sun (which in reality governs much of life on Earth), a ‘ Mean Sun’ is used instead. See Para 0433 and also separate entry (at Para 0401) for Mean Sun.
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True (Theoretical) Moonrise and Moonset. See separate entry (at Para 0401) for True (Theoretical) Rising and Setting (Sun and Moon).
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True (Theoretical) Rising and Setting (Sun and Moon). The time of True (Theoretical) Rising and Setting occurs when the centre of a heavenly body is on the observer’s Celestial Horizon, to the east or west of his Meridian. At these times the True Zenith Distance is 90°. Except in the case of the Moon, this phenomenon cannot be observed directly from the Earth’s surface due to Atmospheric Refraction raising the image of the body appreciably above the Visible Horizon.
True(Theoretical)Sunrise/Sunset must NOT be confused with Visible Sunrise Sunset The special cases affecting the Sun and Moon are as follows:
The Moon. When the Moon’s centre lies on the Celestial Horizon, due to Horizontal Parallax, the Moon’s centre appears practically on the Visible Horizon. See Para 0702. The Sun. When the Sun’s centre lies on the Celestial Horizon, the Sun’s Lower Limb appears one semi-diameter above the Visible Horizon. See Paras 0107, 0702 and 0723.
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True (Theoretical) Sunrise and Sunset. See separate entry (at Para 0401)for True (Theoretical) Rising and Setting (Sun and Moon).
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True Zenith Distance (TZD). See Observed (True) Zenith Distance (TZD) at Para 0401 above.
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Twilight. See separate entries (at Para 0401) for: Astronomical Twilight (AT) Evening Civil Twilight (ECT) Evening Nautical Twilight (ENT) Midnight Sun Morning Civil Twilight (MCT) Morning Nautical Twilight (MNT) Total Darkness
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Uniform Time System. At sea the world is divided into twenty-four Time Zones. Each zone is 15° wide and in each zone is numbered and lettered; this arrangement is known as ‘Standard(or Zone) Time’. The 12th zone is divided by the International Date Line ( IDL), the part to the west being 12 and that to the east +12. The zone number indicates the number of hours by which Zone Time must be decreased or increased to obtain Universal Time UT . On land, countries may modify the Standard (or Zone)Time to suit local needs. The Time Zone kept on land is decided by national laws and is known as Standard Legal Time (or ‘ Legal Time’). See Paras 0201, (0202 / Fig 2-1, Fig 2-2), (0203), (0204), (0205), (0206). Brackets indicate associated information.
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Universal Time (UT or UT1). Universal Time (UT or UT1) is the Mean Solar Time (MST) of the Prime Meridian obtained from direct astronomical observation and corrected for the effects of small movements of the Earth relative to the axis of rotation ( Polar Variation). See Paras 0201, 0205, 0209, 0210, 0211, 0435.
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BR 45(2)
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Upper Limb (UL). The Upper Limb of the Sun or Moon is the portion of its circumference furthest from the Visible Horizon, as seen from an observer on the Earth’s surface. See Para 0704.
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Upper Mer Pass / Upper Meridian Passage (of a heavenly body) . Upper Mer Pass / Upper Meridian Passage is normally referred to as Mer Pass / Meridian Passage. See Paras 0602, 0603, 0612a nd also separate entry for Mer Pass / Meridian Passage (of a heavenly body) .
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“v corrn” / “v” (velocity correction from The Nautical Almanac). “v” / “v corrn” is a velocity correction to the hourly difference in Greenwich Hour Angle, tabulated in The Nautical Almanac and is used with the (yellow) ‘Increments and Corrections’ tables at the back of The Nautical Almanac to calculate the precise Greenwich Hour Angle of the Sun, Moon or Planets with NP 400 (Sight Form) and NP 401 method of solving the PZX triangle. See Para 0543b.
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Vertical Circles. All Great Circles passing through the Observer’s Zenith (Z) are necessarily perpendicular to the Celestial Horizon and are known as Vertical Circles. See Para 0119.
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Very High Altitude (Tropical) Sights. Very High Angle (Tropical) Sights are those observations of heavenly bodies where the Zenith Distances (90° Observed (True) Altitudes), when converted to nautical miles, are so small as to make it necessary to plot them as circles, centred on the Geographic Positions of the bodies. In practice, Very High Altitude (Tropical) Sight s may only be usefully observed between Sextant Altitudes of about 88½°-89½° and in these circumstances, it is possible to obtain a ‘3 Position Line’ fix around the time of the Sun’s Mer Pass in a period of about 10 minutes. There are also some practical difficulties in observing a heavenly body with a Sextant at an Altitude approaching 90°. See Paras 0521, 0523 and 0550.
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Visible Hemisphere. The Celestial Horizon divides the Celestial Sphere into hemispheres, the upper one of which (containing the Observer’s Zenith ‘Z’ ) is the known as the Visible Hemisphere, and the other one as the Lower Hemisphere. Subject to Atmospheric Refraction, all heavenly bodies in Visible Hemisphere are visible to the observer but bodies in the Lower Hemisphere cannot be seen. See Para 0502 (Note 5-1).
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Visible Horizon. The Visible Horizon is position on the Earth’s surface where a line of sight from an observer, at a given Height of Eye and in given conditions of Refraction, meets the Earth’s surface as a tangent to that surface. The Visible Horizon appears as a circle bounding the observer’s view at sea. See Para 0116 and separate entries (at Para 0401) for: Celestial Horizon, Plane of the Celestial Horizon
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Visible Moonrise and Moonset. See separate entry (at Para 0401) for Visible Rising and Setting (Sun and Moon).
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Visible Rising and Setting (Sun and Moon). Visible Rising and Setting occur when the Upper Limb of a heavenly body is just appearing above or disappearing below the observer’s Visible Horizon. In the cases of the Sun and Moon, the tables in The Nautical Almanac give the times at which these phenomena occur.
True(Theoretical)Rising/Setting Rising/Setting For the Moon:
must
NOT
be
confused
with Visible
See Paras (0320, 0321, 0322 - non specific with NAVPAC 2), and 0703, 0730, 0731, 0740, 0741, 0742.
For the Sun: See Paras 0107, 0320, 0321, 0322, 0702, 0703, 0720, 0721, 0722, 0725, 0740, 0741, 0742.
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Visible Sunrise and Sunset. See separate entry (at Para 0401)for Visible Rising and Setting (Sun and Moon).
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Waning (of Moon). ‘Waning’ is the name given to the change in the Moon’s phases when it moves from a Full Moon, through the Last Quarter to a New Moon. During this period, the part of the Moon visible to an observer on Earth decreases day-by-day. See Para 0452.
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Waxing (of Moon). ‘Waxing’ is the name given to the change in the Moon’s phases when it moves from a New Moon, through the First Quarter to a Full Moon. During this period, the part of the Moon visible to an observer on Earth increases day-by-day. See Para 0452.
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Winter Solstice. See separate entry (at Para 0401)for Solstice.
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Zenith. See Observer’s Zenith (Z) at Para 0401 above.
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Zenith Distance. The Zenith Distance is the Angular Distance between the Observer’s Zenith and the position of a heavenly body. See Para 0524 and separate entries (at Para 0401) for: Calculated (Tabulated) Zenith Distance Observed (True) Zenith Distance (TZD)
•
Zone Time. See separate entry (at Para 0401) for Standard (or Zone) Time.
0402-0419.
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SECTION 2 - HOUR ANGLES 0420. Hour Angles - Explanation and Definitions Hour Angles and their specific variants were introduced at Para 0106 but may be defined more precisely as follows: Sidereal Hour Angle (SHA). The Sidereal Hour Angle (SHA) is the Angular a. Distance, measured westwards, from the Meridian of the First Point of Aries ( ) to the Meridian of the heavenly body (Fig 4-1). It is almost completely static for stars and is tabulated once per 3 days for each star and planet in The Nautical Almanac. The SHA of a planet is only used when using The Nautical Almanac Planet Diagram or setting a Star Identifier or Star Globe (see Paras 0133, 0324 and Annex 5A). Note 4-1. At Fig 4-1 (facing page) the SHA of star X is labelled and is also represented by the Angular Distance X (measured westwards). Right Ascension (RA). Right Ascension (RA) is the Angular Distance, measured b. eastwards (rather than westwards as in SHA), from the Meridian of the First Point of Aries ( ) to the Meridian of the heavenly body. ie. RA = 360° - SHA. This measurement is mostly used by astronomers but has a navigation application when using the Star Identifier and Star Globe (see Para 0324 and Annex 5A). RA is not labelled at Figs 4-1, 4-2 or 4-3. Note 4-2. At Fig 4-1 (facing page) the RA of star X is NOT labelled but is represented by the Angular Distance X measured eastwards (ie 360°- X measured westwards).
c. Greenwich Hour Angles (GHA). The Greenwich Hour Angle (GHA) is the Angular Distance, measured westwards from the projection of the Greenwich Meridian onto the Celestial Sphere and the Meridian of the heavenly body. The GHA of the First Point Aries ( ) and the GHAs of the Sun, Moon and Planets are tabulated second-bysecond in The Nautical Almanac. Adding SHA of the body to the GHA of Aries ( ) (minus 360° if required) gives the GHA of the body. See Fig 4-1 and Paras 0421-0422. Note 4-3. At Fig 4-1 (facing page) the GHA of star X and the GHA of are both labelled and are also represented by the Angular Distances GX and G respectively (both measured westwards).
d. Local Hour Angle (LHA). The Local Hour Angle (LHA) is the Angular Distance, measured westwards, of the projection of the observer’s Meridian onto the Celestial Sphere and the Meridian of the heavenly body. It equates to the GHA of the body +/- the observers’s Longitude. See Fig 4-1 and Paras 0421-0422. Note 4-4. At Fig 4-1 (facing page) the LHAs of star X measured westwards from the observer O at H and K are labelled, and are also represented by the Angular Distances O(H)X and O(K)X respectively.
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0421. Hour Angles and Declination - Pictorial Representation & Standard Nomenclature Key Celestial Sphere definitions from Paras 0401 and 0420 are shown in pictorial form at Fig 4-1 below, which is viewed from the Greenwich Celestial Meridian. Fig 4-1 also adopts the standard nomenclature convention for lettering astro-navigation diagrams which will be followed through the remainder of this book. Reading from the Celestial Poles and then left to right, the nomenclature is as follows: P, P’ The north and south Celestial Poles Q, Q’ The Celestial Equator O Observer’s Meridian - may be suffixed K or H as appropriate, see O(H), O(K) O(H) Observer’s Meridian when observer is at H (Longitude West) X Celestial Meridian of a heavenly body (may be either side of G) G Greenwich Celestial Meridian Celestial Meridian of the First Point of Aries ( ) O(K) Observer’s Meridian when observer is at K (Longitude East) Z The Observer’s Zenith (Z) is not shown in Fig 4-1 RA The Right Ascension (360°- SHA) is not shown in Fig 4-1
Fig 4-1. Hour Angles and Declination (Viewed from Greenwich Celestial Meridian)
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0422. Greenwich Hour Angle (GHA) and Local Hour Angle (LHA) of a Heavenly Body. GHA. From the definition at Para 0420c, it can be seen at Fig 4-1 and Fig 4-2 a. that the Angular Distance GX represents the GHA of the heavenly body. While the GHA is tabulated in The Nautical Almanac second-by-second for the Sun, Moon, Planets and Aries ( ), to do so for all 57 stars would produce an unacceptably large publication, running to several volumes. However, the GHA of a star can easily be found instead, by adding the SHA of the star (which is an almost fixed value and represented by the Angular Distance X), to the tabulated GHA of Aries (GHA , represented by the Angular Distance G ).
b. LHA. By adding or subtracting (+E,- W) the Angular Distance of the Longitude of the Observer’s Meridian (either O(H) or O(K) at Fig 4-2; for simplicity abbreviated to H or K below), to the Greenwich Hour Angle GX , the Local Hour Angle (HX or KX) of the heavenly body, measured westwards, is found (see example on facing page).
Fig 4-2. GHA and LHA of a Heavenly Body.
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c. LHA Calculation - Observer East of Greenwich . In the case of an observer east of the Greenwich Meridian at O(K) - for simplicity abbreviated to K below - the calculation for a star is as follows (GHA of Sun, Moon and Planets are tabulated ): GHA = G (Stars only) (measured clockwise) SHA of X = (Stars only) (measured clockwise) X GHA of X = GX = X + G (-360° if req)(measured clockwise) Longitude = GK (measured anti-clockwise) LHA of X = KGX = GX +KG (measured clockwise) = GHA + Longitude (East) d. LHA Calculation - Observer West of Greenwich. In the case of an observer west of the Greenwich Meridian at O(H) - for simplicity abbreviated to H below - the calculation is as follows: GHA and SHA of X calculations for GHA of stars as at Para 0422c above. GHA of X = GX (measured clockwise. 360° may be added if required) Longitude = GH ( measured clockwise ie. the long way round) LHA of X = HX (measured clockwise ie. the long way round) = GX + (360° - GH) = GX - GH (since any sum greater than 360° is unaffected if 360° is subtracted) GHA - Longitude (West) = e. LHA Calculation - Summary. The above calculations can be summarised as follows: GHA of the Sun, Moon and Planets is Tabulated in The Nautical Almanac . GHA of a Star = GHA + SHA of X, + or - 360° if required LHA of a heavenly body (X) = GHA of X + Observer’s Longitude (East) or, = GHA of X - Observer’s Longitude (West)
Example 4-1. If the SHA of a star in Fig 4-2 is 166° 19.2', the GHA of is 256° 20.0', the Longitude of the Meridian through H is 164° 47´W, and that of the Meridian through K is 121° 13´E then the LHA can be calculated as follows: At H
At K
GHA of SHA of X
256° 20.0' + 166° 19.2'
*GHA of X
422° 39.2
GHA of SHA of X
256° 20.0' + 166° 19.2'
GHA of X
422° 39.2 - 360° 00.0'
GHA of X 422° 39.2 Longitude (W) - 164° 47.0'
GHA of X Longitude (E) +
062° 39.0' 121° 13.0'
LHA of X
LHA of X
183° 52.0'
257° 52.2'
Example 4-1.
Summary of LHA Calculation
* Note 4-5. If the GHA of a body is less than the numerical value of the observer’s Longitude (W), then 360° may be added to the GHA when calculating LHA.
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SECTION 3 - SOLAR TIME 0430.
Purpose Sections 3-5 of Chapter 4, concerning Solar, Sidereal and Lunar Time, are primarily for Royal Navy officers holding or studying for the ‘Specialist N’ qualification. Due to the advent of time systems based on atomic-standard clocks (see Chapter 2), computer programs capable of instantaneous reduction of astro-navigation sights (see Chapter 3) and the withdrawal of the Sidereal Stop Watch (previously used for one variant of manual rapid sight reduction), a knowledge of Solar, Sidereal and Lunar Time is of less significance now than hitherto. However, ‘Solar Time’ information is still extant in the maritime domain and is published in the daily pages of The Nautical Almanac. Implicit with their ‘expert’ status, it remains relevant for the Navigation Specialists of the Royal Navy to retain a knowledge of the astronomical factors involved in ‘Time’ as part of their general understanding of the workings of the Celestial Sphere. The following paragraphs are intended to provide a readily available reference for this subject. 0431.
The Solar Day and Solar Time The basis of time measurement in astro- navigation is the period of rotation of the Earth. The rotation of the Earth results in the apparent rotation of the Celestial Sphere with relation to a fixed observer, so that heavenly bodies appear to be crossing and returning to the Observer’s Meridian once a day. A ‘ Day’ is the interval that elapses between two successive transits of a heavenly body across the same Meridian. All heavenly bodies are thus timekeepers but some are more useful than others. The Sun is not a perfect timekeeper as it is relatively close to the Earth and its apparent speed along the Ecliptic is not constant. However, the Sun is central to life on Earth and because of this, throughout history it has been used for t imekeeping purposes. These range from the simple constraints of only being able to work in the fields during daytime, to the complex sundials of the type built by Henry VIII at the Royal Palace of Hampton Court. 0432.
The Apparent Solar Day The interval that elapses between two successive transits of the Sun across the same Meridian is an Apparent Solar Day. By the time the Earth has made one revolution (360°) measured against a star crossing the Observer’s Meridian, the Earth will have moved along its orbit and its position relative to the Sun will have altered by a measurable amount. Thus for the Sun to cross the Observer’s Meridian for a second time the Earth will have rotated slightly more than one 360° rotation. Depending on its position in the annual orbit, this difference can be up to 1° of rotation (ie. 361°). This complicated by the Earth not moving along its elliptical orbit around the Sun at a constant speed. Its speed is greatest when nearest the Sun and least when furthest from the Sun; thus the difference is a variable a mount both in quantity and sign (see Para 0439). Due to these factors the Apparent Solar Day is NOT a time interval of fixed length. 0433.
The True Sun and the Mean Sun The apparently ‘irregular’ movement of the Sun (see Para 0432) is revealed to an observer on Earth by variations in the apparent speed of the Sun along the Ecliptic. If this motion is projected on to the Celestial Equator , the Hour Angle of the Sun ( referred to hereafter as the‘True Sun’ ) may be measured, and as expected, this shows a non-uniform rate of change. The Hour Angle of the True Sun does not therefore give a practical unit of measurement. To overcome this difficulty, and yet retain a link to the True Sun (which in reality governs much of life on Earth), a ‘ Mean Sun’ is introduced, defined as follows: The Mean Sun is an imaginary body which is assumed to move in the Celestial Equator at a uniform speed around the Earth and to complete one (360°) revolution in the time taken by the True Sun to complete one (360°) revolution in the Ecliptic. 4-34 Change 1
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0434.
The Mean Solar Day / Time and UT , the Civil Day and the Astronomical Day
a. The Mean Solar Day. The interval between two successive transits of the Mean Sun across the same Meridian is called the Mean Solar Day. In one Mean Solar Day the Mean Sun moves westwards from the Meridian and completes one circuit of 360° in Longitude in the 24 Mean Solar Hours into which the Mean Solar Day is divided. The rate of travel of the Mean Sun is thus 15° of Longitude per hour, and thus 1° of Longitude is equivalent to 4 minutes of time. b. Mean Solar Time, UT and GMT. The Mean Solar Hour is divided into minutes and seconds; it equates exactly to the UT/ UT1 and GMT hour (Paras 0209 and 0210). c. The Civil Day and the Astronomical Day. The Civil Day (which uses the am / pm notation) and the Astronomical Day (which uses 24 hour notation) both contain 24 Mean Solar Hours (abbreviated hereafter ‘hours’). The Civil Day and the Astronomical Day are deemed to start at midnight (when the sun is at its lower transit of the Observer’s Meridian. ie. Its Hour Angle is exactly 12 hours before / after its upper transit of the Observer’s Meridian when the Mean Sun is at its highest point in the daytime sky ). 0435.
Local Mean Time (LMT) and Universal Time (UT) /Greenwich Mean Time (GMT)
a. Local Mean Time (LMT) . Local Mean Time ( LMT ) is the mean time kept at any place when the Local Hour Angle of the Mean Sun is measured from Meridian of that place. However, as the Local Hour Angle of the Mean Sun is measured from the Greenwich Meridian and the Civil/Astronomical Day are both measured from 180° (12 hours) from the Greenwich Meridian (see Para 0434c), LMT is defined as follows: LMT at any instant is the Local Hour Angle of the Mean Sun at that instant, measured westwards from the Meridian of that place, +/- 12 hours .
b. Universal Time (UT) / Greenwich Mean Time (GMT). Greenwich Mean Time (GMT ) is the Local Mean Time on the Greenwich Meridian, but has been largely replaced by the term UT . However, as the Local Hour Angle of the Mean Sun is measured from the Greenwich Meridian and the Civil/Astronomical Day are both measured from 180° (12 hours) from the Greenwich Meridian (see Para 0434c), GMT (and also UT ) are defined as follows: UT / GMT is the Greenwich Hour Angle of the Mean Sun at that instant, +/- 12 hours. 0436.
Longitude and Time Since all places on earth are identified by reference to the Greenwich Meridian, Longitude must provide the connection between LMT at any place and UT / GMT . Take for example, New York which is roughly 75° west of Greenwich. The Mean Sun, travelling west at 15° per hour covers this Angular Distance in 5 hours, thus New York is ‘5 hours west of Greenwich’. When the Mean Sun reaches New York’s Meridian, its Local Hour Angle with reference to this Meridian is 0 hours, but with reference to the Greenwich Meridian it is 5 hours, because that is the period since the Mean Sun crossed the Greenwich Meridian. Similarly, when the Mean Sun crosses the Greenwich Meridian, the Local Hour Angle in New York is (24 hours 5 hours) = 19 hours. It can be seen that this calculation may also trigger a date change. What has been shown for this example of New York holds good in principle for any other place, and leads to the rule at Para 0437 of applying Longitude (expressed in time) to convert the LMT on one Meridian to/from the LMT on the Greenwich Meridian (UT / GMT ). 4-35 Original
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0437.
Conversion between UT / GMT and LMT Applying the principle at Para 0436, the following rules (also at Para 0205)are established:
If a Longitude is West, ADD the time equivalent of the Longitude when changing from Local Mean Time to GMT (and vice versa - SUBTRACT if changing from UT / GMT to LMT ). If a Longitude is East, SUBTRACT the time equivalent of the Longitude when changing from Local Mean Time to GMT (and vice versa - ADD if changing from UT / GMT to LMT ). Examples 4-2 and 4-3. What are the LMTs if UT/GMT is 23 hrs 31 mins 25 secs on 14 September, (1) at 48° West, and (2) at 22½° East. Note that this is changing from UT / GMT to LMT. Example 4-2: at 48° West Date
Example 4-3: at 22½° East
Hrs Mins Secs
14 Sep UT / GMT
23
31
25
03
12
00
14 Sep LMT (48°W) 20
19
25
Long W. (-)
Date
Hrs Mins Secs
14 Sep UT / GMT Long E. (+) 15 Sep LMT
23
31
25
01
30
00
01
01
25
Examples 4-2 and 4-3. Worked Examples of Converting UT / GMT to LMT ( Note that the date has also changed in Example 4-3 at 22½° East ) 0438.
Use of Standard Time and Zone Time It is clearly impracticable for each place to keep the time in its own Meridian, nor is it practicable for places all over the world to keep the same time. Thus the system of ‘Standard (or‘Zone) Time’ which includes dates has been agreed internationally (see Paras 0201-0204). UT / GMT is used as the standard Time Zone for worldwide reference books such as The Nautical Almanac, is the Time Zone in which Ship’s Chronometers and Deck Watches are kept and is also used for signal message Date-Time-Groups (DTGs). It should be noted that Tides Tables, which are specific to local areas, normally provide information in Standard Legal Time (See Para 0202) but care must be exercised when any Daylight Saving Time (DST) is in force. 0439.
The Equation of Time Although the assumption of an imaginary Mean Sun makes the ordinary clock possible, this same assumption also gives rise to a problem. The navigator, seeking to fix his position by the Sun, necessarily measures the altitude of the True Sun, and the True Sun keeps Apparent Solar Time (Paras 0432-0434). The instant of this observation is from a Deck Watch which t hat keeps Mean Solar Time. The navigator must be able to connect Mean Solar Time with Apparent Solar Time. The connection is the ‘Equation of Time’ which is defined as: The Equation of Time is the difference of Mean Solar Time from Apparent Solar Time Equation of Time = LHA Mean Sun - LHA True Sun
The value of the Equation of Time varies in size and sign depending on the seasonal position of the Earth in its orbit around the Sun (Para 0432). On about 15 April, 14 June, 1 September and 24 December it becomes zero and changes sign; its extreme values are +14 and -16 minutes. The value of the Equation of Time is tabulated in The Nautical Almanac twice daily. To overcome these difficulties, the tables in The Nautical Almanac allow for the Equation of Time and are entered with the argument of UT(GMT). No further correction is needed. 4-36 Original
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SECTION 4 - SIDEREAL TIME 0440.
Purpose. See Para 0430 for explanation of the purpose of Sections 3-5 of Chapter 4.
0441.
The Sidereal Day and Sidereal Time It was stated at Para 0431 that a ‘Day’ is the interval that elapses between two successive transits of a heavenly body across the same Meridian. All heavenly bodies are thus timekeepers but some are more convenient than others. If the heavenly body selected for observation is a star, the interval between successive transits across the same Meridian is known as a ‘Sidereal Day’, to distinguish it from a ‘Solar Day’ (or more fully, an Apparent Solar Day or a Mean Solar Day see Paras 0432-0434). The Sidereal Day is sub-divided into hours, minutes and seconds. For convenience, the First Point of Aries ( ) is taken instead of an actual star (see Para 0104) and the Sidereal Day is therefore defined as follows: A Sidereal Day is the interval between two successive transits of the First Point of Aries across the same Meridian.
0442.
Length of the Sidereal Day It was established at Para 0432 that the Earth rotates through about 361° during one Apparent Solar Day, whereas during a Sidereal Day the Earth completes exactly one revolution (360°), measured against any distant star crossing the Observer’s Meridian. Although the Sidereal Day provides a precise and regular time interval, due to variations in the length of the Apparent Solar Day of between +14 and -16 minutes (see Para 0432 and 0439), the numerical difference between the Sidereal Day and the Apparent Solar Day is also a variable amount both in quantity and sign. However, the difference between the Sidereal Day and the Mean Solar Day is reasonably constant at about 4 minutes, which is the extra time taken by Earth to turn through the extra amount. In summary, the Sidereal Day is not a practical unit of time in a world governed by the Sun, and except in observatories where it has uses in providing time interval, it may be ignored for clock purposes but see Para 0443 for its important use as an Angular Distance.
0443.
Local Sidereal Time (LST) Notwithstanding its limitations of use as a clock system, Sidereal Time as an Angular Distance is of real importance to the navigator because it enters the problem of establishing a star’s Hour Angle and thus helps solve the navigational problem. The navigator is not concerned with the duration of time which has elapsed since the First Point of Aries ( ) crossed the local meridian, otherwise the Sidereal Hour and the Sidereal Minute - time units derived from the Sidereal Day and differing slightly from Mean Solar Day/Hour/Minute - would become involved and the connection between the two sets of units would have to be investigated more thoroughly. This labour, however, is avoided when the navigator treats Sidereal Time as an Angular Distance, because the units of arc in which he expresses it are constant units suitable for expressing the Angular Distance of any heavenly body from his Meridian. To express the Angular Distance of the First Point of Aries ( ) from an Observer’s Meridian, ‘Local Sidereal Time’ is defined as follows: Local Sidereal Time ( LST ) is defined as the LHA of First Point of Aries ( ).
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0444. Relationship between UT / GMT and GHA Aries ( )
a. Relationship of Mean Sun’s GHA and SHA , and its UT/GMT. The movement of the Mean Sun in the Celestial Equator (see Para 0433) enables a relation to be established between the UT / GMT at which a star is observed and its Greenwich Hour Angle at that instant. The Mean Sun’s uniform movement in the Celestial Sphere, along which path the Sidereal Hour Angles are measured, implies an equally uniform decrease in the Mean Sun’s Sidereal Hour Angle during the year. Point X, which lies on the Celestial Equator in Fig 4-3, may therefore be taken as the Mean Sun at the moment under consideration. Just as a star ’s Greenwich Hour Angle and a star’s Sidereal Hour Angle are related (see Para 0420c), it is apparent from Fig 4-3, that the Mean Sun’s Greenwich Hour Angle and the Mean Sun’s Sidereal Hour Angle are similarly related as follows: GHA Aries ( ) = GHA Mean Sun - SHA Mean Sun + (360° if req) But as shown at Para 0435b: GHA Mean Sun = UT +/- 12 hours GHA Aries ( ) = UT +/- 12 hours - SHA Mean Sun + (360° if req)
b. Tabulation of GHA Aries ( ) Against UT. The SHA Mean Sun decreases at a constant rate and can be predicted for any instant. It is thus possible to calculate GHA Aries at any instant. GHA Aries ( ) is tabulated against UT in The Nautical Almanac.
Fig 4-3. 0445-0449. Spare.
4-38 Original
Mean Sun’s SHA, GHA of (
) and Mean Sun’s GHA
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SECTION 5 - LUNAR AND PLANETARY TIME 0450.
The Hour Angle of the Moon
a. Relationship of Moon’s GHA, Moon’s SHA and UT / GMT. If two successive transits of the Moon were observed across the same Meridian, the interval between them would be one Lunar Day. As shown at Fig 4-4, since the Moon itself is describing an orbit around the Earth in the same direction as the Earth’s spin, the interval between the two transits of the same Meridian would be longer than the Mean Solar Day.
Fig 4-4. The Orbit of the Moon during a Mean Solar Day (Not to Scale)
At Fig 4-4, AA´ is a measure of the Mean Solar Day, but while the Earth has moved from A to A´, the Moon has reached C, and so the Earth will have to turn through a further angle approximately equal to B´A´C before it is on the Observer’s Meridian again. (Distances in Fig 4-4 are not to scale; as the Sun is so far away, the lines shown as ‘Observer’s Meridian’ at A and A’ are in reality almost parallel.) The time taken to turn the extra angle B´A´C varies between 39 and 64 minutes but averages 50 minutes. The units derived from the Lunar Day are Lunar Units. It is not necessary, however, to work in Lunar Units to find the Hour Angle of the Moon. The formula for the Hour Angle of a heavenly body (see Para 0420c and 0434) applies equally to the Moon, thus: GHA Aries ( ) = GHA Moon - SHA Moon + (360° if req) But as shown in Para 0435b: GHA Moon = UT +/- 12 hours GHA Aries ( ) = UT +/- 12 hours - SHA Moon + (360° if req)
b. Tabulation of GHA Moon Against UT / GMT. The SHA of the Moon can be predicted and when combined with GHA Aries ( ) as above, gives GHA Moon. As a result of such calculations, GHA Moon is tabulated against UT in The Nautical Almanac. 4-39 Change 1
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0451.
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The Lunation or Lunar Month
a. Length of the Lunar Month. The Lunation or Lunar Month is the interval between two successive New Moons (when the Moon lies in a straight line between the Earth and the Sun and therefore appears ‘black’) and is important in tidal prediction. The Moon makes one complete revolution about the Earth in 27 a Mean Solar Days, but if the Moon were a New Moon at the beginning of this period, when the Earth is a t A in Fig 45, it would not be a New Moon at the end of the period, because it would not lie in a straight line with the Sun and the Earth, which is now at B. To achieve this position it must move along its orbit round the Earth, and while this is happening, the Earth continues along its own orbit round the sun to a position C. A further 2 1/6 Mean Solar Days (approximately) elapse before the Moon is again a New Moon, and a Lunation or Lunar Month is therefore equivalent to (27 1/3 + 21/6) or 29½ Mean Solar Days.
Fig 4-5. The Lunar Month
b. Time Difference of Lunar Day and Mean Solar Day. During a Lunar Month the Moon must cross the Observer’s Meridian once fewer times than the Sun, and this fact establishes the 50-minute difference between the Mean Solar Day and the Lunar Day because: 28½ Lunar Days = 29½ Mean Solar Days 1 Lunar Day = 29½ Mean Solar Days divided by 28½ 1 Lunar Day = 24 hours and 50 minutes (Mean Solar Time)
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0452.
Phases of the Moon
a. Tabulated Data in Nautical Almanac. On each 3-day double tabular page, The Nautical Almanac tabulates the semi-diameter of the Moon for each day, the age of the Moon in days, its percentage illuminated each day and a symbol indicating the phase for 1200 (UT ) on the middle day. Full Moons are indicated by a white circle and New Moons by a black circle, with intermediate phase diagrams indicating the proportion of the Moon which is illuminated. These intermediate phase diagrams do not indicate which side of the Moon is illuminated from all Latitudes but are set for UK and other (mostly northerly) Latitudes where the Sun passes to the south at Meridian Passage (see Para 0325a). The dates and times of the Moon’s phases for the entire year are given in UT on Page 4 of The Nautical Almanac. b. Changes of the Moon’s Phases. Fig 4-6 provides a simplified diagram of the Moon’s orbit around the Earth in relation to the Mean Sun (ignoring the movement of the Earth in its orbit around the Sun). From this it can be seen that at New Moon the illuminated side of the Moon is not visible from the Earth. However as the Moon’s orbit progresses to the First Quarter , an observer on Earth first sees a thin crescent of illuminated Moon which increases (Waxes) to half the Moon being illuminated. It then waxes to three-quarters of the Moon being illuminated before reaching a Full Moon when the whole surface of the Moon is illuminated. The illuminated sector of the Moon progressively decreases (Wanes) to the Last Quarter and to the New Moon. It should be noted that although Fig 4-6 gives an accurate picture of the Moon’s phases from a position outside the Solar System, it does NOT make clear how the Moon’s crescent will appear to an observer on the Earth’s surface. For an understanding of which way the crescent faces during Waxing and Waning , and thus an instant appreciation of the Moon’s phase by a single observation, an analysis of the Sun’s and Moon’s Hour Angles is needed (see Para 0452c-f).
Fig 4-6. Phases of the Moon during Lunar Month (simplified) 4-41 Original
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c. Hour Angles of the Sun and Moon at the Time of New Moon. It can be seen from Fig 4-6 that the Moon always has its illuminated ‘convex’ edge nearest to the Sun. It is also apparent that at the time of a New Moon, the Moon and the Sun occupy positions in the sky very close to each other and thus will have very similar Local Hour Angles (LHA); a quick look at The Nautical Almanac’s GHA column (see Note 4-6 below) for the Sun and Moon at the time of New Moon will confirm this. It is for this reason that the Moon cannot be seen from Earth at New Moon; partly because the other side of the Moon is being illuminated and partly because being so close to the Sun, the Moon is only above the horizon in daylight. Note 4-6. Longitude must be applied to both GHAs to obtain LHAs (see Paras 0420d and 0421), but as it will be the same Longitude in both cases and only the relative LHAs are needed, it is sufficient to compare GHAs.
d. Change in Hour Angles of the Sun and Moon: New Moon to Full Moon. As the Moon moves towards the First Quarter and thence to Full Moon, the Sun’s LHA advances more rapidly than the Moon’s. As Hour Angle is always measured westwards (see Paras 0420 and 0421) this means that as the Sun’s LHA increases relative to the Moon’s LHA, its WEST side will be illuminated, until at Full Moon the whole Moon is illuminated. At this time, the Sun’s LHA is 180° (12 hours) ahead of the Moon’s LHA, which explains why at the Equinoxes the Moon rises at the time the Sun sets (the ‘Harvest Moon’ phenominum). A glance at The Nautical Almanac’s GHA column for the Sun and Moon (see Note 4-6 above) from the time of New Moon to Full Moon will confirm these relative changes of LHA. e. Change in Hour Angles of the Sun and Moon: Full Moon to New Moon. As the Moon moves towards the Last Quarter and thence to New Moon, the Sun’s LHA continues to advance more rapidly than the Moon’s LHA, but as it is now MORE than 180° AHEAD of the Moon’s LHA, it is more convenient to think of it as LESS than 180° BEHIND and thus eastward of the Moon. This means that from Full Moon onwards it will illuminate the EAST side of the Moon until, at New Moon, none of the Moon is illuminated. At this time, the Sun’s LHA is once again synchronised with the Moon’s LHA, and the cycle repeats itself. Another glance at the GHA column for the Sun and Moon in The Nautical Almanac (see Para 0420d) from the time of Full Moon to New Moon will confirm these relative changes of LHA. f. Moon’s Phases, Waxing and Waning: Identification by Single Observation. The implications of the relative movement of the Sun’s LHA compared to the Moon’s LHA are that the phase of the Moon (and whether it is Waxing or Waning ) can be established by a single glance at the Moon without recourse to tables. The Moon always has its illuminated ‘convex’ edge nearest to the Sun (see Para 0452c above). When Waxing the Moon has its west side illuminated (see Para 0452d above) and when Waning has its East side illuminated (see Para 0452e above). From this a simple rule for the Moon’s phases emerges: The Moon’s illuminated ‘convex’ edge is at the West when Waxing; The Moon’s illuminated ‘convex’ edge is at the East when Waning.
This can be neatly summarised as: ‘West when Waxing; East when Waning’.
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0453.
The Hour Angle of the Planets The Planets belong to the solar system and for the purpose of finding their Hour Angles, their motion in the Celestial Sphere may be treated in exactly the same way as for the Moon (see Para 0450) and thus: GHA Aries ( ) = GHA Planet - SHA Planet + (360° if req) But as shown in Para 0435b: GHA Planet = UT +/- 12 hours GHA Aries ( ) = UT +/- 12 hours - SHA Planet + (360° if req)
The SHA of the Planets can be predicted and when combined with GHA Aries ( ) as above, gives GHA Planet. As a result of such calculations, GHA Planet for Venus, Mars, Jupiter and Saturn are tabulated against UT in The Nautical Almanac.
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CHAPTER 5 IDENTIFICATION OF HEAVENLY BODIES, ASTRONOMICAL POSITION LINES, OBSERVED POSITION AND SIGHT REDUCTION PROCEDURES CONTENTS SECTION 1 - IDENTIFICATION OF HEAVENLY BODIES
The Mathematics of Identifying Heavenly Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Star Globe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Star Identifier and The Nautical Almanac Planet Diagram . . . . . . . . . . . . . . . . . .
Para 0501 0502 0503
SECTION 2 - ASTRONOMICAL POSITION LINES Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Position Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plotting Position Circles - Ordinary Sights and Very High Altitude (Tropical) Sights . The Intercept (Marq St Hilaire) Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Assumptions made when an Astronomical Position Line is Plotted . . . . . . . . . . . . . . . Plotting Sheets and Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0520 0521 0522 0523 0524 0525 0526
SECTION 3 - CALCULATING ALTITUDE, AZIMUTH AND TRUE BEARING
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Means of Solving the PZX Triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solution of PZX Triangle for Zenith Distance - Cosine Method . . . . . . . . . . . . . . . . . . Solution of PZX Triangle for Azimuth - Cosine Method . . . . . . . . . . . . . . . . . . . . . . . Solution of PZX Triangle for Azimuth - Other Methods . . . . . . . . . . . . . . . . . . . . . . . . Azimuth and True Bearing of a Heavenly Body (RN and UK Maritime Usage) . . . . . Differences in Meaning of ‘Azimuth’, ‘Azimuth Angle’ and ‘True Bearing’ . . . . . . . .
0530 0531 0532 0533 0534 0535 0536
SECTION 4 - SIGHT REDUCTION PROCEDURES
Summary of Methods Available for Sight Reduction and their Accuracies . . . . . . . . . Use of NAVPAC 2 (See Chapter 3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Explanation of Marine Navigation Sight Reduction Tables (NP 401 series) . . . . . . . . Use of Marine Navigation Sight Reduction Tables (NP 401 series) . . . . . . . . . . . . . . Use of Air Navigation Sight Reduction Tables (NP 303 series) . . . . . . . . . . . . . . . . . . Use of Nautical Almanac Formulae and Procedures for Programmable Calculators . . Use of Concise Nautical Almanac Reduction Tables . . . . . . . . . . . . . . . . . . . . . . . . . .
0540 0541 0542 0543 0544 0545 0546
SECTION 5 - VERY HIGH ALTITUDE (TROPICAL) SIGHTS
Practical Observation at all Altitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Planning, Taking and Reduction of Very High Altitude (Tropical) Sights . . . . . . . . . . Plotting Very High Altitude (Tropical) Sights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0550 0551 0552
SECTION 6 - HIGH LATITUDE (POLAR) SIGHTS
Taking High Latitude (Polar) Sights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reducing High Latitude (Polar) Sights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plotting High Latitude (Polar) Sights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0560 0561 0562
ANNEXES Annex A:
Description and Setting of the Star Globe
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CHAPTER 5 IDENTIFICATION OF HEAVENLY BODIES, ASTRONOMICAL POSITION LINES, OBSERVED POSITION AND SIGHT REDUCTION PROCEDURES SECTION 1 - IDENTIFICATION OF HEAVENLY BODIES 0501.
The Mathematics of Identifying Heavenly Bodies Methods of identifying heavenly bodies are covered at Paras 0130-0133 and 0323-0324. However, the mathematics of these methods were not explained, although this is essential if the means by which they operate is to be understood. Fig 5-1 shows the Celestial Sphere with a heavenly body ‘X’ with an observer on the Meridian of ‘Q’. The figure is oriented so that the Celestial Horizon is horizontal and thus the Observer’s Zenith (Z) is at the 12 o’clock position.
Fig 5-1 Obtaining SHA and Dec
a. The identity of a star (X) can be established when its Sidereal Hour Angle (or 360° RA) and Declination (shown as dashed lines at Fig 1-13) are known. The observer must deduce these from the star’s True Bearing and Altitude. So, in Fig 5-1 it is required to find X’ (SHA of X) and X’X ( Declination of X ), from AX ( Altitude of X ), the angle PZX (the Azimuth of X) and the angle ZPX (which is the LHA of X found from the Deck Watch Time). ZPX is represented by QX’ (when the observer is on the Meridian at Q). b. Since X’ (SHA) = QX’ (LHA of X ) Q (LHA of ) , the LHA of X is known and LHA of Aries ( ) = GHA of Aries ( ) ± Longitude, the SHA of X may be calculated. c. In the triangle PZX, PZ (Co-Latitude), ZX (90° Altitude of X) and the angle PZX (the Azimuth of X ) are known, so the Angular Distance PX may thus be calculated. However, X’X = 90°- PX , so X’X (the Declination of X ) may be easily calculated. 5-3 Original
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0502.
The Star Globe.
a. Solution of Heavenly Body’s SHA and Declination. Para 0501 demonstrates how the SHA of X and the Declination of X may be found, provided that the time of observation or prediction is known, and given its altitude, True Bearing and access to a Nautical Almanac or equivalent. It is of course possible to run this calculation in reverse to calculate the predicted altitude and True Bearing of a known heavenly body at any time. b. Mechanical Model of the Celestial Sphere. While studying the Celestial Sphere, it is infinitely preferable to have a dynamic 3-dimensional model rather than a series of 2-dimensional diagrams. For many years, such a model - The Star Globe - was issued to all ships to provide a simple and speedy mechanical solution to the problem of star/planet identification at morning and evening stars. However, with the advent of NAVPAC 1, this expensive and delicate instrument was withdrawn from service. c. Use of the Star Globe for Teaching Astro-Navigation Theory . The Star Globe is easy to use and provides a very clear demonstration of the orientation of the Visible Hemisphere (see Note 5-1 below) of the Celestial Sphere for any time and position on the earth’s surface. Although this instrument has been declared obsolete for general use in the Royal Navy, a small number of Star Globes (Epoch 1975) have been preserved at the Navigation Section of the School of Maritime Operations (N Section, SMOPS) at HMS DRYAD and are now used for the sole purpose of teaching astro-navigation theory. A full description and instructions for use are at Annex 5A. Note 5-1. Visible Hemisphere and Lower Hemisphere. The Celestial Horizon divides the Celestial Sphere into hemispheres, the upper one of which (containing the Observer’s Zenith ‘Z’) is the known as the Visible Hemisphere , and the other one as the Lower Hemisphere. Subject to Atmospheric Refraction, all heavenly bodies in Visible Hemisphere are visible to the observer but bodies in the Lower Hemisphere cannot be seen. The Star Globe displays the Visible Hemisphere and the first 6° of the Lower Hemisphere below the Celestial Horizon. The remainder of the Lower Hemisphere is covered by the Star Globe’s box and mounting arrangements. 0503.
The Star Identifier and The Nautical Almanac Planet Diagram The Star Identifier (NP 323) works in a similar manner to the Star Globe and is described in full at Para 0132. It displays heavenly bodies drawn on the Plane of the Celestial Horizon (see Note 5-2 below.) The Nautical Almanac Planet Diagram is explained at Para 0133. Note 5-2. Plane of the Celestial Horizon. Where it is convenient to show the whole (visible) sky, it must be drawn on the Plane of the Celestial Horizon , as if the Celestial Sphere was seen from a position directly above the Observer’s Zenith (Z). Z appears in the centre of a circle which is the Visible Horizon. The Celestial Equator appears as a curve offset from the c entre by an amount equal to the observer’s Latitude. 0504-0519. Spare
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SECTION 2 - ASTRONOMICAL POSITION LINES 0520.
Introduction Instructions on how to plot Astronomical Position Lines are at Para 0351, but only with an outline explanation of why plotting is carried out in this way. For the convenience of readers, the explanation from Para 0351a is repeated at Para 0521 and a full explanation of this concept follows. Concept (Repeated from Para 0351a) An Astronomical Position Line is actually a small element of the circumference of a Small Circle (see Para 0110) centred on the Geographic Position (see Para 0109) of the star with a radius equivalent to ‘90° - Altitude’, converted into nautical miles. This radius is usually between 1200 n. miles ( Altitude 70°) and 4200 n. miles ( Altitude 20°) in length, and is impossible to plot on any chart of a reasonable scale. However, if the Calculated (Tabulated) Altitude for the DR position is subtracted from the Observed (True) Altitude and the result (converted into nautical miles and known as the ‘Intercept’ ) is plotted from the DR /EP position either ‘To’ or ‘From’ the True Bearing of the star, then plotting at a reasonable scale on a normal chart is possible. Given the large radius of the Small Circle, it is accepted that for short distances the Astronomical Position Line may be considered to be a straight line. 0521.
0522.
The Position Circle It can be seen from Fig 5-2 that the observer’s position is at ‘z’ on the circumference of the Small Circle radius ZX, when it is projected onto the Earth’s surface at ‘zx’ about a centre ‘x’(Geographic Position of heavenly body X). The radius ZX = 90°- AZ, when AZ is the Observed (True) Altitude of the heavenly body. The Angular Distance ‘zx’( which equals ZX) may be converted to nautical miles (1° = 60 n. miles). The circles ZX and ‘zx’ are known as Position Circles.
Fig 5-2. The Position Circle
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0523.
Plotting Position Circles - Ordinary Sights and Very High Altitude (Tropical) Sights The difficulty of plotting most Position Circles ‘zx’ on a chart is explained at Para 0521. However, in the case of Very High Altitude (Tropical) Sights around 89° (see Para 0525, 05500552), the Position Circle is very small and this method is a realistic option. With most ordinary sights even if it were decided to attempt to plot such large distances on a normal mercator chart, the necessary accuracy would be very difficult to achieve due to the distortion of the Latitude scale in this projection. Thus another method of plotting most astro-sights is needed. 0524.
The Intercept (Marq St Hilaire) Method
a. Zenith Distances. The Zenith Distance is the Angular Distance between the Observer’s Zenith and the position of a heavenly body. The Observed (True) Zenith Distance ZX and the Calculated (Tabulated) Zenith Distance Z 2 X are shown at Fig 5-3. In this example the Observed (True) Position Circle is shown as the outer circle and the Calculated (Tabulated) Position Circle as the inner circle. In order to keep Fig 5-3 simple, both circles are shown on the surface of the Celestial Sphere but should be imagined as having been projected down onto the Earth’s surface (in a similar manner to Fig 5-2). The Intercept is the angular difference between Zenith Distances ZX and Z 2 X.
Fig 5-3. True and Calculated Zenith Distances and their Position Circles
b. Difference Between Zenith Distances. Fig 5-3 shows that if the tangents to both Position Circles near the Chosen Position (see Para 0401) are plotted ( vicinity of Z / Z 2 in Fig 5-3), they will approximate the Position Circles and the result will be two straight parallel lines (see Para 0524d opposite). Importantly, the Calculated (Tabulated) Position Circle will always pass through the Chosen Position (DR/ EP). The Observed (True) Position Circle will pass through the Observed (True) Position. c. Example. A similar situation is at Fig 5-4 where an example of a Calculated (Tabulated) Altitude of 40° 00.0' and an Observed (True) Altitude of 40° 05.0' has been used. These give Zenith Distances (90°-Alt) of 50° 00.0' and 49° 55.0' respectively. 5-6 Original
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Fig 5-4. Zenith Distances, Intercept and the Astronomical Position Line
d. Use of the Intercept. At Fig 5-4, the Astronomical Position Line (on which the observer’s position lies), and the Chosen Position line (on which the Chosen Position (DR/EP) lies) are tangents to the circumference of the Position Circle and so are oriented at right angles to the direction of the centre (X) of the Position Circle. Thus they are plotted at their Zenith Distances, as a Rhumb Lines at right angles to the True Bearing of X. Rather than plot tangents from both Position Circles, it is only necessary to plot the Astronomical Position Line at the Intercept distance from Chosen Position (DR/EP), provided it can be established whether to plot it‘To’ or ‘From’ the direction of X. e. Direction of Plotting of Intercept. To establish whether to plot the Intercept in the direction ‘To’ or ‘From’ the direction of X, consider the example at Fig 5-4. Here the Observed (True) Zenith Distance (normally abbreviated to TZD) was less than the Calculated (Tabulated) Zenith Distance (normally abbreviated to CZD) and it is clear that the Intercept has to be plotted towards the True Bearing of X. However, Zenith Distances are defined as 90° - Altitude (see Para 0522) as shown below: Calculated (Tabulated) Zenith Distance of 50° 00.0' = Calculated (Tabulated) Altitude of 40° 00.0' Observed (True) Zenith Distance of 49° 55.0' = Observed (True) Altitude of 40° 05.0'
Thus, as in this case when the Calculated (Tabulated) Altitude (40° 00.0') is smaller (tinier) than the Observed (True) Altitude (40° 05.0') the intercept is plotted ‘To’ the direction of the heavenly body ‘X’. This gives rise to the rule for plotting intercepts normally remembered by the rhyme quoted at Para 0351c: ‘TAB TINIER TOWARDS’
The converse also applies, as shown in Fig 5-3, where TZD > CZD, so the Calculated Altitude > True Altitude. The rhyme refers to the Altitudes, not the Zenith Distances. f. Azimuth. The Azimuth of the heavenly body X is given by the angle PZX (see Para 0501 and Fig 5-1, and also Figs 5-2 and 5-3). 5-7 Original
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0525.
Assumptions made when an Astronomical Position Line is Plotted Four assumptions are made when an Astronomical Position Line is plotted as a (straight) Rhumb Line on a Mercator chart, but all three are justified in normal circumstances because the error induced is negligible. Only in the case of Very High Altitude (Tropical) Sights, when the Observed (True) Zenith Distance (TZD) and thus the associated Position Circle are very small (see Paras 0522-23), are these assumptions inadmissible. The solution for plotting Very High Altitude (Tropical) Sights is to plot the TZD directly from the Geographic Position of the heavenly body as an arc of a circle. The detailed procedures for taking, reducing and plotting this are at Paras 0550-0552. The four admissible assumptions for normal use are:
•
The True Bearing of the Geographic Position of the heavenly body is the same at all points in the vicinity of the Chosen Position (DR / EP) and the Observed Position (Obs Pos).
•
The direction of the Intercept , which is laid off as a (straight) Rhumb Line, coincides with the Great Circle forming the actual line of True Bearing ‘To’ (or ‘From’) the heavenly body.
•
The Astronomical Position Line itself, which is plotted as a (straight) Rhumb Line, coincides with the arc of the Observed (True) Position Circle over the short plotting distances involved on the chart.
•
When plotting multiple Astronomical Position Lines, they are all Run-on / Run-back to a common time (see Para 0351b). It should be noted that NAVPAC 2 does this automatically (see Para 0351c).
0526.
Plotting Sheets and Diagrams Theoretically, an Astronomical Position Line can be plotted on any chart which provides coverage of the required area. However, this is often impractical because the scale of the available chart(s) may be unsuitable. In addition, the construction of Intercepts and individual Position Lines may seriously detract from other information, particularly if astro-navigation is being carried out for training or comparison. The manual plotting of sights is therefore usually carried out on a separate sheet which may also be retained to provide a full record of the sights being taken. If necessary, the Observed Position may be transferred onto the chart being used for navigation. The UK Hydrographic Office (UKHO) produces a series of Mercator Plotting Sheets D6321-D6343 covering Latitudes from 0° to 69°. These may be used by marking on Meridians for East or West Longitudes as required, but in southerly Latitudes the sheet must first be inverted. Additionally, ‘Plotting Sheets for Astro Fixing - D6018' may be obtained from UKHO in pads of 25 sheets. These may be used at any Latitude, but additional Meridians and a separate scale of Longitude need to be constructed, following the instructions printed on the form. These sheets are ideal for plotting the results of simultaneous sights or a Sun-run-Sun, but are generally too limited in coverage for a full ‘day’s run’. CAUTION CARE MUST BE TAKEN ON PLOTTING SHEETS TO LABEL THE SEQUENCE OF MERIDIANS OF LATITUDE AND PARALLELS OF LONGITUDE CORRECTLY, PARTICULARLY IF RECENT WORK HAS BEEN CARRIED OUT IN THE OTHER HEMISPHERE WHERE OPPOSITE CONVENTIONS APPLY. 0527-29.
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SECTION 3 - CALCULATING ALTITUDE, AZIMUTH AND TRUE BEARING 0530.
Introduction Section 3 deals with the methods of determining the Calculated (Tabulated) Altitude, the Calculated (Tabulated) Azimuth and its associated True Bearing . Once these are established, the Intercept may be calculated by subtraction, and the Astronomical Position Line plotted. 0531.
Means of Solving the PZX Triangle In order to determine the Calculated (Tabulated) Altitude, the Calculated (Tabulated) Azimuth and its associated True Bearing , it is necessary to solve the spherical triangle PZX. From Fig 5-5 it can be seen that two sides and the included angle are known, as follows:
• • •
The angle ZPX is the Calculated (Tabulated) LHA of the heavenly body. The side PZ is the Co-Latitude of the Chosen (DR /EP) Position . The side PX is the Calculated (Tabulated) Co-Declination of the heavenly body.
Fig 5-5. PZX Triangle and Other Tabulated Angular Distances based on Chosen Position 0532.
Solution of PZX Triangle for Zenith Distance - Cosine Method As two sides (PZ, PX) and the included angle (ZPX) of the spherical triangle PZX are known, it can be solved by the Cosine Formula (see BR 45(1) App 1), although other methods are possible. The side ZX (the Calculated (Tabulated) Zenith Distance CZD) is given by: Cos ZX = Cos PZ . Cos PX + Sin PZ . Sin PX . Cos ZPX
However: Cos ZX = Cos (90°-Tab Al t) and may be expressed as Sin Tab Alt (see BR 45(1) App 1). Cos PZ = Cos (90°- Lat), and may be expressed as Sin Lat (see BR 45(1) App 1). Cos PX = (90°-Dec), and may be expressed as Sin Dec (see BR 45(1) App 1). Angle ZPX is the LHA of X (see Para 0422), so Cos ZPX may be expressed as Cos LHA. Thus the above Cosine Formula may be more conveniently expressed as: Sin Tab Alt = Sin Lat . Sin Dec + Cos Lat . Cos Dec . Cos LHA 5-9 Original
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0533.
Solution of PZX Triangle for Azimuth - Cosine Method Having established the value of the side ZX (see Fig 5-5 on preceding page), the Cosine Formula can conveniently be used to determine the angle PZX (the Azimuth of X), as follows: Cos PX = Cos PZ . Cos ZX + Sin PZ . Sin ZX . Cos PZX Cos PZX = Cos PX - Cos PZ . Cos ZX Sin PZ . Sin ZX
This expression may be modified in a similar way to the ‘Calculated (Tabulated) Zenith Distance / Calculated (Tabulated) Altitude’ formula at Para 0532 to read: Sin Azimuth = Sin Dec - Sin Lat . Sin Alt Cos Lat . Cos Alt
Azimuth may be converted to True Bearing as described at Para 0535 and shown at Fig 5-6. 0534.
Solution of PZX Triangle for Azimuth - Other Methods Calculation of Azimuth using NAVPAC 2 or a calculator and the formula at Para 0533 is simple, accurate and effective. However, for historical reasons various dating from precalculator times, other methods exist and are described briefly below. See also Paras 0540-0545.
a. Weir’s Azimuth Diagrams. Two diagrams (5000 and 5001) exist and cover Latitudes 0°-65° and 65°-80°. They comprise of superimposed Latitude ellipses and Hour Angle hyperbolas and an outer Azimuth (True Bearing - see Para 0536) ring on a full size Admiralty chart-sized diagram. The diagrams are entered with arguments of Latitude, Hour Angle and Declination, and after a small amount of plotting a reasonably accurate Azimuth (True Bearing - see Para 0536) can be read off. Full instructions for the rather complex plotting procedures are printed on each diagram. b. ABC Tables. The ABC Tables are contained in NP 320 (Nories Nautical Tables) which also contain a brief explanation of the use. The basis of the computation of these tables is the Four-Part Formula which connects adjacent parts of a spherical triangle. In this case these are Co-Declination (sometimes referred to as Polar Distance), Hour Angle, Co-Latitude and Azimuth. The Four-Part Formula expressed in its most convenient form and related to each ABC Table becomes: Tan Dec . Cosec Hour Angle - Cot Hour Angle . Tan Lat = Cot Azimuth. Sec Lat (Table B) (Table A) (Table C)
In practice, Table A is entered with Latitude and Hour Angle to obtain ‘Correction A’ , Table B is entered with Declination and Hour Angle to obtain Correction B’ , which are added or subtracted depending on their respective Names and the rules on each page. The resultant ‘Correction (A ± B)’ and Latitude are used to enter Table C in order to extract the Azimuth. Table C uses a variant of the Four Part Formula which can be expressed as: Correction (A ± B) . Cos Lat = Cot Azimuth Example 5-1.
• • • • •
Latitude 47°N, Declination of Star 52° N and Hour Angle 50°.
From Table A (Lat 47° & Hour Angle 50°) Corrn A = 0.90 S (ie OPPOSITE to Lat) From Table B (Dec 52°N) and Hour Angle 50° Corrn B = 1.67N (see rule at Table) From summation rule at Table C (the DIFFERENCE between Corrns A & B as their NAMES are DIFFERENT), Corrn (A ± B) = 0.77N = Corrn C From Table C (Corrn C 0.77N and Lat 47°), Azimuth = N62.3° W (see rule at Table) True Bearing is thus 360° - 62.3° = 297.7° (see Para 0535 and Fig 5-6)
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0535.
Azimuth and Bearing of a Heavenly Body (RN and UK Maritime Usage)
a. True Bearing. The direction of a heavenly body seen from an observer is its True Bearing and this is measured conventionally as the angle from the Meridian of True North measured clockwise, ie. 0° to 360°. (See Para 0536 below) b. Azimuth. The Azimuth (of a Heavenly Body) is the angle between the observer’s Meridian and the Vertical Circle through the heavenly body. (See Para 0536 below) c. Conversion of Azimuth to True Bearing. Azimuth is measured and named East or West from the Observer’s Meridian ( if LHA of Body <180° Azimuth is West, if LHA of Body > 180° Azimuth is East). Azimuth is named ‘N’ or ‘S’ from the Elevated Pole. Azimuths are always less than 180° and are linked to the True Bearing as shown in the two cases at Fig 5-6. (See Para 0536 below)
Fig 5-6. Conversion of Azimuth to True Bearing 0536. Differences in Meaning of ‘Azimuth’, ‘Azimuth Angle’ and ‘True Bearing’. Some differences of meaning and usage of the terms ‘Azimuth’, ‘Azimuth Angle’ and ‘Bearing / True Bearing’ have evolved between astronomers and some mariners as follows:
a. RN and UK. In the RN and other UK maritime communities, in astro-navigation, the meaning of ‘Azimuth’ and ‘True Bearing’ are as at Para 0535. b. Astronomers. Astronomers use the term ‘Azimuth’ in the sense that Para 0535 uses ‘True Bearing’ (ie measured clockwise from north from 0° to 360°). c. USN and US. In the USN and other US maritime communities, in astro-navigation, the term ‘Azimuth’ is used in the same way as astronomers use it, and another term ‘Azimuth Angle’ , is used to take the meaning of ‘Azimuth’ at Para 0535. d. NAVPAC 2. NAVPAC 2 uses the astronomer’s version of ‘Azimuth’ to mean ‘True Bearing’. 0537-0539. Spare
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SECTION 4 - SIGHT REDUCTION PROCEDURES 0540.
Summary of Methods Available for Sight Reduction and their Accuracies Five methods for sight reduction calculations are available to the mariner; t heir accuracy and the degree of labour involved vary. Details of the procedures for each method (except for NAVPAC 2 which is at Chapter 3) are Paras 0541-0546. Details of Meridian Passage and Polaris calculations are at Para 0348 and Chapter 6. The five available methods are:
•
NAVPAC 2 (Windows-based PC program). The program will calculate an Observed Position to an accuracy of 0.15 nautical miles.
•
Marine Navigation Sight Reduction Tables (NP 401 series). The tables, which are arranged in 6 volumes each of which covers 15° of Latitude, will generally calculate an Observed Position to an accuracy between 0.2 and 0.3 nautical miles.
•
Air Navigation Sight Reduction Tables (NP 303 series). Vol 1 of NP 303 covers all Latitudes and is the only volume of the series used within the RN. NP 303 will generally calculate an Observed Position to an accuracy of 0.5 nautical miles.
•
Nautical Almanac Formulae and Procedures for Programmable Calculators. The potential accuracy of these formulae is comparable to NAVPAC 2 (ie within 0.15 nautical miles) but will in practice depend on the precision of the ephemeral data entered and the capability and use of the calculator.
•
Concise Nautical Almanac Reduction Tables. These concise tables will generally calculate an Observed Position to an accuracy of 1.0 nautical miles, although this could increase to 2.0 nautical miles in certain circumstances.
0541.
NAVPAC 2 Details of the procedures for using NAVPAC 2 on a Windows-based PC for sight reduction calculations are at Chapter 3, and an extract of HM Nautical Almanac Office’s NAVPAC 2 User Instructions is at Annex 3A. 0542.
Explanation of Marine Navigation Sight Reduction Tables (NP 401 series).
a. Arrangement of Tables. These tables (NP 401) provide computed values of Altitude and Azimuth for arguments of Latitude, Hour Angle and Declination tabulated at intervals of 1°. The tables are arranged in six volumes, each nominally covering 15° of Latitude. However, each volume is arranged in two 8-degree sections (or zones) of Latitude; thus the first and last Latitude in each volume overlap those of the preceding and succeeding volumes. NP 401 (a joint US/UK publication) uses the US notation and abbreviations of Azimuth Angle (Z) and Azimuth (Zn) to mean what is known in the RN as Azimuth and True Bearing respectively (see Para 0536). Each volume contains full user instructions and to avoid confusion with these, the terms Azimuth Angle (Z) and True Bearing (Zn) will be used when explaining NP 401 in this section. NP 401 is normally used with the Sight Form (NP 400 or NP 400a) to simplify calculations. b. Arguments. The tables are entered with the Tabulated (or Calculated ) arguments (to the nearest whole degree) of Local Hour Angle (LHA), followed by Latitude, and either Declination (SAME name as Latitude) or Declination (CONTRARY name to Latitude). Whilst neither Latitude nor Declination are sides of the PZX Triangle (see Para 0531 and Fig 5-5), Co-Latitude and Co- Declination are, and the tables make this conversion to provide convenient entry arguments for the user. An extract of a double page from NP 401 is at Fig 5-7 opposite, and shows the arrangement of arguments. 5-12 Original
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Fig 5-7. (0542) c.
Extract of Double-Page from NP 401 Showing Arrangement of Arguments Arrangement of Arguments. The tables arrange the arguments as follows:
•
Choice of Page. It can be shown (see Para 0542e) that up to four ‘different’ PZX triangles can be solved using the same table. To save space, the tables a re arranged to allow this multiple application. The page required is selected by LHA, as follows:
Left-hand Pages. Left-hand pages always show LHAs in the range of 0° to 90° and 360° to 270°, for Latitude and Declination of the SAME name. Right-hand Pages. Right-hand pages ( LHA read from the TOP) are always in the range from 0° to 90° and 360° to 270°, for Latitude and Declination CONTRARY name. Right-hand pages ( LHA read from the BOTTOM) are always in the range from180° to 90° and 180° to 270° for Latitude and Declination of the SAME name. A horizontal line in the table shows the SAME/CONTRARY boundary.
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Latitude. The horizontal argument is Latitude, each of the eight columns on a page being headed by a whole number (integer) degree.
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Declination. The vertical argument is Declination from 0° to 90°, which is always entered as the whole number of degrees equal or below to the actual value (eg. If actual Declination = 68° 53', use 68° for entry to the table). 5-13 Original
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(0542) d. Results from Entering Arguments. On entering the arguments, the table provides Tabulated Altitude (Hc), Altitude Difference (d) and Azimuth Angle (Z). The Tabulated Altitude (Hc) and Azimuth Angle (Z) obtained require further interpolation, as follows:
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Tabulated Altitude (Hc) results from using ‘round-figure’ integer arguments of LHA, Latitude and Declination. Although the differences from the exact LHA and the exact DR/EP Latitude can be resolved by plotting, interpolation for Declination is required to establish the exact calculated Altitude.
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Altitude Difference (d) or ‘d’ is the difference of Altitude in minutes of arc of one Declination entry and that for the next higher degree, and is used with the interpolation table (see Para 0542g) to establish the exac t calculated Altitude.
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Azimuth Angle (Z), once converted to True Bearing (Zn), is normally required to an accuracy of ½° when plotting sights and it may be interpolated to the actual (rather than rounded) value of Declination by inspection, although care must be exercised, particularly when the increments between successive tabulations of Azimuth Angle (Z) amount to several degrees. Each double page of the tables give the rules (which vary with hemisphere and LHA - see Para 0535) for converting the interpolated Azimuth Angle( Z) to True Bearing (Zn).
e. Reason for Multi-Application Arrangement of LHA Argument. It can be seen from Para 0535 and Fig 5-6, that depending on the Elevated Pole and the position of the heavenly body, within the PZX Triangle, there can be four variants of True Bearing (Zn) from a single Azimuth Angle (Z). Eg For an Azimuth Angle (Z) of 45°, depending on the circumstances and the choice of four heavenly bodies observed, the True Bearing (Zn) could be: N45°E = 045°, or S45°E = 135°, or S45°W = 225°, or N45°W = 315° . In exactly the same way, within the PZX Triangle (see Para 0531 and Fig 5-5), where the second angle is the LHA (the angle between the observer’s Meridian and that of each heavenly body), there can be up to four variants of LHA which give the same numerical value, although 2 are positive and 2 are negative (equating to SAME/CONTRARY). This can be demonstrated by Fig 5-8 which is a simple Cosine curve from which it may be seen that: Cos 45° = Cos 315° = +0.707 and, Cos 135° = Cos 225° = - 0.707 Applying this principle to the tables in NP 401, it can be seen that with care, the same table can be used to solve the spherical triangle for up to four LHA and Latitude SAME / CONTRARY combinations. See also Para 0741a.
Fig 5-8. Cosine Curve, Showing Similar Numerical Values of 45°,135°, 225° and 315°
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(0542) f. Selection of the ‘Chosen Position’ to Avoid Latitude and LHA Interpolation. As stated at Para 0542d, the need to make tabular interpolation for the exact values of LHA and Latitude can be avoided by offsetting the plotting of intercepts. This saves both time and the need for much more complex and bulky tables. Instead of plotting the intercepts from the DR/EP position (see Para 0524), as is done when using non-tabular calculator or computer methods (Eg NAVPAC 2), with NP 401 a separate ‘Chosen Position’ is selected for each sight from which the intercept is plotted, so that the errors of entering the tables with a rounded integer figure for LHA and Latitude are exactly compensated. However, the procedure does introduce the possibility of some small errors which are considered at Chapter 9. The ‘Chosen Position’ selection is as follows:
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Chosen Latitude. The ‘Chosen Latitude’ should be the nearest whole degree to the DR. If the DR Latitude is 46° 45´N, the ‘Chosen Latitude’ is 47° N.
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Chosen Longitude. The ‘Chosen Longitude’ is selected so that when applied to the GHA of the body ( ± depending on whether Longitude is E or W, and ± 360°), the resulting LHA is an integer figure. The Nautical Almanac tabulates GHA of heavenly bodies in arc and a suitable Chosen Longitude may easily be selected by inspection. The following examples illustrate this.
Example 5-2. If DR Longitude is 26° 38´W, and the GHA is 58° 18´.3, the Longitude of the Chosen Position will be that nearest to 26° 38´W which makes the LHA a whole degree. Thus:
GHA Chosen Longitude
53° 18.3' 26° 18.3' W ( )
LHA
27° 00.0'
Example 5-3. If DR Longitude is 26° 38´E with the same GHA, then:
GHA Chosen Longitude
53° 18.3' 26° 41.7' E (+)
LHA
80° 00.0'
Example 5-4. If DR Longitude is 166° 38´W with the same GHA, ie greater than the GHA then 360° must be added to the GHA:
GHA
53° 18.3' 360° 00.0' (+)
Chosen Longitude
413° 18.3' 166° 18.3' W ( )
LHA
247° 00.0´
Example 5-5. If the DR Longitude is East and the sum of the GHA and Chosen Longitude exceeds 360°, then 360° must be subtracted:
GHA Chosen Longitude
253° 18.3' 166° 41.7' (+) 420° 00.0' 360° 00.0' (-)
LHA
60° 00.0'
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(0542) g. Interpolation Tables for Declination - Chosen Declination. As stated at Para 0542d, tabular interpolation for Declination is required to compensate for entering the main tables with an integer ‘Chosen Declination’ rather than its exact value. The only alternative to this would be enormously bulky and expensive tables. The Interpolation Tables are split and are located inside the front cover (0.0' to 31.9') and back cover (32.0' to 59.9') of each NP 401 volume; an extract is at Fig 5-9 opposite. The slightly complex procedure for their use is as follows:
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Vertical Argument. The vertical argument is the excess minutes of actual Declination over the integer Declination used to enter the main tables . This is called the ‘ Declination Increment ’ ( Dec. Inc.) and ranges from 0.0' to 59.9'.
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Horizontal Argument. The horizontal argument is the tabulated ‘Altitude Difference (d)’ (see Para 0542d), extracted from the body of the main tables in minutes of arc with sign plus or minus. To save space, the ‘d’ argument is divided into two parts: the first being multiples of 10 minutes of ‘d’ from 10´ to 50´, the second, the remainder (units and decimals), in the range 0´.0 to 9´.9. The interpolation table for ‘tens’ of ‘d’ comprises a column of values for each multiple of 10 minutes set against the vertical argument of Dec. Inc. For the ‘units’ the values are arranged in sub-tables against each range of one minute of Dec. Inc. (10 horizontal lines) with the decimal portion (.0 to .9) as the vertical argument in each sub-table.
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Resulting First Difference Corrections. The interpolation correction for ‘tens’ of ‘d’ is extracted opposite the appropriate Dec.Inc. The correction for the ‘units’ is found in the appropriate sub-table opposite the range of one minute in which the Dec.Inc. occurs. The corrections for ‘tens’ and ‘units’ are then summed. These corrections, known as ‘First Difference Corrections (FDC)’, are then applied (±) to Tabulated Altitude in the same sense of the sign of ‘d’ to obtain the Corrected Tabulated Altitude (Corr Tab Alt) . Calculation and use of the FDC s are shown in the following example:
Example 5-6. LHA 331°, Chosen Latitude 48°N, Declination 2° 28.2'N, Chosen Declination 2° (SAME name).
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The Main Tables (see Fig 5-7 on page 5-13) are entered for Latitude 48° and LHA 331°.
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For declination 2° (SAME ) the Tabulated Altitude (Hc) is found to be 37° 38.9' and ‘d’ is +54.7'.
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Entering the Interpolation Table (Fig 5-9 opposite) for Dec. Inc. 28.2', the correction for ‘tens’ of ‘d’ (50') is 23.5'(+). The correction for ‘units’ (4.7') is 2.2'(+).
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ie.
Tab Alt 37° 38.9' FDC (‘tens’) + 23.5' FDC (‘units’) + 2.2' Corr. Tab Alt 38° 04.6'
‘d’= +54.7' (‘tens’ 50.0' and ‘units’ 4.7')
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Double Second-Difference (DSD) Corrections. On the occasions when the rate of change of Altitude is large relative to a 1° change in Declination, the quantity of ‘d’ will change rapidly, and it may be necessary to make an additional interpolation correction known as the ‘Double Second-Difference (DSD) correction. This correction can be applied for special precision on any occasion, but to indicate when it is necessary to apply it in normal sight work, the quantity ‘d’ in the body of the tables is printed in italics followed by a dot.
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Fig 5-9. Extract of Interpolation Table from NP 401
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(0542g cont)• Resulting Double Second-Difference (DSD) Correction. Second differences are the differences between successive values of ‘d’ , and these are not tabulated; thus the DSD has to be obtained mentally by determining the difference between the tabulated values for ‘d’ immediately below and above the ‘d’ for the Chosen Declination. Using the argument DSD in the column of the interpolation table headed ‘Double Second Diff and Corr’ , the correction is taken from the critical table opposite the appropriate Dec. Inc. The DSD correction is always positive and is applied (+) to Altitude. Calculation and use of the FDC s are shown in the following example: Example 5-7 . LHA 29°, Chosen Latitude 51°N, Declination 46° 35.8'N, Chosen Declination 46° (SAME name), Dec. Inc 35.8'.
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The Main Tables (see Fig 5-7 on page 5-13) are entered for Latitude 51° and LHA 29°. For Declination 46° (SAME name) the Tabulated Altitude (Hc) is found to be 70° 17.1' and ‘d’ is 24.4 ’ with the italics and dot indicating that the DSD correction should be applied. Take the difference between the ‘d’ on the line below that for the Tabulated Altitude (21.8') and the ‘d’ on the line above (26.8') to obtain the DSD (21.8' ~ 26.8' = 5´.0). From the Interpolation Table, obtain the First Difference Correction FDC (tens and units) for Dec. Inc 35.8' and ‘d’ +24.4', by the method previously described. Enter the critical table opposite Dec. Inc 35.8' with DSD 5.0' to obtain the DSD correction 0.3'(+). Tab Alt 70° 17.1' ie. ‘d’ = +24.4' (‘tens’ 20.0' and ‘units’ 4.4') FDC (‘tens’) + 12.0' FDC (‘units’) + 2.6' ‘d’ below = 21.8, ‘d’ above = 26.8 DSD Corrn + 0.3' DSD = 26.8' - 21.8' = 5.0' Corr. Tab Alt 38° 04.6'
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Use of the Sight Form (NP 400 / NP 400A). To reduce the complexity of using h. the NP 401 tables and the possibility of an accidental arithmetic error, a printed Sight Form is supplied in booklets of 24 sheets (NP 400a) or as single sheets (NP400) by the UKHO. Each sheet allows space for calculations for 4 heavenly bodies. It may also be used with NP 303 and as a general aid-memoire.
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Advantages of the Sight Form. This form provides guidance on the sequence in which calculations should be made and also a reminder in some cases of whether to add or subtract certain values. It is also useful as a reminder for calculation of Deck Watch Time, the correct plotting of DR/EP and Chosen Positions, the correct Run-on or Run-back time / distance for each sight, and for the sequence of corrections that must be made to the Sextant Altitude before it can be used to calculate an Intercept . In the worked examples at Paras 0543 and 0544 extracts of the Sight Form are used to demonstrate the calculations.
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Time Necessary for Calculation with NP 401. A navigator familiar with NP 401 should be able to complete a 4-body calculation using the Sight Form in 18 minutes from a standing start. Allowing a further 2 minutes for plotting, using this method it should thus be possible to obtain an Observed Position to an accuracy limited only by skill with the Sextant , within about 20 minutes of finishing observation of Morning or Evening Stars.
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0543. Use of Marine Navigation Sight Reduction Tables (NP 401 series).
a. Summary of NP 401 Procedure Using a Chosen Position . Following the full explanation of NP 401 at Para 0542, and the procedure for plotting sights at Para 0524, it is possible to summarise the entire process as follows. •
Select a Chosen Latitude nearest in whole degrees to the DR / EP Latitude.
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Obtain the GHA of the observed body from The Nautical Almanac, and select a Chosen Longitude, nearest to the DR / EP Longitude, which will make the LHA a whole number of degrees.
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Select the volume of the tables in which the Chosen Latitude is contained and the section covering the appropriate 8-degree zone of Latitude.
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Enter the appropriate section using the LHA to find the double-page required.
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Using Latitude and Declination (SAME) or Declination (CONTRARY), determine whether to use the right-hand or left-hand page.
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Enter the column for Chosen Latitude opposite the Chosen Declination and obtain Tabulated Altitude (Hc) and Altitude Difference (d). If ‘d’ is printed in italics and followed by a dot, note that a Double Second Difference (DSD) correction will be required.
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Obtain the tabulated Azimuth Angle (Z) by interpolation to the actual Declination.
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From the rule printed at the top or bottom of the appropriate page, convert Azimuth Angle (Z) to True Bearing (Z n ).
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Enter the Interpolation Table (inside front/back covers) with the Declination Increment (Dec. Inc) against and the ‘tens’ and ‘units’ of ‘d’ to obtain the First-Difference Correction (FDC). Apply the correction with the sign of ‘d’ .
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Obtain the DSD correction if required. Always apply the correction as a positive correction to the Tabulated Altitude to obtain the ‘Corrected Tabulated Altitude’ (Corr. Tab Alt).
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Compare the ‘Corr. Tab Alt ’ with the Observed (True) Altitude (ie Sextant Altitude corrected for Index Error , Dip and Refraction). The difference is the Intercept.
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Plot the Intercept from the appropriate Chosen Position (including the Run-on or Run-back to allow for time differences(see Para 0351) either Towards or Away from the body’s True Bearing (see Para 0524), using the rule: ‘TAB TINIER TOWARDS’.
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Note that each sight will have a different Chosen Position and care is needed not to plot the wrong Intercept from the wrong Chosen Position.
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In the Sight Form (NP 400/400a) the Stars, Planets, Sun and Moon do not all have exactly the same Nautical Almanac inputs and corrections, due to differing celestial motions. The differences between them are shown in the two (following) worked examples and in The Nautical Almanac.
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An extract from The Nautical Almanac (1997) is at Appendix 2 and will allow the reader to check inputs to worked examples.
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(0543) b. Worked Example of Sun/Moon Sight using NP 401 and The Sight Form. Two worked examples using NP 401 and the Sight Form NP 400 / NP 400a, are as follows: Example 5-8. Sun and Moon Sight . At 1000 (+4) on 23rd October 1997, in DR position 16° 50´N, 65° 47´W, the following observations were taken: Body Sun LL Moon LL
DWT 14 00 05 14 03 00
Sextant Altitude 47° 29.9' 40° 20.9'
Height of eye 9.7 metres (32 feet), Index Error -2.3', DWE 15 secs fast. Assume the ship is stopped and thus there is no Run-on or Run-back between sights. Draw the position lines obtained and determine the Observed Position. •
Comment on Example 5-8 . The position lines and Observed Position are shown at Fig 5-10 below, based on the calculations from a completed Sight Form (NP 400) at Fig 5-11 opposite. The Sun’s Intercept was plotted from ‘A’ (17°N 65° 52.9'W) and the Moon’s Intercept from ‘B’ (17°N 65° 44.0W). The following additional points are relevant when studying the completed Sight Form. Items contained within double quotation marks are so marked to indicate their exact notation on the Sight Form.
No “v” correction is necessary for the Sun. For the Sun, Moon (and Planets) the Declination (called “Tabulated Dec” on the form) and “d”, are copied from The Nautical Almanac at the same time as GHA, and for the Moon only “HP” (Horizontal Parallax). (See Para 0401 for definition / explanation of “Parallax”). The “d corr n” should be extracted from the interpolation tables in The Nautical Almanac with the “GHA Increment ” and “v corr n”. “Tab. Dec.” is obtained by choosing the nearest Declination below the “Dec.” and is the vertical argument for entering NP 401. “1st Alt. Diff.±” refer to the ‘Tens’ and ‘Units’ First Difference Corrections (FDC) respectively, described at Para. 0542g.
Fig 5-10. Plotting of Sun / Moon Sight from Example 5-8
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Fig 5-11. Use of Sight Form (NP 400/400a) to Calculate Intercepts from Example 5-8 5-21 Original
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(0543b cont.) Example 5-9: Planet and Star Sight. At 1900Z on 23rd October 1997, in DR position 14° 05' S, 8° 50' W, the following observations were taken: Body Venus Vega
DWT 18 56 45 19 00 09
Sextant Altitude 39° 59.9' 30° 37.7'
Height of eye 9.7 metres (32 feet), Index Error -2.3', DWE 10 secs slow. Assume the ship is stopped and thus there is no Run-on or Run-back between sights. Draw the position lines obtained and determine the Observed Position. •
Comment on Example 5-9. The position lines and Observed Position are shown at Fig 5-12 below, based on the calculations from a completed Sight Form (NP 400/400a) at Fig 5-13 opposite. Venus’ Intercept was plotted from ‘A’ (14°S 009° 01.8'W) and the Vega’s Intercept from ‘B’ (14°S 009° 05.7'W). The following additional points are relevant when studying the completed Sight Form. Items contained within double quotation marks are so marked to indicate their exact notation on the Sight Form.
For a star, the “Tabulated GHA” is the GHA of Aries to which the star’s SHA is added to give GHA of the star .
The star’s “Tabulated Declination” is copied from The Nautical Almanac at the same time as the “SHA”, and if the star is one of the selected 57, these quantities can be obtained directly from the daily pages; otherwise they may be obtained from the main star table near the back of the book.
Fig 5-12.
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Plotting of Planet/Star Sight from Example 5-9
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Fig 5-13. Use of Sight Form (NP 400/400a) to Calculate Intercepts from Example 5-9 5-23 Original
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0544. Use of Air Navigation Sight Reduction Tables (NP 303 series)
a. Description. NP 303 Volume 1, although designed for the rapid reduction of sights in Air Navigation, is also suitable for use at sea and covers all Latitudes for 7 selected stars. All NP 303 volumes have the same theoretical basis as NP 401 (see Para 0542). NP 303 Volumes 2 and 3 have similar content to NP 401 but with a different layout optimised for air navigation and so are not used in the RN. An extract from NP 303 Volume 1 is at Fig 5-14 opposite and shows the selection of the seven best stars available for observation according to the observer’s position and time. NP 401 provides greater accuracy, but use of NP 303(1) is much faster if the selected stars can be observed. Arguments. The entry arguments for NP 303(1) are Chosen Latitude and the b. LHA of Aries ( ), and the resulting outputs are the Tabulated Altitude (Hc) and the tabulated True Bearing (Zn) of 7 selected stars. The LHA of Aries ( ) is based on a Chosen Longitude to bring the LHA to a whole number of degrees. For the best accuracy, a correction for the Earth’s Precession and Nutation (See Paras 0544e and 0544f below) is needed. The layout of NP303(1) is as follows:
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The first argument is by page; pages are headed by whole degrees of Latitude (North or South). From 69°N to 69°S the tabulations for a single Latitude occupy a complete opening of two facing pages. From 70° to 89° (N and S), tabulations for a single Latitude occupy one page only.
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The second (vertical) argument is LHA Aries ( ) from 0° to 360° at intervals of 1°, except between Latitudes 70° and 89° where the intervals are at 2°. Each page is divided into 2 columns of LHA Aries ( ) in order to maximise the information on each page.
Layout. As can be seen from Fig 5-14 opposite, the 7 selected stars are grouped c. in blocks of 15 lines of LHA Aries ( ). In Latitudes up to 69° this equates to 15° of LHA Aries( ) and in higher Latitudes to 30° of LHA Aries ( ). In all cases, the 7 selected stars remain the same for each 15-line group. This grouping can be seen in Fig 5-14 opposite, which also shows typical changes in the selection of stars from one group of entries to the next. Each selection of 7 stars is arranged from left to right in clockwise order of True Bearing , and 3 stars in each selection are marked with an asterisk a s being suitable in obtaining an observed position. A total of 41 stars are used in Volume 1, of which19 are first magnitude (brighter than magnitude 1.5). First magnitude star names are shown in capital letters.
d. Results. On entering the correct page, column and line of NP 303 (Volume 1), the outputs are Tabulated Altitude (Hc) and True Bearing (Zn). From these the intercept is plotted from the Chosen Position. Corrections. As NP 303 Volume 1 is tailored for a specific ‘Epoch’ year, in e. surface navigation a small correction to the Observed Position should be made to allow for the Earth’s Precession and Nutation (see Para 0544f) if the tables are used in the 5 years either side of the ‘ Epoch’ year. The correction is based on the LHA of Aries ( ) and Latitude, and is applied as a True Bearing and distance to the Observed Position (or Astronomical Position Line). An approximate correction (designed for aircraft use) may be obtained from Table 5 of NP 303(1) but a more accurate version for surface navigation is provided as a separate pull-out supplement to NP303(1).
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Fig 5-14. Extract of NP 303(1) Showing Choices of the 7 Selected Stars Precession, Nutation and Epoch. The Earth is not a sphere but an irregular f. ellipsoid with an equatorial ‘bulge’. The gravitational attractions of the Sun, Moon and Planets acting on the ellipsoid cause a conical motion ( Precession) of the Earth’s rotational axis about the vertical to the plane of the Ecliptic and a further very much smaller continuous but slightly erratic sinusoidal oscillation ( Nutation) superimposed about the Precession motion. Nutation is caused by the varying positions of the bodies (especially the Moon) within the solar system. The result of Precession is a slow westward movement of the intersection between the plane of the Celestial Equator and the plane of the Ecliptic, and thus the Equinox. This causes the positions of the First Point of Aries and First Point of Libra to move slowly with time, and for this reason Precession is sometimes called Precession of the Equinoxes. The time for one complete rotation of Precession is 25,800 years. Thus the SHA and Declinations of stars are subject to small variations over time, and it is for this reason NP 303 (and the Star Globe) are set for an Epoch year but may be used for 5 years before and after this Epoch year. Small annual corrections may be applied from the Epoch year for best accuracy. 5-25 Original
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g. Planning and Reduction of Observations. A Chosen Latitude is selected at the whole degree nearest the DR / EP Latitude of the proposed time of observation (similar to NP 401 procedure). The GHA of Aries ( ) is extracted from The Nautical Almanac and a Chosen Longitude applied to it to obtain LHA of Aries ( ) as a whole number of degrees (similar to NP 401 procedure). The tables are then entered with the Chosen Latitude and LHA of Aries ( ) to find the seven selected stars. Example 5-10. It is proposed to take stars at about 1720(+2) on 13th July, 1997 in DR 42° 12´S, 30° 55´W. Find the stars available for working by NP 303(1).
Chosen Latitude
42° S
Tabulated GHA Aries(UT 17 h) Increment (20m)
186° 36´.7 5° 00´.8
GHA Aries Chosen Longitude
191° 37´.5 30° 37.5W
LHA Aries
161°
Example 5-10. Summary of LHA Calculation
Entering the table for Latitude 42°S, LHA Aries 161° (see Fig 5-14), the selected stars are found to be: Regulus, *Spica, Rigil Kent, *Achernar, Canopus, Sirius and *Procyon. Example 5-11. At about 1720Z on 13th July, 1997, in DR 42° 12´S, 29° 47´W, the following observations were taken: Body Canpous Rigil Kent
DWT Sextant Altitude 05 22 05 45° 38.5' 05 25 22 51° 49.7'
Height of eye 10.9 metres (36 feet), Index Error +1.2', DWE 10 secs fast. Assume the ship is stopped and thus there is no Run-on or Run-back between sights. Find the Intercepts and True Bearings of the heavenly bodies. •
5-26 Original
Comment on Example 5-11 . Items contained within double quotation marks are so marked to indicate their exact notation on the Sight Form.
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The working of the sight is at Fig 5-15. “Corr. Tab Alt” and “True Bearing” are obtained from NP 303(1) (see Fig 5-14).
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The plotting of the sights to obtain the position lines is done in the same way as shown in NP 401 Examples 5-10 and 5-11 (see Figs 5-10 and 512).
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A correction to allow for the effects of Precession and Nutation (see Paras 0544e and 0544f) must be applied as a True Bearing and distance to an Observed Position (or Astronomical Position Line) for star sights worked out by NP 301(1). In the example shown opposite, the position must be moved 1.6 miles towards 120°.
•
An extract from The Nautical Almanac (1997) is at Appendix 2 and will allow the reader to check inputs to worked examples.
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Fig 5-15. Use of Sight Form (NP 400/400a) to Calculate Intercepts from Example 5-11 5-27 Original
BR 45(2) VERBATIM EXTRACT FROM THE NAUTICAL ALMANAC 0545. Use of Nautical Almanac Formulae and Procedures for Programmable Calculators The instructions contained in The Nautical Almanac for reducing sights using a programmable calculator or computer and basic formulae (also to be found in BR 45(5) Chapter 4A, pages 4A-52 to 4A-58) are reproduced verbatim as follows:
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BR 45(2) VERBATIM EXTRACT FROM THE NAUTICAL ALMANAC 0546. Use of Concise Nautical Almanac Reduction Tables The instructions contained in The Nautical Almanac for reducing sights using The Nautical Almanac Concise Sights are reproduced verbatim as follows. (This explanation and a copy of the tables themselves may also to be found in BR 45(5) Chapter 4A, pages 4A-59 to 4A93.)
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An extract of The Nautical Almanac Concise Reduction Tables is at Fig 5-16 (see Page 5-38). The full Concise Reduction Table is also at BR 45(5) Annex 4A Pages 4A-62 to 4A-93 .
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Fig 5-16. Extract of Nautical Almanac Concise Reduction Tables. The full Concise Reduction Table is also at BR 45(5) Annex 4A Pages 4A-62 to 4A-93 .
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BR 45(2)
SECTION 5 - VERY HIGH ALTITUDE (TROPICAL) SIGHTS 0550. Practical Observation at All Altitudes Use of Very High Altitude (Tropical) Sextant Observations. At Sextant a. Altitudes approaching 90° it is possible to obtain a ‘3 Position Line’ fix at the Sun’s Mer Pass.
b. Normal Range of Sextant Altitude Observations. The normal observation range of Sextant Altitudes of heavenly bodies is between 30° and 60° (Para 0339j). It is possible to observe heavenly bodies outside this range of altitudes, but inexperienced Sextant users will find it progressively more difficult to do so accurately towards the extremes of altitude. In practice, for the reasons explained below, heavenly bodies are normally observed within the normal range of 30° to 60°, with occasional observations between Sextant Altitudes of 10° - 30° and 60° - 70° when there are no alternative bodies for observation (see Paras 0550c and 0550d). In addition‘Very High Altitude (Tropical) Sight ’ observations of the Sun at Sextant Altitudes of 88½°- 89½° may be taken (see Para 0550e), but considerable skill with a Sextant is need to achieve accurate results. c. Low Altitude Sextant Observations. At Sextant Altitudes below 30°, the arc through which the star ‘moves’ when the Sextant is ‘swung’ (see Para 0339l) becomes increasingly constrained and thus it becomes progressively more difficult to judge the instant at which the heavenly body’s arc of movement becomes a tangent to the horizon. At Sextant Altitudes below 10° this effect is very pronounced and in addition the altitude corrections for refraction become more difficult to predict accurately. However, the large radius of the Position Circle generated by a low Sextant Altitude does mean that the associated Position Line approximates a straight line very closely (see Paras 0351a / 0521) and thus minimises any ‘Intercept’ method plotting errors in this respect. High Altitude Sextant Observations. At Sextant Altitudes above 60°, the arc d. through which the star ‘moves’ when the Sextant is ‘swung’ (see Para 0339l) becomes increasingly large and thus it becomes progressively more difficult to judge the direction at which the heavenly body has reached its maximum altitude in the Sextant field of view. Above Sextant Altitudes of 70°, the small radius of the Position Circle generated means that the associated Position Line no longer approximates a straight line (see Paras 0351a /0521); if long Intercepts are used, plotting becomes progressively less accurate. Very High Altitude (Tropical) Sextant Observations. At Sextant Altitudes e. approaching 90°, the True Bearing effect at Para 0550d is so marked that it is possible to keep the Sun in the Sextant ’s field of view while the observer makes a 360° turn on the spot. Such extreme circumstances make it difficult to ‘swing’ the Sextant and look down the correct True Bearing to observe the maximum altitude of the Sun. However, in the hands of a skilful Sextant user it is possible to make an accurate observation of the Sun at a Sextant Altitude of up to 89½°, and in practice, this is the only body which can be observed in this way. The resultant Position Circle has such a small radius that it has to be plotted on the chart as a circle, centred on the Geographic Position of the Sun. This method introduces a further error, due to the distortions of plotting a true circle on a Mercator chart. In practice this method of plotting can only be used without significant error for an Observed (True) Altitude (ie Sextant Altitude corrected for errors) of 88½° and above. The maximum plotting errors for various Observed (True) Altitudes of the Sun using this method are: 2.8' error at 86°, 0.5' error at 87°and 0.25' error at 88½°. Due the combination of the plotting and Sextant errors, Very High Altitude (Tropical) Sight s may only be usefully observed between Sextant Altitudes of about 88½°-89½°. 5-39 Original
BR 45(2)
0551. Planning, Taking and Reduction of Very High Altitude (Tropical) Sights
a. Occurrence of Very High Altitude (Tropical) Sights. Very High Altitude (Tropical) Sights of the Sun only occur when the observer’s Latitude is within about 1½° of the Sun’s Declination. This limits these observations to tropical Latitudes (ie between 23½° North and South). Very High Altitude (Tropical) Sights of the Sun taken around the time of Mer Pass give a ‘3 Position Line’ astro-fix over a period of 6-10 minutes. b. Planning of Very High Altitude (Tropical) Sights. If the ship will pass within 1½° of the Sun’s Declination at Mer Pass, a calculation should be made to establish the optimum time interval between the ‘triple’ 3 Sun sights, so that the middle ( Mer Pass) sight provides a latitude, and the other two provide good cuts of about 45° to the Latitude. Depending on the angular difference between the observer’s Latitude and the Sun’s Declination this time interval will vary, but is likely to be between 3 and 5 mi nutes. It is also prudent to plan two further observations, one before and one after the ‘triple’ observation, at the same time interval. This will be a invaluable to help the observer’s eye and hand to become familiar with the peculiar difficulties of taking sights at such very high altitudes and also to provide spare backup readings in case an error is made with one of the primary ‘triple’ sights. Avoiding a Mirror Image of the True Fix. It is also important to note whether c. the ship is to pass to the North or South of the Sun when it crosses the Observer’s Meridian and plot the results accordingly, as it is perfectly possible to plot the mirror image of the true fix on the wrong side (North or South) of the Sun’s Geographic Position. This error is most likely if the observer is very close to the Geographic Position of the Sun at the time of observation, but it is possible with any Very High Altitude (Tropical) Sight unless particular care is taken. Calculation of the Sun’s Predicted Geographic Positions. Start by calculating d. the time of the Sun’s Mer Pass (see Paras 0325 / 0326 and Para 0606) and use this as the preferred time for the middle observation. The use of the Chart Method described at Para 0606 will be found to be the most convenient method of doing this. With the exact Mer Pass time, establish the Sun’s Geographic Positions for the other observations and their optimum times. The whole planning procedure is as follows:
•
The Sun’s Declination equates to the Geographic Position’s Latitude.
•
The Sun’s Geographic Position’s Longitude equates to: Sun’s
GHA (± 360° if required) + Longitude (E) = 360°
Sun’s GHA (±
5-40 Original
360° if required) - Longitude (W) = 360°
Having established and plotted the Sun’s Geographic Position for Mer Pass, from the chart select two further Longitudes (at the same Latitude) which would provide a good cut of Position Lines. From the Longitudes of these Geographic Positions, carry out the same (above) calculation in reverse, to establish the optimum times for the first and third observations of the ‘triple’ observation.
Repeat this procedure to establish times for two further observations (one before and one after the ‘triple’) both as practices and backup readings.
These 5 times are the planned times of observation.
Do NOT use these ‘planning’ Geographic Positions for plotting the fix.
BR 45(2)
e.
Taking Very High Altitude (Tropical) Sights.
(1) Closing Up. The observation team should close up in good time and start tracking the Sun through the Sextant to allow the observer’s eye and hand to become familiar with the difficulties of taking sights at such very high Altitudes. (2) True Bearing Shift and Field of View. As the Sun’s Altitude increases it will become increasingly difficult to determine the direction in which to point the Sextant in order to achieve the maximum altitude in the Sextant ’s field of view. This is particularly the case as the time of Mer Pass is reached; in this phase the Sun’s True Bearing shifts very rapidly from the East, through North or South to West and the observer needs to be very alert to keep up. The ships course may need to be adjusted to give the observer a clear field of view over the required range of True Bearings. (3) Countdown and Records. The observer’s assistant should give a regular countdown of time to the planned moments of observation. It is not essential to take the observations at the exact moment planned, but is better to take them when the observer is happy with the Sextant Altitude at a time close of the planned moment for observation. Differences of up to 15-30 seconds in the actual time of observation from the planned time of observation can be accommodated in the plotting of results without too much penalty, but any greater differences will result in progressively worse cuts of the Position Lines. The exact Deck Watch Time of each observation must be recorded, together with the Sextant Altitude. (4) Hot Sextant Errors. By their very nature, observations of Very High Altitude (Tropical) Sights of the Sun take place in very hot conditions and (unlike a simple Mer Pass sight) it is not possible to avoid exposing the Sextant to the direct heat of the Sun for a long period. It is thus essential to allow the Sextant time to heat up to the ambient temperature (especially if it has been stored in an air conditioned area) and to remove all the errors while it is in the ‘hot’ state. Failure to do this will result in sufficiently large errors in the observed Sextant Altitude to negate the accuracy of the fix completely, which in turn wil l bring the whole procedure into disrepute. f. Reduction of Very High Altitude (Tropical) Sights. The reduction of Very High Altitude (Tropical) Sights of the Sun is very simple and requires the following steps: •
Correct Sextant Altitude for Index Error , Height of Eye and Altitude corrections ( Altitude corrections include Semi-Diameter and Refraction).
•
Correct Deck Watch Time for Deck Watch Error to arrive at UT .
•
Calculate the Geographic Positions for each sight (see Table 5-1).
•
Calculate the Run on / Run back for each sight.
•
Calculate the True Zenith Distance (90°-Altitude) for each sight (see Table 5-2).
•
Plot the TZD from the ‘Run’ Geographic Position for each sight (see Table 5-2), taking care NOT to plot a mirror image of the true fix.
•
Read off the Observed Position.
An example of these calculations and a plot of the results will be found on the next two pages. 5-41 Original
BR 45(2)
Very High Altitude (Tropical) Sight Example 5-12. At Zone Time 1225( -6), on 20 January 1997, in DR position 20° 55.0'S 86° 45.0'E, course 300°, speed 18, the following observations of the Sun (LL) were taken (Deck Watch Error, Index Error, Height of Eye and Refraction corrections have already been applied to these results). Sun LL DWT Observed (True) Altitude (1) 06 20 02 UT 88° 42.1' (2) 06 24 02 UT 89° 05.9' (3) 06 28 02 UT 88° 41.9' Obs. 1
06 20 02 UT
Dec
Geographic Position (1) Obs. 2
06 24 02 UT
06 28 02 UT
GHA Sun Long (E) Total
272° 15.1' 087° 44.9' 360° 00.0' 087° 44.9'E
GHA Sun Long (E) Total
273° 15.1' 086° 44.9' 360° 00.0' 086° 44.9'E
GHA Sun Long (E) Total
274° 15.0' 085° 45.0' 360° 00.0' 085° 45.0'E
20° 05.9'S
Dec
Geographic Position (2) Obs. 3
S 20° 05.9'
True Bearing 046° approx 000° approx 313° approx
S 20° 05.8'
20° 05.8'S
Dec
Geographic Position (3)
S 20° 05.8'
20° 05.8'S
Table 5-1. Calculation of Geographic Positions
The 3 Geographic Positions must be Run on / Run back to a common time (0625 UT ) on course 300° speed 18, as follows: Obs (1) - 06 20 02 UT Run on 1.5 n miles, Obs( 2) - 06 24 02 UT Run on 0.3 n miles, Obs (3) - 06 28 02 UT Run back 0.9 n miles. From the Observed (True) Altitude, the True Zenith Distance (90° - Altitude) is calculated (see Table 5-2 below). Observation
Obs (1)
Obs (2)
Obs (3)
Approx Bearing of Sun
046°
000°
313°
90° Observed (True) Altitude TZD (angle) TZD (n miles )
90° 00.0' 88° 42.1' 01° 17.9' 77.9 n miles
90° 00.0' 89° 05.9' 00° 54.1' 54.1 n miles
90° 00.0' 88° 41.9' 01° 18.1' 78.1 n miles
Geographic Position (from Table 5-1)
20° 05.9'S 087° 44.9'E
20° 05.8'S 086° 44.9'E
20° 05.8'S 085° 45.0'E
Run on / back
On 1.5 n miles
On 0.3 n miles
Back 0.9 n miles
Table 5-2. Calculation of True Zenith Distances, with Summary of Approximate True Bearings of Sun, Geographic Positions and Runs
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0552. Plotting Very High Altitude (Tropical) Sights The True Zenith Distances (see Table 5-2) are plotted as the arcs of circles from their respective ‘run’ Geographic Positions. Care must be taken NOT to plot a mirror image of the true fix. The results of Table 5-2 are plotted at Fig 5-17 below.
Fig 5-17. Plot of Very High Angle (Tropical) Sight Example 5-12 Results (see Table 5-2)
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SECTION 6 - HIGH LATITUDE (POLAR) SIGHTS 0560. Taking High Latitude (Polar) Sights a. Use of a Sextant in Polar Temperatures. When a Sextant is brought from the warmth of the ship or submarine into the open air at high Latitudes, condensation will form on the mirrors and glasses. This will freeze almost instantaneously, making the Sextant unusable. To prevent this happening, place the Sextant inside an airtight polythene container before taking it outside. Then allow it to cool down in the open air. On removal from the container, about 10 minutes will be available for taking observations before the mirrors ice over.
b. Abnormal Refraction. Conditions of Abnormal Refraction sometimes cause errors of 2 or 3 in lower Latitudes. In polar regions, Abnormal Refraction errors measured in degrees are not uncommon and an extreme value of 5° has been reported. This error would cause the Sun to rise ten days earlier than expected and would produce an error of 300 miles in a Position Line. c. Temperature and Pressure. If conditions of temperature and pressure appear to be other than standard, the additional correction shown in Table A4 i n The Nautical Almanac must be used. (Table A3 gives the normal Altitude corrections to Apparent Altitude of 10 down to zero for the Sun, Stars and Planets.) If more extreme conditions are likely to be encountered application should be made to the UK Hydrographic Office (UKHO) for additional tables. d. False Horizons and Dip. When navigating close to ice, the estimated height of ice above water at the horizon must be subtracted from own height of eye before applying Dip. Corrections tabulated for Dip allow for standard Refraction, but when conditions are abnormal the correction will be wrong. Time Zones. Time Zones have little width or meaning near the poles, so UT e. (GMT) is normally kept. 0561. Reducing High Latitude (Polar) Sights High Latitude (Polar) Sights may be reduced by NAVPAC 2 or the normal use of NP 401, but when in Latitudes above 87½° an abbreviated method of reduction (see Para 0561c below) and plotting is possible using the Pole as the Chosen Position. This latter method is only likely to be taken by submariners, unless overland expeditions are anticipated. NAVPAC 2. NAVPAC 2 is the simplest and easiest method for reducing High a. Latitude (Polar) Sights. The DR / EP position may be used as the basis for the calculation, but if it is preferred to plot intercepts from the Pole, the Latitude to be used on the NAVPAC 2 Sights-Fix page may be set to the Pole (but see the caveat at Para 0561c below). However, NAVPAC 2 will not accept 90°00.0' (it resets to 00° 00.0'); the Latitude should be set to 89° 59.9' instead. The accuracy of the calculation is unaffected by either of these options. NP 401 using a ‘Normal’ Chosen Position. NP 401 may be used in the b. conventional manner with a ‘Normal’ Chosen Position at all Latitudes and an example of this calculation is at the High Latitude (Polar) Sights Example 5-13 on the page opposite; the resulting plot is shown at Fig 5-19. Fig 5-19 also shows the alternative method of plotting when the Pole is used as the Chosen Position (see Para 0561c below).
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BR 45(2)
High Latitude (Polar) Sights Example 5-13: Using a ‘Normal’ Chosen Position . At 1235(Z) on 17 April 1994, in DR position 88° 48.0'N 014 18.0'E, stopped in the water, the following observations were taken. What was the observed position at 1235(Z)? Body DWT Sextant Alt Sun LL 12 31 27 UT 11° 35.0' Moon LL 12 35 29 UT 19° 17.9' Deck Watch Error 1 minute 5 seconds slow, Index Error +0.5, Height of Eye 6.1 metres, thickness of ice on horizon 1.0 metre, temperature -7°C, pressure 990 mb.
Fig 5-18.
High Latitude (Polar) Sights Example 5-13, Using ‘Normal’ Chosen Position Nautical Almanac extract (1994) is at Para 0561e. 5-45 Original
BR 45(2)
c. Using the Pole as the Chosen Position. NP 401 is not required for this method and the reduction calculation is less laborious than with NP 401. Provided the DR/EP position is within 2½° of the Pole and the Sextant Altitude is less than 70, the Pole itself can be used as the Chosen Position. An example of this calculation is at High Latitude (Polar) Sight s Example 5-14 (with the same data as in Example 5-13) on the page opposite; the resulting plot is shown at Fig 5-19 below. Fig 5-19 also shows the alternative method of plotting when a ‘Normal’ Chosen Position is used (see Para 0561b above). • The GHA is the direction of the Intercept from the Pole (Chosen Position). •
Above Sextant Altitudes of 70°, the small radius of the Position Circle generated means that the associated Position Line no longer approximates a straight line (see Paras 0351a / 0521); if long Intercepts are used, plotting becomes progressively less accurate.
d. NP 303 Volume I. For selected stars, High Latitude (Polar) Sights may be reduced with NP 303 in lieu of NP 401 (see Para 0561b above). The accuracy of reduction is sacrificed slightly for the sake of speed (see Para 0544).
Fig 5-19. Plot of High Latitude (Polar) Sights Examples 5-13 and 5-14 Note 5-3. Fig 5-19 (above) shows the sight plotted for the‘NP 401’ and ‘Polar’ methods from the results of Figs 5-18 and 5-19. True Bearings f or the NP 401 method are plotted by drawing a line from the Chosen Position through the Pole and taking this as the 000° line. A protractor, centred on the Chosen Position and aligned with the 000° line is then used to plot the Intercepts.
5-46 Original
BR 45(2)
High Latitude (Polar) Sights Example 5-14: Using the Pole as Chosen Position . At 1235(Z) on 17 April 1994, in DR position 88° 48.0'N 014 18.0'E, stopped in the water, the following observations were taken. What was the observed position at 1235(Z)? Body DWT Sextant Alt Sun LL 12 31 27 UT 11° 35.0' Moon LL 12 35 29 UT 19° 17.9' Deck Watch Error 1 minute 5 seconds slow, Index Error +0.5, Height of Eye 6.1 metres, thickness of ice on horizon 1.0 metre, temperature -7°C, pressure 990 mb.
Fig 5-20.
High Latitude (Polar) Sights Example 5-14, Using Pole as Chosen Position Nautical Almanac extract (1994) is at Para 0561e. 5-47 Original
BR 45(2)
e.
Extract of The Nautical Almanac (1994) for use with Examples 5-13 and 5-14.
Fig 5-21. Extract from The Nautical Almanac (1994) for use with Examples 5-13 and 5-14. 0562. Plotting High Latitude (Polar) Sights Mercatorial Plotting Sheets. These are available up to 69, after which plotting a. sheet 5004 should be used up to 75°. It is of note that the Intercept is, in reality, a Great Circle (Para 0524) and the Position Line itself is a Small Circle (Para 0521), although they are normally approximated to straight lines without significant error at moderate Latitudes. In high Latitudes, due to the errors associated with the convergence of Meridians at the Pole, for the best accuracy Intercepts and Position Lines should be plotted as curves; this is especially so if the Intercept is long. This is impracticable on a Mercator projection and so other methods are needed above Latitude75°. USHO 5600. Between 75°of Latitude and the Pole, a polar stereographic b. projection (see BR 45(1) Chapter 4) is required. The US Hydrographic Office polar plotting sheet USHO 5600 is ideal and can be obtained from America by the UK Hydrographic Office (UKHO). There is no British equivalent.
c. Form S.376. Form S.376 (Manoeuvring Form) is recommended between 88°of Latitude and the Pole. An example of the use of Form S.376 for this purpose is at Fig 519. USHO 5600 portrays only a quadrant, which may be inconvenient so close to the Pole. True Bearings on Polar Projections. True Bearings must be measured by d. protractor (or station pointer) from the relevant point of reference on polar stereographic projections. When the ‘Polar’ method is used True Bearings are plotted from the Pole and thus the printed graticule may be used for True Bearings. When using the NP 401 method and plotting from the Chosen Position (or any other position) the procedure at Note 5-3 should be used (see under Fig 5-19, at Para 0561d). 5-48 Original
BR 45(2)
ANNEX A DESCRIPTION AND SETTING OF THE STAR GLOBE 1.
Description of the Star Globe The Star Globe is used to explain astro-navigation theory (see Para 0502). It consists of a globe on which the stars, parallels of Declination, the Celestial Equator , the Ecliptic and the Celestial Meridians at 15° intervals are shown. Approximately one Visible Hemisphere can be seen at a time. The Celestial Equator carries two scales: on the north side RA in degrees so that LHA can be set onto it directly, and on the south side, RA in units of time. The globe revolves about the Axis through the Celestial Poles, in a vertical brass ring which is graduated in degrees and represents the Observer’s Meridian. The Pole can be elevated for setting Latitude. The outer edge of the Azimuth ring is graduated in degrees. A four-quadrant hemispherical cage graduated in degrees is fitted over the globe; the Observer’s Zenith lies at the point of intersection of the quadrants. In summary, the globe can be easily set to show the Visible Hemisphere at the correct orientation for any time and place of observation.
Fig 5A-1. Star Globe 5A-1 Original
BR 45(2)
2.
Setting the Star Globe Planets may be marked on the globe in chinagraph using their tabulated Declination and Right Ascension RA (which is 360°- SHA). The Elevated Pole is set to the Altitude on the quadrant corresponding to the observer’s Latitude. The globe is revolved until the computed LHA of Aries appears under the Meridian ring; this quantity is the same as the RA. The brass cage is turned until one of the Altitude quadrants lies along the True Bearing of the body on the Azimuth ring, and then move the small cursor to the required Altitude. The cursor will indicate the Star that has been observed, or, if no Star is indicated, the position of the Planet.
Example 5A-1. At ZT 0600(+1) on 21st October, 1997, in DR position 45°N, 15°W, the altitude of a bright body bearing 200° is 26°. What is it?
ZT Zone
0600 21st October +1
UT/Date
0700 21st October
GHA Aries Longitude
134° 45´.9 15° 00´.0W
LHA Aries
120° (to nearest whole degree)
Example 5A-1. Summary of LHA Calculation
1. Elevate the north Celestial Pole on the globe to correspond to Latitude 45°. 2. Revolve the globe in the ring until Meridian 120° appears under the Meridian ring. 3. Turn the brass cage until one of the Altitude quadrants lies along True Bearing 075° and then move the cursor along this quadrant to 26°. Sirius lies under the cursor. Example 5A-2. At ZT 1900( 4) on 21st October, 1997, in DR position 30°S, 55°E, the altitude of the brightest of 2 bodies close together bearing 260° is 40°. What is it?
ZT Zone UT/Date
1900 21st October 4 1500 21st October
GHA Aries Longitude
255° 05´.6 55°E
LHA Aries
310° (to nearest whole degree)
Example 5A-2. Summary of LHA Calculation
1. Elevate the south Celestial Pole on the globe to correspond to Latitude 30°. 2. Revolve the globe in the ring until the Meridian 310° appears under the Meridian ring. 3. Adjust the brass cage to bearing 260° and the cursor to Altitude 40°. No bright star appears in the position indicated, the position lies close to the Ecliptic and the body must therefore be a planet. From the scale along the Celestial Equator, its Right Ascension is seen to be 252°. The SHA is therefore 108° and its Declination is about 25°S. The Nautical Almanac shows that Venus and Mars have SHAs and Declinations approximating to these values on the day. Venus, being known to be the brightest of the two, was the body observed.
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CHAPTER 6 MERIDIAN PASSAGE AND POLARIS CONTENTS SECTION 1 - MERIDIAN PASSAGE
Definition and Use of Meridian Passage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Upper Meridian Passage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lower Meridian Passage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Moment of Meridian Passage - Maximum Altitude and Time . . . . . . . . . . . . . . . . Reason for Possible Difference in Maximum Altitude and Time of Mer Pass . . . . . . . Meridian Passage of the Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Meridian Passage of the Moon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Meridian Passage of Aries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Upper Meridian Passage of Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lower Meridian Passage of Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Meridian Passage of Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculation of Latitude at Meridian Passage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Para 0601 0602 0603 0604 0605 0606 0607 0608 0609 0610 0611 0612
SECTION 2 - POLARIS
Position and Movement of Polaris around the North Celestial Pole . . . . . . . . . . . . . . . Obtaining Latitude by the Altitude of Polaris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Obtaining True North by the Bearing of Polaris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Observation of Polaris at Twilight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NAVPAC 2 - Polaris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0620 0621 0622 0623 0624
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INTENTIONALLY BLANK
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CHAPTER 6 MERIDIAN PASSAGE AND POLARIS SECTION 1 - MERIDIAN PASSAGE 0601. Definition and Use of Meridian Passage. The Meridian Passage (Mer Pass) of a heavenly body occurs when it is in the Observer’s Meridian or in the Meridian 180° from the Observer’s Meridian. At that moment, the Local Hour Angle of the heavenly body will be either 0° or 180°, and the heavenly body is either due North or due South (ie. bearing 180° or 000°) from the observer. The Position Line obtained, being at right-angles to the bearing, will instantly give the observer’s Latitude. Although sights can be taken for the Meridian Passage of any heavenly body, it is normally only observed for the Sun. Occasionally, Jupiter and Venus may also be usefully observed by day. 0602.
Upper Meridian Passage Upper Meridian Passage occurs when the heavenly body is on the Observer’s Meridian. The Local Hour Angle of the body is then 0°. In the northern hemisphere, the True Bearing of the heavenly body is 180° or 000° depending on whether the Latitude is greater or less than its Declination (both with the SAME name); when the Latitud e and Declination have CONTRARY names the bearing away from the North Pole and thus is 180°. In the southern hemisphere, these bearings are reversed. A diagram showing an example of Upper Meridian Passage for the northern hemisphere with Latitude greater than Declination and both with SAME names is at Fig 6-1 below. A further example for the southern hemisphere with Latitude less than Declination and both with SAME names is at Fig 6-2 overleaf. These diagrams also show the Lower Meridian Passage (see Para 0603 below).
Fig 6-1. Mer Pass (Northern Hemisphere): Latitude > Declination, SAME Names
6-3 Original
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0603.
Lower Meridian Passage
a. Occurrence. Lower Meridian Passage occurs when the heavenly body is on the Meridian that differs in Local Hour Angle from the Observer’s Meridian by 180°. A limited explanation of Lower Meridian Passage is also contained at Para 0348i for those readers who do not require to study the theory of the phenomenon. b. Bearing. The Local Hour Angle of the heavenly body is 180° at Lower Meridian Passage and in the northern hemisphere, when the body is visible, the bearing is always towards the North Pole and so 000°, irrespective of whether the Declination or the Latitude has the larger value. In the southern hemisphere the bearing is always the bearing is always away from the North Pole and so 180°. A diagram showing an example of Lower Meridian Passage for the northern hemisphere with Latitude greater than Declination and both with SAME names is at Fig 6-1 (previous page). A further example for the southern hemisphere with Latitude less than Declination and both with SAME names is at Fig 6-2 below. These diagrams also show the Upper Meridian Passage (see Para 0602 above).
Fig 6-2. Mer Pass (Southern Hemisphere): Latitude < Declination, SAME Names
c. Limitations. When the Latitude and Declination have CONTRARY names, the Lower Meridian Passage can never be observed, because the body is below the horizon. Except in very high Latitudes in summer, the Sun’s Lower Meridian Passage cannot be observed. A few stars may be observed at Lower Meridian Passage. For these reasons, the mariner is chiefly concerned with the Upper Meridian Passage. d. Nomenclature. Unless otherwise stated, within BR 45 the term ‘ Meridian Passage’ / Mer Pass always refers to Upper Meridian Passage. The Lower Meridian Passage is also known as the ‘Meridian Passage Below the Pole’ but this usage is rare. 6-4 Original
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0604.
The Moment of Meridian Passage - Maximum Altitude and Time
a. Misconception about Mer Pass Sights. There is a widely held misconception that the moment of Meridian Passage always occurs at the highest observed Altitude of the heavenly body. This concept is true for a stationary observer, or one travelling due east or west. However, if the observer’s movement has any appreciable north/south component, then taking the Mer Pass sight at the moment of highest Altitude rather than when it is in the Observer’s Meridian (ie bearing 180° or 000°), will induce an error of up to 5 nautical miles. An explanation of the reasons for this potential error are at Para 0605 below. b. Timing of Mer Pass Sights. Attempting to establish the moment of Mer Pass by taking an accurate bearing of a high heavenly body has practical difficulties and introduces the risk of error due to compass inaccuracie s. Thus the accepted method is to take Mer Pass at the exact time predicted for this phenomenon . This may be established to the nearest second by using the time selection in NAVPAC 2's ‘Findit’ program in an iterative manner (see Para 0326) or by making a manual calculation to the nearest minute from The Nautical Almanac (see Para 0325b). The use of NAVPAC 2 is the preferred method for the reasons given in Para 0326. See also Para 0348. 0605.
Reason for Possible Difference in Maximum Altitude and Time of Mer Pass To a stationary observer, the Altitude of a heavenly body at Mer Pass is the maximum Altitude observed, and to obtain an accurate Sextant Altitude, it is only necessary to watch the body over a short period and record the maximum altitude observed. Three factors govern the change in a heavenly body’s Altitude to a greater or lesser degree: the rotation of the Earth, the Declination of the heavenly body and any component of North-South movement.
a. Rotation of the Earth. The rotation of the Earth ensures that a body appears to rise in the East, attains a maximum altitude and sets in the West. This gives rise to the normal movement of the Sun and other heavenly bodies across the sky and with which everyone is familiar. b. Declination of the Heavenly Body. The effect of Declination is not of concern in practice, as the error induced is too small to be significant. In theory, any change in the time of observation induces a change in Declination which alters the position of X or X’ (Figs 6-1 and 6-2) in relation to Z and thus alters the Altitude. However, the short time difference between Mer Pass and the moment of greatest Altitude is too small to change the Declination of the heavenly body significantly and this error may be ignored. c. North-South Component of Movement. Any North-South component of movement introduces a small but significant error, because it is equivalent to a movement of Z (see Figs 6-1 and 6-2). The Earth’s rotation by itself would give the altitude its greatest value when the heavenly body reached the Observer’s Meridian. If the ship is moving towards the body (ie North or South), the Altitude will increase for a further period until the rate at which the body’s Altitude is decreasing due to the Earth’s rotation becomes equal to the rate at which the movement of the ship is increasing the Altitude. The greatest Altitude therefore occurs after Mer Pass. Conversely, if the ship is moving away from the heavenly body, the greatest Altitude occurs before Mer Pass. The time difference between the two Altitudes may lead to an error of up to 5 nautical miles for a ship with a North-South course component, depending on course and speed. There is no error for a ship on an East-West course. 6-5 Original
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0606.
Meridian Passage of the Sun
a. Background. No appreciable error is introduced if it is assumed that the Sun’s apparent motion to the westward is exactly 15° of Longitude per hour. The tabulated GHA of the Sun in The Nautical Almanac shows that the hourly change in GHA is almost exactly 15° throughout the year. b. Calculation Method. The time of the Sun’s Mer Pass may thus easily be calculated at shown at Para 0325b. Example 3-2 which was given at Para 0325 (Mer Pass at 1210, at 25° W, in Time Zone O(+2)) shows this calculation and is repeated below for the convenience of readers. Mer Pass Time from Nautical Almanac
1210
Longitude (W+ or E-) 25°W
+0140
Local Mean Time UT (GMT)
1340Z
Zone(+2) (+ = subtract) (- = add) Zone Time
-0200 1140(O)
Example 3-2 (Repeated from Para 0325). Summary of Sun Mer Pass Calculation
c. Chart Method. The time of Mer Pass calculated above may need to be refined with a second approximation. Successive approximations can be avoided altogether when the ship’s track is plotted on the chart. The Zone Times of Mer Pass for a few Meridians in the vicinity of the ship’s position are written against these Meridians on the chart. The time when the Sun and the ship are on the same Meridian can then be obtained to the nearest half minute by inspection. If unexpected alterations of course or speed occur before Mer Pass, the new Mer Pass time is merely read off the chart. A plot of Example 3-2 above is shown at Fig 6-3 with Mer Pass at 1140 with the ship on course 295°, speed 20. If the ship alters to course 025° at 1050, by inspection, Mer Pass is at 1138½.
Fig 6-3. Plotting of Mer Pass Times by the Chart Method 6-6 Original
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0607.
Meridian Passage of the Moon
a. Background. The Meridian Passage of the Moon is important in tidal prediction, but is otherwise unlikely to be of importance to the navigator. Unlike the Sun (see Para 0606), an appreciable error is introduced if it is assumed that the Moon’s apparent motion to the westward is exactly 15° of Longitude per hour. The GHA of the Moon in The Nautical Almanac shows that the hourly change in GHA has quite wide variations. b. Moon’s Mer Pass at Greenwich Meridian. It was shown at Para 0451 that a Lunar Day is longer than a Mean Solar Day by between 39 minutes and 64 minutes, averaging 50 minutes. The exact difference in the time of the Moon’s Mer Pass at the Greenwich Meridian is obtained by subtracting the time of Mer Pass on one day from the time of Mer Pass on the next. c.
Moon’s Mer Pass at Observer’ Meridian - the ‘Daily Difference’ . To calculate the time of the Moon’s Mer Pass at the Observer’s Meridian it is first necessary to take account of:
•
The observer’s Longitude
•
The time it has taken the Earth to rotate through this angle of Longitude.
•
As the Moon moves around its orbit of the Earth, in the time it has taken the Earth to rotate through the angle of Longitude, the Moon turns through an additional angle as it orbits the Earth. This can be seen more clearly over a 24 hour period at Fig 6-4.
Fig 6-4. The Orbit of the Moon during a Mean Solar Day (Not to Scale)
At Fig 6-4, AA´ is a measure of the Mean Solar Day (ie 360° change in Longitude), but while the Earth has moved from A to A´, the Moon has reached C, and so the Earth will have to turn through a further angle approximately equal to B´A´C before it is on the 6-7 Original
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Observer’s Meridian again. (Distances in Fig 6-4 are not to scale; as the Sun is so far away, the lines shown as ‘Observer’s Meridian’ at A and A’ are in reality almost parallel.) The time taken to turn the extra angle B´A´C varies between 39 and 64 minutes and is known as the ‘Daily Difference (MP)’ . The value of the Daily Difference for any particular day can be established by comparing the times of Mer Pass for the Moon in The Nautical Almanac for that day and for the day before/after it. Note 6-1. The term ‘Daily Difference’ is also used for Moonrise and Moonset, but that value is the difference between consecutive Moonrises/Moonsets, rather than consecutive Mer Pass’ as in this case. To avoid confusion, when the term ‘Daily Difference’ is used in BR 45 Vol 2, it is suffixed (MP), (MR) or (MS) as appropriate.
d. Calculation of ‘Difference of Time for Longitude’ for Moon’s Mer Pass. To calculate the time of Mer Pass for the Moon it is necessary to establish the proportion of the Daily Difference (MP) which must be applied to the tabulated Mer Pass time for the Greenwich Meridian: this is known as the ‘Difference of Time for Longitude (MP)’ . From Fig 6-4 it can be seen that: Difference of Time for Longitude(MP) = Observers Longitude x Daily Difference(MP) 360° Example 6-1. If an observer was at 75° W and the Daily Difference (MP) was 54 minutes, what is the Difference of Time for Longitude(MP) :
Difference of Time for Longitude (MP)
= 75° x 54 360°
= 11¼ minutes
Example 6-1. Summary of Difference of Time for Longitude (MP) Calculation
e. Method of Calculation of the Moon’s Mer Pass at Observer’ Meridian. The Zone Time of the Moon’s Mer Pass at the observer’s Observer’s Meridian is obtained as follows. Two examples of this calculation are on the opposite page:
6-8 Original
•
The Local Mean Time of the Moon’s Mer Pass on the Greenwich Meridian is established from the tabulated value for each day at the bottom of the right hand daily pages of The Nautical Almanac.
•
Comparison to the preceding day ( Longitude East) or to the following day ( Longitude West) allows the Daily Difference (MP) to be established by simple subtraction.
•
From the Daily Difference (MP) and observer’s Longitude, the Difference of Time for Longitude (MP) may be established by the calculation at Para 0607d above or by using TABLE II - FOR LONGITUDE at the back of The Nautical Almanac using the same arguments. The Difference of Time for Longitude (MP) is added ( Longitude West) or subtracted ( Longitude East) to the Local Mean Time of the Moon’s Mer Pass.
•
The observer’s Longitude is applied in the usual way (add if West or subtract if East).
•
Time Zone in use is applied in the same way as in SR / SS calculations (see Para 0322). This results in the Local Mean Time of Mer Pass on the Observer’s Meridian.
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Example 6-2. What is the Zone Time (+4) of the Moon’s Mer Pass in 63° 30'W? The Time of the Moon’s Mer Pass at the Greenwich Meridian is 1834 and the Daily Difference (MP) to the following day (because Longitude is West ) is 46 minutes:
Mer Pass Time (LMT) from Nautical Almanac Difference of Time (following day) for Longitude (from TABLE II or 63½ x 46÷360) (W+ or E-) Corrected Time of Mer Pass at 63° 30'W Longitude (W+ or E-) 63° 30'W
1834 +8 1842 +0414
Local Mean Time UT (GMT) at 63° 30'W
2256Z
Zone(+4) (+ = subtract) (- = add)
-0400
Zone Time of Mer Pass
1856(+4)
Example 6-2. Summary of Moon Mer Pass Calculations
Example 6-3. What is the Zone Time (-9) of the Moon’s Mer Pass i n 128° 15'E? The Time of the Moon’s Mer Pass at the Greenwich Meridian is 1834 and the Daily Difference (MP) to the preceding day (because Longitude is East ) is 44 minutes:
Mer Pass Time (LMT) from Nautical Almanac Difference of Time (preceding day) for Longitude (from TABLE II or 128½ x 44÷360) (W+ or E-) Corrected Time of Mer Pass at 128° 15'E Longitude (W+ or E-) 128° 15'E
1834 -16 1818 -0833
Local Mean Time UT (GMT) at 128° 15'E
0945Z
Zone(-9) (+ = subtract) (- = add)
+0900
Zone Time of Mer Pass
1845(-9)
Example 6-3. Summary of Moon Mer Pass Calculations
6-9 Original
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0608.
Meridian Passage of Aries The time of Meridian Passage of the First Point of Aries over the Greenwich Meridian is given in The Nautical Almanac for the middle day of the three days on the double page. The interval between successive Meridian Passages is 23h 56m, so that the times for intermediate days and other Meridians can easily be derived. The method of calculating the precise time of the Meridian Passage of Aries on any day for any Meridian is to find the UT (GMT) at which the LHA of Aries is zero (or 360°). There are two other points to note:
•
When converting the ‘difference’ (see examples) from arc to time, The Nautical Almanac ‘Increments and Correction’ Tables for Aries must be used (in reverse) and not the ‘Arc to Time’ Table (which is for the Mean Sun).
•
In certain cases it may be doubtful which day should be used for extracting the GHA of Aries from The Nautical Almanac; this can easily be resolved by first finding the approximate UT of Mer Pass of Aries at the required Longitude, as shown in Example 6-5 below. See extracts of The Nautical Almanac at Appendix 2.
Example 6-4. What is Zone Time (+4) of the Mer Pass of Aries in 57° 51'W on 13 July 1997?
LHA Aries
000° 00.0'
Longitude (W+ or E-)
057°
GHA Aries
057° 51.0'
Nearest GHA Aries for UT in whole hours (08)
051° 14.5'
= 8 hours
Difference (from‘Increments and Correction’ Tables)
006° 36.5'
= 26 min 22 secs 0826 22 (Z) 13 July
Local Mean Time of Mer Pass of Aries
Zone(+4) (+ = subtract) (- = add)
- 0400
Zone Time of Mer Pass of Aries
0426 22 (+4) 13 July
Example 6-4. Summary of Mer Pass of Aries Calculations Example 6-5. What is Zone Time (-10) of the Mer Pass of Aries in 154° 05'E on 13 July 1997?
Approx LMT Mer Pass of Aries
0436
Longitude 154° 05'E (W+ or E-)
1016
Approx UT (GMT) Mer Pass of Aries
1820
LHA Aries
000° 00.0'
Longitude (W+ or E-)
154° 05.0'E
GHA Aries
205° 55.0'
Nearest GHA Aries for UT in whole hours (18)
200° 40.0'
= 18 hrs (12 July)
Difference (from‘Increments and Correction’ Tables)
005° 15.0'
= 20 min 56 secs
Local Mean Time of Mer Pass of Aries
Zone(-10) (+ = subtract) (- = add) Zone Time of Mer Pass of Aries
13 July 12 July
1820 56 (Z) 12 July +1000 0420 56 (-10) 13 July
Example 6-5. Summary of Mer Pass of Aries Calculations 6-10 Original
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0609.
Upper Meridian Passage of Stars The method of calculating precise time of the Meridian Passage of a Star on any day for any Meridian is to find the UT (GMT) at which the sum of the LHA Aries and the SHA of the Star is zero (ie. LHA Star = 0° or 360°). There are two other points to note:
•
When converting the ‘difference’ (see examples) from arc to time, The Nautical Almanac ‘Increments and Correction’ Tables for Aries must be used (in reverse) and not the ‘Arc to Time’ Table (which is for the Mean Sun).
•
In certain cases it may be doubtful which day should be used for extracting the GHA of Aries from The Nautical Almanac; Mer Pass of the star occurs after that of Aries by 360°- SHA and can be resolved as at Example 6-7 . See also Appendix 2.
Example 6-6. What is Zone Time (+4) of Mer Pass of Aldebaran in 57° 51'W on 13 July 1997?
LHA Aldebaran (= LHA Aries + SHA
360° 00.0'
SHA Aldebaran
291° 03.6'
LHA Aries (LHA Aldebaran - SHA Aldebaran)
068° 56.4'
Longitude (W+ or E-)
057° 51.0'W
GHA Aries
126° 47.4'
Nearest GHA Aries for UT in whole hours (13)
126° 26.8'
= 13 hours
Difference (from‘Increments and Correction’ Tables)
000° 20.6'
= 01 min 22 secs 1301 22 (Z) 13 July
Local Mean Time of Mer Pass of Aldebaran
Zone(+4) (+ = subtract) (- = add)
- 0400
Zone Time of Mer Pass of Aldebaran
0901 22(+4) 13 July
Example 6-6. Summary of Mer Pass of Aldebaran Calculations Example 6-7. What is Zone Time (-10) of Mer Pass of Aldebaran in 154° 05'E on 13 July 1997?
Approx LMT Mer Pass of Aries
0436
360° - SHA Aldebaran = 360°-291° = 069°
0436
Approx UT (GMT) Mer Pass Aldebaran
0912
Longitude 154° 05'E (W+ or E-)
-1016
Approx UT (GMT) Mer Pass of Aldebaran
2256
LHA Aldebaran (= LHA Aries + SHA Aldebaran)
360° 00.0'
SHA Aldebaran
291° 03.6'
LHA Aries(LHA Aldebaran - SHA Aldebaran
13 July
12 July
428° 56.4'
Longitude (W+ or E-)
154° 05.0'E
GHA Aries
274° 51.4'
Nearest GHA Aries for UT in whole hours (22)
260° 49.9'
= 22 hrs (12 July)
Difference (from‘Increments and Correction’ Tables)
014° 01.4'
= 55 min 57 secs
Local Mean Time of Mer Pass of Aldebaran
2257 57 (Z) 12 July
Zone(-10) (+ = subtract) (- = add)
+1000
Zone Time of Mer Pass of Aldebaran
0857 57 (-10) 13 July
Example 6-7. Summary of Mer Pass of Aldebaran Calculations
6-11 Original
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0610.
Lower Meridian Passage of Stars Should the time of a star’s Lower Meridian Passage be required, it can be calculated in the same way as the Upper Meridian Passage except that the LHA of the star is 180° instead of 0° or 360°. 0611.
Meridian Passage of Planets The times of Meridian Passages of the four navigational planets over the Greenwich Meridian are given in the daily pages of The Nautical Almanac for the middle day of the three days on the double page. Times for intermediate days and Meridians can readily be derived and for normal navigational practice this approximation is sufficient (see Example 6-8 below). However, in some cases this approximation may be up to 3 minutes in error according to the daily differences in times of the Meridian Passages. If a precise time of Meridian Passage is required, the same procedure should be followed as for Aries (ie finding the UT (GMT) at which the LHA of the planet is zero - see Para 0608 and Example 6-9 below). Example 6-8. What is the approximate Zone Time (+5) of Mer Pass of Venus in 76° 10'W on 13 July 1997? See extracts of The Nautical Almanac at Appendix 2.
Mer Pass Time (LMT) from Nautical Almanac
1358
Longitude (W+ or E-) 76° 10'W
+0505
Local Mean Time UT (GMT) at 76° 10'W
1903Z
Zone(+5) (+ = subtract) (- = add)
-0500
Zone Time of Mer Pass
1403(+5)
Example 6-8. Summary of Approximate Mer Pass of Venus Calculations
Example 6-9. What is the precise Zone Time (+5) of Mer Pass of Venus in 76° 10'W on 13 July 1997? See extracts of The Nautical Almanac at Appendix 2.
Approx LMT Mer Pass of Venus
1358
Longitude 76° 10'W (W+ or E-)
+0505
Approx UT (GMT) Mer Pass of Aries
1903Z
LHA Venus
000° 00.0'
Longitude 076° 10'(W+ or E-)
076° 10.0'
GHA Venus
076° 10.0'
Nearest GHA Venus for UT in whole hours
075° 30.9'
= 19 hrs (13 July)
Difference (from‘Increments and Correction’ Tables)
000° 39.1'
= 02 min 36 secs
Local Mean Time of Mer Pass of Venus
Zone(+5 ) (+ = subtract) (- = add) Zone Time of Mer Pass of Venus
13 July 13 July
1902 36 (Z) 13 July -0500 1402 36 (-10) 13 July
Example 6-9. Summary of Precise Mer Pass of Venus Calculations
6-12 Original
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0612.
Calculation of Latitude at Meridian Passage
a. The Four Cases of Meridian Passage Calculations. As stated at Paras 0348f-i, there are three possible cases for the calculation of Latitude from the Upper Meridian Passage of a heavenly body and one additional case for the Lower Meridian Passage of a heavenly body. Once the Sextant Altitude has been corrected for Refraction etc, Latitude may be calculated very simply in each case from the Declination and the Observed (True) Altitude of the heavenly body .
b.
•
Upper Mer Pass: Latitude > Declination with SAME names (N / S)
•
Upper Mer Pass: Latitude < Declination with SAME names (N / S)
•
Upper Mer Pass: Latitude and Declination with CONTRARY names (N / S)
•
Lower Mer Pass: Independent of values of Declination, Latitude and NAME.
Upper Mer Pass: Latitude > Declination with SAME Names. Fig 6-5 shows an Upper Mer Pass situation in the northern hemisphere with Latitude > Declination and SAME names. It can be seen by inspection that:
O(H)X= Observed (True) Altitude (ie Sextant Altitude, corrected for errors etc) ZX = 90° - Observed (True) Altitude (ie 90° - O(H)X ) XQ = Declination ZQ = Latitude It may also be seen by inspection that: ZX = ZQ ( Latitude) - XQ ( Declination) = 90° - O(H)X (Observed (True) Altitude) Latitude = 90° - Observed (True) Altitude + Declination or Latitude = Declination - Observed (True) Altitude + 90° (see Para 0348f)
Fig 6-5. Upper Mer Pass: Latitude > Declination with SAME Names (Latitude = Declination - Observed (True) Altitude + 90°) 6-13 Original
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c.
Upper Mer Pass: Latitude < Declination with SAME Names . Fig 6-6 shows an Upper Mer Pass situation in the northern hemisphere with Latitude < Declination and SAME names. It can be seen by inspection that:
O(H)X= Observed (True) Altitude (ie Sextant Altitude, corrected for errors etc) ZX = 90° - Observed (True) Altitude (ie 90° - O(H)X ) XQ = Declination ZQ = Latitude It may also be seen by inspection that: ZX = XQ ( Declination) - ZQ ( Latitude) = 90° - O(H)X (Observed (True) Altitude) Latitude = Declination + Observed (True) Altitude - 90° (see Para 0348g)
Fig 6-6. Upper Mer Pass: Latitude < Declination with SAME Names (Latitude = Declination + Observed (True) Altitude - 90°)
6-14 Original
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d.
Upper Mer Pass: Latitude and Declination with CONTRARY Names. Fig 6-7 shows an Upper Mer Pass situation in the northern hemisphere. It should be noted that the heavenly body X is below the Celestial Equator (ie Declination CONTRARY name to Latitude) but above the Celestial Horizon. It can be seen by inspection that: O(H)X= Observed (True) Altitude (ie Sextant Altitude, corrected for errors etc) ZX = 90° - Observed (True) Altitude (ie 90° - O(H)X ) QX = Declination ZQ = Latitude
It may also be seen by inspection that: ZX = ZQ ( Latitude) + QX ( Declination) = 90° - O(H)X (Observed (True) Altitude) Latitude = 90° - Observed (True) Altitude - Declination (see Para 0348h)
Fig 6-7. Upper Mer Pass: Latitude and Declination with CONTRARY Names (Latitude = 90° - Observed (True) Altitude - Declination)
6-15 Change 1
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e. Lower Mer Pass: Independent of values of Declination, Latitude and Name. The Lower Mer Pass of the Sun is rarely encountered as it occurs at around midnight, some 12 hours before or after the Upper Mer Pass transit. The Sun is not visible at midnight except in very high Latitudes at certain times of the year. However, certain stars do make Lower Meridian Passages in moderate Latitudes at times when they are visible, and if observed, it is possible to derive the observer’s Latitude by a simple calculation. In practice, Lower Meridian Passage sights are not normally observed as such and so the appropriate formula is not provided at Para 0348i. However, the formula and a full explanation of the calculation is shown at Fig 6-8 below. It can be seen by inspection that: O(H)X= Observed (True) Altitude (ie Sextant Altitude, corrected for errors etc) ZX = 90° - Observed (True) Altitude (ie 90° - O(H)X ) XQ = Declination ZQ = Latitude It may also be seen by inspection that, based on the Celestial Equator as a baseline: | |
ZX = 180° - ZQ ( Latitude) - XQ’ ( Declination) = 90° - O(H)X (Observed (True) Altitude) Latitude = 180° - 90° + Observed (True) Altitude - Declination or Latitude = 90° + Observed (True) Altitude - Declination
|
Fig 6-8. Lower Mer Pass: Independent of values of Declination, Latitude and Name. (Latitude = 90° + Observed (True) Altitude - Declination)
6-16 Change 1
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SECTION 2 - POLARIS 0620.
Position and Movement of Polaris around the North Celestial Pole.
a. Position and Use of Polaris. Polaris (the Pole Star) is the name given to the secondmagnitude star which lies close to the North Celestial Pole. If its position coincided exactly with the North Celestial Pole, a Sextant observation of Polaris would provide an instantaneous measurement of Latitude, because the Observed (True) Altitude of the North Celestial Pole would equal the Latitude of the observer (see Fig 6-9). In addition, a compass bearing of Polaris would provide an instantaneous check for true North and thus any compass error. However, with small, easily applied corrections, both these problems are overcome.
Fig 6-9. Daily Movement of Polaris around the North Celestial Pole
b. Daily Movement of Polaris. To be in coincidence with the North Celestial Pole the Declination of Polaris would have to be 90°N; in fact the Declination of Polaris is approximately 89°N. The Polar Distance (Co-Declination) is thus approximately 1°, and in the course of a day, Polaris describes a Small Circle about the North Celestial Pole with an angular radius of approximately 1°. This is shown by (an exaggerated) Small Circle (displayed as a ‘dashed’ line) centred about the North Celestial Pole in Fig 6-9 below). The Observed (True) Altitude of Polaris is thus not quite equal to the Latitude of the observer and the compass bearing of Polaris is not always exactly true North. Note 6-2. The Small Circle centred about the North Celestial Pole in Fig 6-9 above has been expanded at Fig 6-10 overleaf, so that further detail can be shown .
6-17 Original
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0621.
Obtaining Latitude by the Altitude of Polaris The Small Circle centred about the North Celestial Pole in Fig 6-9 has been expanded at Fig 6-10 below, so that further detail can be shown.
a. Construction of Point Y. If a point Y is constructed on the Observer’s Meridian O(H)P at an Angular Distance equal to AX (the Observed (True) Altitude of Polaris (X) measured from the Celestial Horizon) so that O(H)Y = AX, then the observer’s Latitude PO(H) can be established as follows: Latitude PO(H) = Observed (True) Altitude (AX) ± Angular Difference PY
Fig 6-10. Daily Movement of Polaris around the North Celestial Pole Expanded Scale (see Fig 6-9). Viewed from directly above the Pole
b. Effect of LHA of Polaris on Sign of PY . In the example shown at Figs 6-9 and 610, by inspection, the Angular Distance PY is positive (+). However, depending on the position of X on the Small Circle during any 24 hour period, it could be negative(-). The sign of Angular Distance PY is thus dependent on the LHA of Polaris (X), and that LHA is also the angle XPY (known as “h”). c. First Approximation of the Correction PY. A point Y' is constructed on the Observer’s Meridian O(H)P so that the perpendicular to O(H)P passes through X. As Polaris describes a Small Circle about the North Celestial Pole with an angular radius of approximately 1°, the arc XY closely approximates the perpendicular XY’. Thus as a first approximation PY almost equals PY'. As both the LHA (h) of Polaris and the angular radius (PX) of Polaris’ movement around the North Celestial Pole are known, PY' can be established by the formula: PY'= PX cos h 6-18 Original
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d. Second and Third Approximations of the Correction PY. The Nautical Almanac makes two further approximations to refine the calculation and tabulates the three corrections which are called a0 , a1 and a2. For mathematical convenience , constants are included in these tabular corrections to make them positive(+) at every value of Polaris’ LHA (h). The constants are arranged so that their sum is exactly 1°, thus: PY = +a0 + a1 + a2 - 1°
e. Latitude from Polaris’ Altitude. The formula at Para 0621a may thus be rewritten as: Latitude = Observed (True) Altitude +a0 + a1 + a2 - 1°
f. Use of The Nautical Almanac Polaris Tables. The method of using The Nautical Almanac Polaris Tables is explained at Para 0348j which includes a worked example of the procedure. An extract of The Nautical Almanac Polaris Tables are at Appendix 2. 0622.
Obtaining True North by the Bearing of Polaris The same principles used for Latitude (Paras 0620-0621 and Para 0348j) may be used to establish the difference between the bearings of Polaris and true North. The Nautical Almanac has a further table, which is entered with the arguments LHA of Aries and approximate Latitude between 0° and 65°. The output of the table is termed “Azimuth” but this term is used in astronomical sense (see Para 0536b) and actually equates to the True Bearing of Polaris. A worked example of the procedure for using the Polaris Azimuth tables is at Para 0348j. Above Latitude 65° North, observational errors in obtaining a bearing of Polaris become significant and it is no longer a sufficiently accurate method for navigational use. 0623.
Observation of Polaris at Twilight Polaris is not a particularly bright star (Magnitude 2.1) and it does not appear to the naked eye until the horizon has become indistinct in the gathering dusk. An effective way of overcoming this difficulty is to subtract a0 from the DR Latitude and add 1°. If this approximate altitude is set on the Sextant , the star will be visible in the telescope long before the naked eye can detect it, enabling an observation to be taken while the horizon is still good. 0624.
NAVPAC 2 - Polaris NAVPAC 2 provides all the data necessary for Polaris calculations and will carry them
out.
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CHAPTER 7 THE RISING AND SETTING OF HEAVENLY BODIES CONTENTS
SECTION 1 - REQUIREMENT AND GENERIC DEFINITIONS
Operational Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . True (Theoretical) Rising and Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Visible Rising and Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Semi-Diameter, Upper and Lower Limb of the Sun or Moon . . . . . . . . . . . . . . . . . . . .
Para 0701 0702 0703 0704
SECTION 2 - SUNRISE, SUNSET AND TWILIGHTS
Visible Sunrise and Sunset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . True Altitude at Visible Sunrise and Sunset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Times of Visible Sunrise and Visible Sunset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time and Altitude of True Theoretical Sunrise and Sunset . . . . . . . . . . . . . . . . . . . . . . . Twilight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Duration of Twilights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Midnight Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Circumpolar Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0720 0721 0722 0723 0724 0725 0726 0727
SECTION 3 - MOONRISE AND MOONSET
Tabulated Times of Moonrise and Moonset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0730 Calculation of Moonrise and Moonset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0731
SECTION 4 - HIGH LATITUDES
Rising and Setting in High Latitudes - Methods of Prediction Available . . . . . . . . . . . Theoretical Explanation of NP 401 Method for Negative Apparent Altitudes . . . . . . . Nautical Almanac and Sight Reduction Tables (NP 401) Method - Procedure . . . . . . .
0740 0741 0742
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CHAPTER 7 THE RISING AND SETTING OF HEAVENLY BODIES SECTION 1 - REQUIREMENT AND GENERIC DEFINITIONS
0701.
Operational Requirement A thorough understanding of the rising and setting of heavenly bodies is essential to the Specialist N. This is not only in order to plan the time at which star sights may be taken, but more importantly, for planning operations which require total darkness, twilight or moonlight. 0702.
True (Theoretical) Rising and Setting The time of True (Theoretical) Rising and Setting occurs when the centre of a heavenly body is on the observer’s Celestial Horizon, to the east or west of his Meridian. At these times the True Zenith Distance is 90°. Except in the case of the Moon, this phenomenon cannot be observed directly from the Earth’s surface due to Atmospheric Refraction raising the image of the body appreciably above the Visible Horizon.
•
The Sun. It is shown at Para 0723 below, that when the Sun’s centre lies on the Celestial Horizon (ie at the moment of True (Theoretical) Rising and Setting), the Sun’s Lower Limb appears one Semi-Diameter above the Visible Horizon. It is for this reason that Sunrise / Sunset compass checks are taken when the Sun’s Lower Limb is one semi-diameter above the Visible Horizon.
•
The Moon. However, it is also shown at Para 0730 below, that when the Moon’s centre lies on the Celestial Horizon (ie at the moment of True (Theoretical) Rising and Setting), due to Horizontal Parallax, the Moon’s centre appears practically on the Visible Horizon. (See Para 0401 for definition / explanation of “Parallax”).
0703.
Visible Rising and Setting Visible Rising and Setting occur when the Upper Limb of a heavenly body is just appearing above or disappearing below the observer’s Visible Horizon. In the cases of the Sun and Moon, the tables in The Nautical Almanac give the times at which these phenomena occur.
0704.
Semi Diameter, Upper and Lower Limb of the Sun or Moon
a. Semi-Diameter. The Semi-Diameter of a heavenly body is half its angular diameter as viewed from the Earth. b. Upper Limb (UL). The Upper Limb of the Sun or Moon is the portion of its circumference furthest from the Visible Horizon, as seen from an observer on the Earth’s surface. c. Lower Limb (LL). The Lower Limb of the Sun or Moon is the portion of its circumference nearest to the Visible Horizon, as seen from an observer on the Earth’s surface. 0705-0719. Spare
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SECTION 2 - SUNRISE, SUNSET AND TWILIGHTS 0720.
Visible Sunrise and Sunset Visible Sunrise or Sunset occurs when the Sun’s Upper Limb appears on the Visible Horizon. At this moment, the Apparent Altitude (equivalent to Sextant Altitude corrected for Index Error and Height of Eye) of the Sun’s Upper Limb is 0° 00.0'. 0721.
True Altitude at Visible Sunrise and Sunset
a. True Zenith Distance of Sun at Visible Sunrise or Sunset . By correcting this Apparent Altitude of 0° 00.0' for the Sun’s Upper Limb at Visible Sunrise or Sunset , first the Observed (True) Altitude and then the True Zenith Distance of the Sun’s centre may be calculated. Thus if the observer is assumed to have no Height of Eye, and the Sun’s Semi-Diameter on the day in question is 16.0', then: Apparent Altitude Refraction Sub-Total Semi-Diameter
0° 00.0' 34.0' 0°
34.0'
16.0'
Observed (True) Altitude
0°
90°
90° 00.0'
True Zenith Distance
90° 50.0'
50.0'
Example 7-1. True Zenith Distance of Sun at Visible Sunrise or Sunset
b. Sequence of Visible Sunrise / Sunset and True Theoretical Sunrise /Sunset. From Example 7-1 is can be seen that the Sun’s centre is 50.0' below the Celestial Horizon when its Upper Limb is just visible above the Visible Horizon, and the True Zenith Distance of the Sun’s centre is 90° 50.0'. For this reason, Visible Sunrise occurs before True Theoretical Sunrise, and Visible Sunset occurs after True Theoretical Sunset . 0722.
Times of Visible Sunrise and Visible Sunset The Nautical Almanac gives the times of Visible Sunrise and Visible Sunset for a range of Latitudes from 60°S to 72°N on the right hand side of the 3-day double pages . These times, which are given to the nearest minute, are strictly the UT of the phenomena on the Greenwich Meridian for the middle day of the three on each page. They are approximately the LMT of the corresponding phenomena on any other Meridian and may be used, with interpolation, for any of the 3 days on the double page. The use of these tables to calculate the Zone Time of Visible Sunrise and Visible Sunset (and Twilights) is explained at Para 0322. 0723.
Time and Altitude of True Theoretical Sunrise and Sunset
a. Times of True Theoretical Sunrise and Sunset . The times of True Theoretical Sunrise and Sunset are not usually required in the practice of navigation, but if they should be, they can be found by solving the spherical triangle for the angle at the Celestial Pole when the True Zenith Distance is 90°. This angle is the LHA of the Sun at True Theoretical Sunrise or Sunset. 7-4 Original
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b. Altitude of the Sun at True Theoretical Sunrise and Sunset. The Apparent Altitude of the Sun at True Theoretical Sunrise and Sunset is important for compass checks. At Fig 7-1, the real and apparent positions of the Sun at True Theoretical Sunrise and Sunset are shown. From Fig 7-1 it will be seen that the Sun appears to be approximately a Semi-Diameter above the Visible Horizon at that moment. (ie 34.0' Refraction - 16.0' Semi-Diameter = 18.0' = approximately one Semi-Diameter).
It is for this reason that Nories Nautical Tables provide Amplitude Tables to calculate the true compass bearing of the Sun when the Sun’s Lower Limb is one Semi-Diameter above the Visible Horizon.
Fig 7-1. Altitude of the Sun at True Theoretical Sunrise or Sunset 0724.
Twilight Twilights were defined at Para 0108, but for the convenience of the reader are repeated here. The use of The Nautical Almanac to calculate the Zone Time of Twilights is at Para 0322.
a. Civil Twilight (CT). The times of Morning Civil Twilight (MCT) and Evening Civil Twilight (ECT) are tabulated in The Nautical Almanac for the moment when the Sun’s centre is 6° below the Celestial Horizon. The times are shown in chronological order and the terms ‘ Morning ’ and ‘ Evening ’ are omitted. This is roughly the time at which the horizon becomes clear (morning) or becomes indistinct (evening). b. Nautical Twilight (NT). The times of Morning Nautical Twilight (MNT) and Evening Nautical Twilight (ENT) are tabulated in The Nautical Almanac for the moment when the Sun’s centre is 12° below the Celestial Horizon. The terms ‘ Morning ’ and ‘ Evening ’ are omitted as the times are in chronological order. Morning and evening stars are usually taken between the times of Civil Twilight (CT) and Nautical Twilight (NT). c. Astronomical Twilight. The time of Astronomical Twilight (AT) is the moment when the Sun’s centre is 18° below the Celestial Horizon. Whilst the Sun’s centre is 18° or greater below the Celestial Horizon, absolute darkness (with respect to the Sun) is deemed to exist and observations by astronomers may usefully take place. The times of Astronomical Twilight (AT) have no significance in solving the astro-navigation problem and so AT times are not tabulated in The Nautical Almanac. 7-5 Original
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0725.
Duration of Twilights
a. Morning Twilight. Morning Twilight , whether Civil, Nautical or Astronomical , begins when the Sun’s centre is at the appropriate angular depression (6°, 12°or 18° respectively) below the Celestial Horizon, and lasts until Visible Sunrise. b. Evening Twilight. Evening Twilight begins at Visible Sunset and lasts until the Sun has reached the appropriate depression (6°, 12° or 18°)below the Celestial Horizon. c. Twilight and Total Darkness. The relative positions of the Sun at True Theoretical Sunset (position X), Visible Sunset (position X’), and at the end of Twilight (position X”) are shown at Fig 7-2. •
Position X” can represent Civil Twilight , Nautical Twilight or Astronomical Twilight depending on the angular depression below the Celestial Horizon.
•
The angles ZPX, ZPX´ and ZPX” are the corresponding Hour Angles of the Sun for these positions, and ZX (90°), ZX´ (90° 50´) and ZX (96°, 102° or108° as required) the respective True Zenith Distances.
•
If the circle of Declination of the Sun does not fall 18° below the horizon, Astronomical Twilight does not end until Visible Sunrise, and then there is no ‘Total Darkness’ overnight. This situation occurs when the observer’s Latitude and the Sun’s Declination the SAME name and their sum is greater than 72° (ie Lat + Dec > 72° 90°-( Lat + Dec) < 18°).
•
Similar limits for Civil Twilight and Nautical Twilight are obtained by using circles of Declination of the Sun of 6° and 12° respectively, instead of 18°.
Fig 7-2. Positions of the Sun at Sunsets and Twilights
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d. Duration of Twilight. The actual duration of Twilight depends on the angle which the Sun’s path makes with the Celestial Horizon. •
High versus Low Latitudes. If the angle which the Sun’s path makes with the Celestial Horizon is small, as it must be in high Latitudes (Fig 7-3a), Twilight lasts considerably longer than it does in low Latitudes where the angle is large (Fig 7-3b). Thus Nautical Twilight in the tropics usually lasts just under an hour, in the south of England at midsummer it lasts through most of short night and off northern Scotland in midsummer it lasts all night.
Fig 7-3a High (Northern) Latitude Sun’s Angle of Descent Small
e.
Fig 7-3b Low (Northern) Latitude Sun’s Angle of Descent Large
Calculation of Twilight and Total Darkness Times.
•
Civil Twilight and Nautical Twilight. The times of Civil Twilight and Nautical Twilight can be obtained from the dedicated tables in The Nautical Almanac (see Para 0322).
•
Astronomical Twilight and Total Darkness. If necessary for operational purposes, Astronomical Twilight and thus the times of Total Darkness may be calculated by the angle X´PX” (in Fig 7-1), which is the difference between the Hour Angles in the two triangles PZX´ and PZX”. From the time of Visible Sunset /Sunrise note the GHA of the Sun, add/subtract 18°, read back into the GHA table and note the times of Astronomical Twilight . Alternatively, NAVPAC 2 will provide the times of Astronomical Twilight on demand.
f. Need for Artificial Light. Artificial light becomes necessary for most purposes when the Sun is 6° or more below the Visible Horizon (ie after Civil Twilight ).
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0726.
The Midnight Sun If the circle of Declination (Fig 7-2) remains above the Celestial Horizon, the Sun can never set and this effect is known colloquially as the ‘Midnight Sun’. From Fig 7-4 it can be seen that in the Northern Hemisphere, the limiting Latitude for the ‘Midnight Sun’ to occur is: 90° minus the Sun’s greatest northerly Declination (90°
23½°) N = 66½° N.
In that Latitude the Sun will remain above the Visible Horizon all night on one occasion only during the year, although as the observer’s Latitude increases, the number of days in a year that the Sun never sets also increases, because smaller Declinations satisfy the condition. For a similar reason, Astronomical Twilight will last all night on one night of the year in (90° 23½° 18°) N = 48° N. These limits, with their names altered to South, also apply in Southern Latitudes.
Fig 7-4. The Midnight Sun
0727.
Circumpolar Bodies Although every heavenly body is circumpolar (in that to an observer on Earth it describes a circle about the Celestial Pole) the term ‘Circumpolar’ is normally used to denote that a heavenly body never sets and is always above the observer’s Visible Horizon. 0728-0729. Spare
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SECTION 3 - MOONRISE AND MOONSET 0730.
Tabulated Times of Moonrise and Moonset
a. Tabulated Times. The precise times of Moonrise and Moonset may be found by solving the triangle PZX for the LHA in the same way as it can be solved for the Sun, but the calculation is even more laborious, the Moon’s Declination and SHA are both changing so rapidly that a method of successive approximation must be employed in order to obtain the proper Declination and GHA at the instant of Moonrise or Moonset. To avoid this, tables are incorporated in The Nautical Almanac giving the times, to an observer on the Greenwich Meridian with no Height of Eye, when the Moon’s Upper Limb is just touching the Visible Horizon (ie Visible Moonrise and Visible Moonset ). b. Position of the Moon at Visible Rising or Setting. At this instant of Visible Moonrise / Moonset , when the Moon’s Upper Limb touches the Visible Horizon, the Observed (True) Altitude of the Moon’s centre is given by the following calculation. This shows that the Moon’s centre is then roughly on the Celestial Horizon: Apparent Altitude Refraction Sub-Total Semi-Diameter
0° 00.0' 34.0' 0°
34.0'
16.0'
Sub-Total
0°
Horizontal Parallax
+ 0° 57.0'
Observed (True) Altitude
00° 07.0'
50.0'
Example 7-2 Observed (True) Altitude of Moon at Visible Moonrise or Moonset 0731.
Calculation of Moonrise and Moonset
a. Layout of Moonrise and Moonset Tables. The exact LMT of Visible Moonrise / Moonset on the Greenwich Meridian is given for 4 days on the right-hand of the 3-day double pages of The Nautical Almanac for a range of Latitudes between 72°N and 60°S. The data for 4th day is tabulated on the same page to aid interpolation without having to turn to the page. Where no phenomenon occurs during a particular day (as happens once a month) the time of the phenomenon on the following day, increased by 24 hours, is given. For example, there is no Visible Moonrise in Latitude 40°S on 21st December 1997 (see Appendix 2). The time 2408 refers to the rising at 0008 on 22nd December. b. Interpolation Requirements. The LMT of Visible Moonrise / Moonset is not constant for all Longitudes and must be corrected for the Daily Difference between consecutive Visible Moonrises or Visible Moonsets at the Latitude considered. The correction for Longitude must be applied to the LMT at the Greenwich Meridian in the same way as the correction is applied to the Moon’s Mer Pass (see Para 0607). Note 7-1. The term ‘Daily Difference’ is also used for Mer Pass of the Moon, but that value is the difference between consecutive Mer Pass’, rather than consecutive Moonrises/Moonsets as in this case. To avoid confusion, when the term ‘Daily Difference’ is used in BR 45 Vol 2, it is suffixed (MP), (MR) or (MS) as appropriate.
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c. Longitude Interpolation Formula. It is also of note that the method of interpolating for Difference of Time for Longitude(MR/MS) correction for Visible Moonrise / Moonset uses the same formula as for the Mer Pass of the Moon’s Difference of Time for Longitude(MP) correction (see Para 0607d), only with the Daily Difference (MR/MS) instead of Daily Difference (MP). The Nautical Almanac Table II(Page xxxii), referred to at Para 0731d below, is thus based on the following formula: Difference of Time for Longitude(MR/MS) = Observer’s Longitude x Daily Difference(MR/MS) 360° d. Method of Calculation of the Moonrise or Moonset at Observer’s Meridian. The Zone Time of the Visible Moonrise / Moonset at the Observer’s Meridian is obtained as follows. Demonstrations of two of these calculations ( Longitudes East and West) are on the facing page at Example 7-3.
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•
The Local Mean Time of the Visible Moonrise / Moonset on the Greenwich Meridian is established from the tabulated value for each day at the nearest Latitudes at the right hand daily pages of The Nautical Almanac.
•
Interpolation for Latitude required is carried out by using The Nautical Almanac Table I (Page xxxii) at the back of the book, for the times on consecutive Latitudes on the day wanted and also on the preceding day ( Longitude East) or to the following day ( Longitude West). The result should be times for the exact Latitude on two consecutive days. In extreme conditions near or symbols, interpolation for Latitude may be possible in only one direction; accurate times are of little value in such circumstances.
•
Taking the difference between the times for the exact Latitude on two consecutive days (see bullet point immediately above), interpolate for Difference of Time for Longitude(MR/MS) using The Nautical Almanac Table II (Page xxxii) at the back of the book. The correction obtained from Table II should be applied to the time for the day wanted. It is normally added if West or subtracted if East, but if, as occasionally happens, the times become ea rlier each day instead of later, the signs of the corrections must be reversed. In extreme conditions near or symbols, interpolation for Difference of Time for Longitude(MR/MS) may be possible only in one direction; accurate times are of little value in such circumstances.
•
The observer’s Longitude is applied in the usual way (add if West or subtract if East).
•
Time Zone in use is applied in the same way as in SR / SS calculations (see Para 0322). This results in the Local Mean Time of Visible Moonrise / Moonset on the Observer’s Meridian.
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Visible Moonrise / Moonset Example 7-3. Moonset on 20th January 1997 at:
What are the Zone Times of Visible Moonrise /
(1) 33° 27.0'S 125° 00.0'E in Zone (-8) and (2) 33° 27.0'S 076° 31.0'W in Zone (+5) (1) 33° 27.0'S 125° 00.0'E Moonrise
LMT in 30°S La. Corr n
1636 (20 Jan)
Long Corr n
(2) 33° 27.0'S 076° 31.0'W
Moonset
0239 (20 Jan)
Moonrise
Moonset
1636 (20 Jan)
0239 (19 Jan)
+7
-7
+7
-7
-18
-17
+11
+10
Corrected LMT
1625 (20 Jan)
0215 (20 Jan)
1654 (20 Jan)
0242 (20 Jan)
Long (-E or +W)
-0820 E
-0820 E
+0506 W
+0506 W
UT (GMT)
0805 (20 Jan)
1755 (19 Jan)
2200 (20 Jan)
0748 (20 Jan)
Zone
+8
+8
-5
-5
Zone Time
1605(-8) 20 Jan
0155(-8) 20 Jan
1700(+5) 20 Jan
0248(+5)20 Jan
Example 7-3. Summary of Visible Moonrise / Moonset Calculations
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SECTION 4 - HIGH LATITUDES 0740.
Rising and Setting in High Latitudes - Methods of Prediction Available There are three methods available:
•
The Nautical Almanac provides dedicated Visible Rising / Setting and Twilight data for the Sun, and Visible Rising / Setting data for the Moon between 72° North and 60° South.
•
NAVPAC 2 will calculate Rising and Setting data for all heavenly bodies, plus Twilight data, accurately to Latitude 89° 59.9'. NAVPAC 2 is the quickest and most convenient method of calculating Rising / Setting /Twilight data.
•
However, if desired, it is possible to use a combination of The Nautical Almanac and Sight Reduction Tables for Marine Navigation (NP 401 series) as described at Para 0742 below to achieve similar results.
Note 7-2. A further method using Rising and Setting Diagrams for High Northern Latitudes (NP 301) is no longer available. Theses diagrams were withdrawn in March 1998. 0741.
Theoretical Explanation of NP 401 Method for Negative Apparent Altitudes
a. PZX and P'Z'X Triangles. Conventionally, NP 401 solves the PZX triangle using the Elevated Pole to obtain Calculated (Tabulated) Altitude and Azimuth. The Celestial Horizon forms a Great Circle dividing the Celestial Sphere into two hemispheres. When using NP 401 for solving problems below the Celestial Horizon (ie negative Apparent Altitudes) the P'Z'X triangle lies completely below the Celestial Horizon and is geared to the Depressed Pole (as indicated at Para 0542e) and shown at Fig 7-5 below. NP 401 gives a choice of two LHAs which solve the PZX and P'Z'X triangles. The choice of the correct LHA for calculation of Visible Rising / Setting and Twilights requires care.
Fig 7-5. Negative Apparent Altitudes - The PZX and P'Z'X Triangles 7-12 Original
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b. Choice of LHA for Calculation. In normal circumstances, the LHA at Sunset is always less than 180° (westwards) and the LHA at Sunrise is always more than 180° (eastwards). If Declination and Latitude are SAME, then LHA is greater than 90°, but if they are CONTRARY then LHA is less than 90°. However, as this problem requires negative Apparent Altitudes, the criteria are different and following guidelines should be used to select the correct LHA. When selected, the LHA is converted to time, and is then added and subtracted to the time of Mer Pass on the day in question. •
If Declination and Latitude are SAME, select the first of the two LHAs printed on the bottom of the page.
•
If Declination and Latitude are CONTRARY, select the first of the two LHAs printed on the top of the page.
Note 7-3. The procedure at Para 0741b (above) uses the figure opposite to the SAME / CONTRARY labelling on the top/bottom of the page.
c. Choice of Azimuth for Calculation. The Azimuth obtained from NP 401 will need to be converted to the Supplementary Azimuth (ie 180°- Azimuth) because NP 401 provides Azimuth relative to the Depressed Pole and this needs to be converted to an Azimuth relative to the Elevated Pole so that the normal True Bearing conversion procedure (see Para 0535) may be used. The True Bearing obtained should be on the same side of the 090° / 270° line as Declination. d. Correction from True Theoretical Rising / Setting to Visible Rising / Setting. The Nautical Almanac and Sight Reduction Tables (NP 401 series) method will give the approximate time of the True Theoretical Rising / Setting to which Refraction and Semi Diameter (combined) plus Dip corrections (and HP correction for the Moon) must be applied to obtain the time of Visible Rising / Setting . This is normally about -1 from the Observed (True) Altitude, and this correction should be applied to the tabulated Altitude (Hc) before the LHA is extracted from NP 401. e. Twilights. Civil Twilight / Nautical Twilight / Astronomical Twilight can be obtained in the same way using an Altitude (Hc) of -6, -12° or -18° respectively (plus the Refraction and Semi-Diameter (combined) and Dip corrections). At the Poles the Sun will rise and set once a year (when its Declination is zero), and in Polar regions, the above calculations are often necessary to determine whether the Sun or stars are visible. 0742.
Nautical Almanac and Sight Reduction Tables (NP 401) Method - Procedure
a. The NP 401 method produces approximate answers due to rounding-up. The procedure is as follows: •
From The Nautical Almanac, extract the approximate Declination of the heavenly body required and round to the nearest whole degree.
•
Calculate Refraction plus Semi-Diameter (combined), plus Dip corrections (& HP if required); apply to the 0°, -6°, -12° or -18° Altitude (Hc), depending whether Rising / Setting, Civil Twilight / Nautical Twiglight / Astronomical Twilight respectively are required. Call this ‘Corrected’ Altitude (Hc)’.
•
Enter NP 401 with arguments of Latitude and approximate Declination; note whether they are SAME or CONTRARY names to establish whether to r ead LHA from the top or bottom of the page (see Para 0741b above). 7-13 Change 1
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•
By inspection of NP 401, use the approximate Declination to find the LHA which gives the approximate ‘Corrected’ Altitude (Hc)’ (see above), and if required, the Azimuth (Z), taking particular care on the following important points: Beware the ambiguity between the two LHAs listed on the NP 401 page which will refer to either Rising or Setting ; the correct choice should be clear by inspection of Azimuth when converted to Supplementary Azimuth and then True Bearing . See Example 7-4.
Note also that the Azimuth at the ‘Corrected Altitude (Hc)’ line, must be converted to ‘ Supplementary Azimuth’ by being subtracted from 180° before being used to calculate True Bearing . (See NP 401(6) Page xv Para 3)
Be very careful to identify a negative rather than a positive Altitude. A ‘CONTRARY / SAME line’ ( Altitude zero) is printed across the tables and NP 401(6) Pages xiv - xv contain detailed guidance for interpolation of positive / negative Altitudes at or near the horizon and use of Azimuths. However, for LHAs at the top of the right hand page, altitudes below the horizon zero line are negative and for LHAs at the bottom of the right hand page, altitudes above the horizon zero line are negative. In short, when an Altitude is taken from the ‘wrong’ side of the ‘CONTRARY / SAME line’, it indicates a negative Altitude.
•
Convert ‘Supplementary Azimuth’ into True Bearing (see Para 0535 and also the instructions at top/bottom of the NP 401 page) and confirm that the correct phenomenon (Visible Rising or Visible Setting) has been identified.
•
Convert the LHA extracted into hours (divide by 15° for most heavenly bodies. In the case of the Moon this will be inaccurate and a better answer is achieved by dividing the LHA by the hourly change in the Moon’s GHA (from The Nautical Almanac) on the day in question (14° 19' in the following example), corrected by adding or subtracting the mean hourly velocity correction “v” on the day in question.
•
Add or subtract this period to the LMT of Mer Pass and apply Longitude and Zone corrections as normal to obtain the Zone Time of Visible Rising /Setting.
b. NAVPAC 2 Method. NAVPAC 2's RiseSet program provides Rising and Setting times for all heavenly bodies and Twilight times for the Sun, at all Latitudes. These times may be transferred to the Almanac and FindIt programs but it should be noted that FindIt works on the centre of the body and so does not allow for the Sun or Moon’s Semi-Diameter or for the observer’s Height of Eye. c. Sight Reduction Tables Method Rising / Setting Example 7-4. A full example of the Sight Reduction Method is on the following pages at Example 7-4, including calculations at Examples 7-4a and 7-4b. For comparison, the results of NAVPAC 2 for the same calculation are summarised at Example 7-4c.
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Sight Reduction Tables Method Rising/ Setting Example 7-4. In DR position 80°S 115°W, on 14th October with a Height of Eye of 8.0 metres, what are the Zone Time and True Bearings of Visible Sunrise and Visible Sunset? Assume that the Sun's Declination on 14 th Oct is 8° S and the LMT of the Sun’s Mer Pass was at 1146.
•
Correction for Refraction ( Apparent Altitude 0°05.0') / Semi-Diameter (combined) plus Dip ( HE 8.0 metres) are -49.2' and -5.0' = -54.2' . The ‘Corrected Altitude (Hc)’ is therefore -54.2' for Visible Sunrise.
•
By inspection, entering NP 401 for Latitude 80S and Declination 8S (ie SAME), find the page (see Fig 7-6) where the tabulated Altitude (Hc) is 54.2' or nearly so above ‘CONTRARY / SAME line’, thus indicating -54.2' (ie a negative Altitude):
Fig 7-6. Extract from NP 401 for Latitude 80°S, Declination 8° S •
From Fig 7-6, by inspection: LHA = 153°, 207° Azimuth(Z) = 153.3
•
From NP 401 instructions (at bottom left corner of Fig 7-6):
•
Supplementary Azimuth = 036.7
LHA > 180° Bearing (Zn) = 180° - Az (Z) But for Az(Z) read ‘Supplementary Azimuth’ (ie 180°- Az(Z)) So, for LHA 207°, Bearing (Zn) = 180° - 036.7 (Z) = 143.3° (ie Sunrise)
From NP 401 instructions (at bottom left corner of Fig 7-6):
LHA < 180° Bearing (Zn) = 180° + Az (Z) But for Az(Z) read ‘Supplementary Azimuth’ (ie 180°- Az(Z)) So, for LHA 153°, Bearing (Zn) = 180° + 036.7 (Z) = 216.7° (ie Sunset)
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•
Using LHA 153°, the Sun will have to travel through 153° of Longitude before and after reaching the Observer's Meridian (ie at Mer Pass), so:
LMT Mer Pass
1146
LMT Sunrise
LMT of Mer Pass - 153°/15° =
1146 - 1012 =
0134
Long (115°W)
+
0740
UT Sunrise
=
0914
Zone (+8)
-
0800
Zone Time Sunrise
=
0114
True Bearing
(See Supplementary Azimuth calculation above) = 143.3°
Example 7-4a. Summary of High Latitude (NP 401 Method)Visible Sunrise Calculation
LMT Mer Pass
1146
LMT Sunset
LMT of Mer Pass + 153°/15° =
1146 + 1012
2158
Long (115°W)
+
UT Sunrise
= 0548
Zone (+8)
-
0800
Zone Time Sunrise
=
2138
True Bearing
0740
(See Supplementary Azimuth calculation above) = 216.7°
Example 7-4b. Summary of High Latitude (NP 401 Method)Visible Sunset Calculation
•
NAVPAC 2 produces accurate answers, although the FindIt program does not allow for the Sun or Moon’s Semi-Diameter or for the observer’s Height of Eye. Having first entered the RiseSet program to establish the initial times of Rising, Setting or Twilight , FindIt may be used to establish the bearing, provide the Altitude is offset for Semi-Diameter or for the observer’s Height of Eye (ie -21.0 approx). The slightly different times from RiseSet and/or FindIt may be used to enter the Almanac program to obtain GHA and Declination. The results of this process are at Example 7-4c.
NAVPAC RiseSet SR/SS Time
FindIt FindIt / Time Almanac GHA
LHA (LHA = GHA -Long W)
FindIt / Almanac Dec
FindIt Altitude
FindIt Bearing
(No SD+Dip)
SR
0117(+8) 0108(+8) 320° 34.2' 207° 42.0'
S 08° 02.2' -00° 20.6' 154° 41.6'
SS
2152(+8) 2202(+8) 274° 01.0' 156° 34.3'
S 08° 21.6' -00° 20.1' 200° 45.2'
Example 7-4c. Summary of NAVPAC 2 High Latitude Visible Sunrise/Sunset Calculations
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CHAPTER 8 REFRACTION, DIP AND MIRAGE CONTENTS
Introduction to Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Refraction Angles and Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Atmospheric Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Abnormal Conditions of Atmospheric Refraction - Abnormal Refraction . . . . . . . . . . . Air Temperature and Atmospheric Pressure Correction Tables . . . . . . . . . . . . . . . . . . . Dip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Methods of Correcting for Abnormal Refraction . . . . . . . . . . . . . . . . . . . . . . . . . Mirages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Para 0801 0802 0803 0804 0805 0806 0807 0808
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CHAPTER 8 REFRACTION, DIP AND MIRAGE 0801.
Introduction to Refraction Light, or other wave energy, is assumed to travel in a straight line at uniform speed, provided the medium through which it is travelling has uniform properties. However, if light passes from a less dense to a more dense medium at an angle to the surface, it will be bent towards the normal in the more dense medium as it is slowed down, and this change of direction is called Refraction. This can be likened to the speed of waves being progressively reduced as shown in Figs 8-1a and 8-1b. 0802.
Refraction Angles and Indices. The amount of change in direction is directly proportional to the angle between the direction of travel and the normal to the surface (angle ABN in Fig 8-1b). The ratio of this angle to the similar angle after Refraction (angle CBN´ in Fig 8-1b) is constant, so as one increases, the other increases at the same rate. Thus, the difference between them (the change in angle) also increases at the same rate. The closer the incident ray is to parallelling the surface, the greater the Refraction. Different substances have different Indices of Refraction (µ) which depend on the density of the material. If in Fig 8-1b ABN is called the Angle of Incidence () and angle CBN´ the Angle of Refraction ( θ). See Para 0401 for definitions of these terms. and are related by Snell’s Law which states that:
| | | |
‘The sines of the Angle of Incidence and Angle of Refraction are inversely proportional to the Indices of Refraction in which they occur’.
| |
Thus, if µ1 is the Index of Refraction in which occurs, and µ2 is the Index of Refraction of the substance in which occurs, then:
| |
If the change in Refraction is sudden, as shown in Fig 8-1b, then the change in direction will also be sudden. However, if a ray of light passes through a medium of gradually changing Index of Refraction, then its path is curved. This is the situation in the Earth’s atmosphere, which generally decreases in density with increased height. This gradual change of direction is called Atmospheric Refraction. For a ray of light which is approaching the observer on or near the surface of the Earth, the bending of the light is called Terrestrial Refraction and affects the Dip of the Visible Horizon.
Fig 8-1a. Light Normal to the Surface
Fig 8-1b. Light at an Angle to the Surface 8-3 Change 1
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0803.
Atmospheric Refraction
a. Effect of Atmospheric Refraction. When a ray of light from a star approaching the Earth enters the Earth’s atmosphere it is bent by Atmospheric Refraction (see Para 0802). The effect of Atmospheric Refraction is to make a heavenly body appear higher in the sky than it otherwise would, and this is shown in Fig 8-2 below. b. Size of Atmospheric Refraction Errors. If a heavenly body is at the Observer’s Zenith (ie approaching the atmosphere at 90°), its light is not Refracted ( ie the error is zero) except for a very slight amount if the various layers of the atmosphere are not exactly horizontal. As the Zenith Distance increases, the Atmospheric Refraction becomes greater. At an Apparent Altitude of 20° the error is about 2.6'; at 10° it is 5.3'; at 5° it is 9.9', and at the horizon 34.5'. c. Atmospheric Refraction Correction Tables. ‘Altitude Correction Tables’ for Atmospheric Refraction (including Semi-Diameters for the Sun and Moon) are given at the front and back of The Nautical Almanac respectively. The values given in these Tables are for Mean Refraction which are average conditions; these correction values are entirely reliable provided that abnormal conditions do not apply (see Para 0804).
Fig 8-2. Atmospheric Refraction
Abnormal Conditions of Atmospheric Refraction - Abnormal Refraction The atmosphere contains many irregularities which are erratic in their influence upon Atmospheric Refraction; where these irregularities exceed the corrections contained in The Nautical Almanac, conditions of Abnormal Refraction are deemed to exist. It is not normally possible to correct for Abnormal Refraction conditions, but the mariner should be aware when they may occur and be prepared for incorrect results. 0804.
|
a. Meteorological and Oceanographic Conditions. The following meteorological and oceanographic conditions are known to create Abnormal Refraction errors:
|
8-4 Change 1
•
After the passage of a squall.
•
After the passage of a weather front.
•
When there is a large difference between air and sea temperatures.
•
On very calm days, when air forms in layers, a mirage condition might exist.
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b. Geographic Areas. The following geographic areas around the world are known to be particularly vulnerable to Abnormal Refraction errors: •
The vicinity of the Grand Banks.
•
The West Coast of Africa from Mogador to Cap Blanc and from the Congo to Cape of Good Hope.
•
The Red Sea.
•
The Persian Gulf
•
Over ice-free water in Polar regions.
•
When offshore winds blow from high snow-covered mountains to nearby tropical seas, as along the west coast of South America.
•
When cold water from large rivers flow into a warm sea, when a strong current flows past a bay or coast, causing colder water to be drawn to the surface , as in:
The Bay of Rio de Janeiro (Brazil)
Off Santos (Brazil)
0805.
The coast of Africa from Cape Palmas to Cape Three Points during the time of the southwest monsoon. The east coast of Africa in the vicinity of Capo Gardafui during the summer.
Air Temperature and Atmospheric Pressure Correction Tables
a. The Nautical Almanac - Altitude Correction Tables. The ‘Altitude Correction Tables’ for Mean Refraction in The Nautical Almanac are based on an air temperature of 50°F (10°C) an atmospheric pressure of 1010mb (29.83 inches of mercury) at sea level on the Earth. At other temperatures the value of the Mean Refraction error is changed, becoming larger at lower temperatures / higher atmospheric pressures and smaller at higher temperatures / lower atmospheric pressures. b. The Nautical Almanac - Additional Correction Table. An ‘Additional Correction Table’ is at Table A4 in the front of The Nautical Almanac, and is used to allow for the combined effects of non-standard temperature and pressure. c. Norie’s Nautical Tables - Refraction Correction Tables. Separate Refraction Correction Tables for temperatures and pressure are also available in Norie’s Nautical Tables. d. Use of Correction Tables. Variations from the Mean Refraction will result in changes of the Refractive Index, but unless the changes are great, the differences are likely to be small. The Nautical Almanac ‘Additional Correction’ Table A4 is normally only used in extremely low temperatures or at very low Apparent Altitudes or a combination of both. In Polar regions, however, particularly near the surface and for altitudes of less than 5°, variations of several minutes are not uncommon.
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0806. Dip Definition of Dip. The Dip of the Visible Horizon (in minutes of arc) is the angle by a. which the Visible Horizon differs from the horizontal at the eye of the observer. It is reresented by angle DOH in Fig 8-3a (see explanation at Para 0806c below). Application of Dip. Dip therefore only applies when the Visible Horizon is used as b. a reference and must be applied to Sextant observations of all heavenly bodies.
c. Calculation of Dip - Without Refraction. If the eye of the observer were at the surface of the Earth, the Visible Horizon and the horizontal plane tangential to the Earth’s surface at the observer’s position would coincide, and there would be no Dip. This is shown at Fig 8-3a , where the observer is on the Earth’s surface at O’, and the angle H’O’X is the Apparent Altitude of heavenly body X . However, as the observer’s Height of Eye rises to position O, it can be seen that the angle DOX (the Apparent Altitude of heavenly body X when at Height of Eye O’O) is greater than angle H’O’X , by an amount equal to angle DOH. Angle DOH is the angle of Dip. OX and O’X are deemed to be parallel. d. Calculation of Dip - With Refraction. The principle of Dip, explained at Para 0806c above remains the same, but Terrestrial Refraction ( Atmospheric Refraction at the Earth’s surface - see Para 0802) bends the observer’s line of sight as shown at Fig 8-3b. While the observer would expect the Visible Horizon to be at position T, due to Terrestrial Refraction, it is actually at position T’. So instead of seeing the line OTD, the observer actually sees the tangent to the curved line OT’, which is the straight line OD’. Thus the angle of Dip (with Refraction) is reduced by the angle D’OD when compared to angle of Dip (without Refraction) Thus the effect of Terrestrial Refraction is to decrease the angle of Dip. The angle of Dip (with Refraction) may be computed by the formula: Angle of Dip (minutes) = 0.97 Height of Eye (feet) = 1.758 Height of Eye (metres)
e. The Nautical Almanac - Dip Table. In practice, The Nautical Almanac tables of Dip include Terrestrial Refraction and so the user does not need to allow for it separately.
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0807.
Other Methods of Correcting for Abnormal Refraction In addition to correction for Atmospheric Refraction by tables, in cases of Abnormal Refraction there are two other methods which may be used to help overcome the problem, including a solution for any abnormal Terrestrial Refraction. However, sights taken with Abnormal Refraction should be used with the utmost caution. Pairs of Stars 180° in Opposition. If it is believed that the Abnormal Refraction is a the same in both directions, one straightforward method of overcoming Abnormal Refraction is to select pairs of stars for observation on opposite sides of the horizon (ie 180° of bearing apart). When the Position Lines are plotted, halve the distance between them, thus taking the mean. By choosing pairs of stars 180° of bearing apart, any a Abnormal Refraction of whatever sort will cancel out. Select a further pair of stars 90° different in bearing from the original pair and repeat the process.
b. Over the Shoulder Sights. Another method of overcoming Abnormal Refraction, but one which requires considerable skill with a sextant, is to take the Sextant Altitude of a reasonably high star normally, and then repeat the observation ‘over the shoulder’ (ie at an angle greater than 90°, above the ‘back’ horizon, 180° from the normal bearing). The difference between the sum of the two Sextant Altitudes (corrected for Index Error ) and 180° is the sum of the Dip and Refraction to the horizon in the two directions. If it is believed that the Abnormal Refraction is the same in both directions, this sum is twice the Dip and Refraction to the horizon in each direction. 0808.
Mirages
a. Definition and Reason. When Refraction is not normal, some form of Mirage may occur. A Mirage is defined as an optical phenomenon in which objects appear displaced, distorted, magnified, multiplied or inverted, owing to varying Atmospheric Refraction in layers close to the surface of the Earth due to large air density differences. This may occur when there is an erratic or irregular change of temperature or humidity in the Earth’s atmosphere with changes in height. b. Effects - Temperature Increase with Height. Increased temperature with height (a temperature inversion) will make the Refraction greater than normal , particularly if accompanied by a rapid decrease in humidity. The effects of Mirage may then be: •
If the object appears elevated and the Visible Horizon seems farther away, it is termed Looming .
•
If the object appears taller than usual, it is termed Towering .
•
If the lower part of a object is raised more than the top and the object appears shorter overall, it is termed Stooping.
c. Effects - Temperature Decrease with Height. If the temperature decrease with height is much greater than normal, Refraction is less than normal . The effects of Mirage may then be: •
Objects will appear lower and the Visible Horizon will seem closer to the observer. This is called Sinking .
d. Geographic Areas where Mirages are Possible . Geographic areas vulnerable to abnormal Atmospheric Refraction errors, including Mirages, are listed at Para 0804b.
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CHAPTER 9 ERRORS IN ASTRONOMICAL POSITION LINES CONTENTS
Contributory Errors to Astronomical Position Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . Errors in the Observed (True) Altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Errors Inherent in the Method by Which the Sight is Reduced . . . . . . . . . . . . . . . . . . . . Errors in Course and Speed Made Good Between Observations . . . . . . . . . . . . . . . . . . . The Cocked Hat formed by Astronomical Position Lines . . . . . . . . . . . . . . . . . . . . . . . . Caution in Applying Common Equal Error Corrections to Cocked Hats . . . . . . . . . . . .
Para 0901 0902 0903 0904 0905 0906 0907
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CHAPTER 9 ERRORS IN ASTRONOMICAL POSITION LINES 0901.
Contributory Errors to Astronomical Position Lines Errors may be introduced in to the Astronomical Position Lines by contributory errors which are of four types:
0902.
a.
Errors in the Observed (True) Altitude (see Para 0902 below).
b.
Time errors (see Para 0903 below).
c.
Errors inherent in the method by which the sight is reduced (see Para 0904 below).
d.
Errors in course and speed made good between observations (see Para 0905 below).
Errors in the Observed (True) Altitude
a. Sources of Error. When the Sextant Altitude of a heavenly body has been corrected for Perpendicularity, Side Error, Index Error, Dip, Refraction, Semi-Diameter and Parallax, the Observed (True) Altitude may still be incorrect owing to a combination of sextant errors, errors of observation and incorrect values of the Dip and Refraction. This resultant error is reflected in the Intercept which may be either too large or too small, and in consequence the Astronomical Position Line itself will be plotted incorrectly. b. Limiting Areas of Error. When a position is decided by the result of two Astronomical Position Lines and they are given an ‘Assessed Possible Error’, the ship may or may not lie within a parallelogram ( Diamond of Error ) with sides parallel to the Position Lines and spaced at the ‘Assessed Possible Error’ distance from them, as shown at Fig 9-1 below. However, using Standard Deviation calculations a more useful Error Ellipse may be calculated (see Fig 9-1 below and BR 45 Vol 1 Chapters 8 and 16). NAVPAC 2 produces an Error Ellipse when three or more observations are made. These estimates of position rely on making a realistic assessment of the possible errors.
Fig 9-1. Position Lines, Diamond of (Possible) Error and Error Ellipse
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c. Reason for Large Errors . The errors most likely to increase the size of t he overall error budget, in order of probability, are:
0903.
•
Operator error in ‘cutting’ the heavenly body onto the horizon. With very great reliance being made on GPS and Loran for offshore navigation, personal operator skill with a sextant has generally reduced in the Fleet. This skill is ‘perishable’ and officers needs to keep in practice with a sextant. This can easily be achieved without great labour if NAVPAC 2 is used to reduce and plot the sights.
•
Incorrect removal of Perpendicularity Error (see Para 0336a). Failure to understand the procedure for identification of Perpendicularity Error and inability to remove it accurately produces Sextant Altitudes with significant errors. This error is especially prevalent in the sights of inexperienced junior officers training for the Navigation Watchkeeping Certificate (NWC). It is essential that their sextants are checked by an experienced officer before sights are taken, until these young officers are able to detect and remove this error accurately themselves.
•
Incorrect allowance for Refraction and Dip. Errors in Sextant Altitude arising from incorrect allowance for Refraction and Dip when Abnormal Refraction exists can give rise to significant errors. These errors are particularly insidious as the user may not even suspect their presence. See Chapter 8 for a detailed explanation of these phenomena and guidance on possible countermeasures against them.
•
Incorrect removal of Side and Index Errors (see Paras 0336b/c). Side and Index Errors are much less likely to cause errors in the Sextant Altitude than undetected Perpendicularity Error . This is because they are easy to identify and their removal is normally addressed, even by inexperienced users. However Side and Index Errors must be corrected after removing Perpendicularity Error , otherwise there is little point.
Time Errors Sources of Error. Time Errors in calculating Astronomical Position Lines are a infrequent, given the current generation of digital Deck Watches and time standard equipment embarked in most naval ships. The most likely errors are to misread the Deck Watch by a full minute at the time of observation (particularly if the analogue minute and second hands are not perfectly aligned), or to apply any known Deck Watch Error with the incorrect sign.
b. Size of Error. Any error in time will give rise to an error in the Calculated (Tabulated) Altitude, equivalent to a displacement in Longitude by an amount equal to the error in Hour Angle expressed in minutes of arc. When the Azimuth of the body observed is 0° or 180° this error is zero (ie Position Line is East-West), and is a maximum when the Azimuth of the body observed is 90° (ie Position Line is NorthSouth). When converting the Longitude error to nautical miles, the same error in time will have a greater effect in distance at the Equator than in high Latitudes due to the compression of Meridians with Latitude. This error distance may be plotted or calculated. The relationships between the error distance, Hour Angle error (ie Longitude error) and Latitude is given (see BR 45 Vol 1 Chapter 4) by the formula: Error Distance = Error in Hour Angle (ie Longitude error ) x Cosine Latitude. 9-4 Original
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c. Direction of Error. The direction of displacement depends on whether the time used for the observation is too large (ie time late) or too small (ie time early) when compared to UT (GMT).
0904.
•
If the time used is too large (ie time late) then the Astronomical Position Lines will be shifted to the West and must be moved East to correct the error.
•
If the time used is too small (ie time early) then the Astronomical Position Lines will be shifted to the East and must be moved West to correct the error.
Errors Inherent in the Method by Which the Sight is Reduced
a. NAVPAC 2. NAVPAC 2 produces a very accurate sight reduction process based on extremely precise ephemeral data and employs iterative processes not appropriate to manual methods. Where there are three or more observations NAVPAC 2 employs a Least Square method of calculation to obtain the Most Probable Position (See BR 45 Vol 1 Annex 16A) and can provide an Observed Position to an accuracy of 0.15 nautical miles (see Para 0540). b. Manual Methods with the Sight Form (NP 400). When using The Nautical Almanac and Sight Reduction Tables for Marine Navigation (NP 401 series) or other similar publications, there are unavoidable errors due to rounding up or down of values in the tables and interpolation between them. These errors are cumulative. There is also the further risk of error through mistakes in the manual process of transcribing data from the tables into NP 400, and also in any mistakes in manual addition and subtraction while working the form. See Para 0540 for the accuracies that the various tabular methods of sight reduction can provide. c. Manual Methods with Formulae. If the basic ephemeral data from The Nautical Almanac is entered into a formula (eg The Cosine Formula or Haversine Formula), then the method employed to solve the equation will have an effect on the accuracy of the answer. If using five-figure logarithms the resulting error will be minimal, but logarithm tables using smaller numbers of significant figures will increase the error budget. Programmable calculators are now widely available and can carry out these calculations to a high degree of accuracy (which can be similar to NAVPAC 2), but this accuracy does depend on the source and accuracy of the ephemeral data used, and the specification and performance of the calculator in use (see Para 0540). d. General Error Information. Attention is drawn to the general information on calculating navigational errors at BR 45 Vol 1 Chapter 16 and Annex 16A. 0905.
Errors in Course and Speed Made Good Between Observations When some time elapses between observations of heavenly bodies (eg. Sun-run-Sun), there is a likelihood that the first Astronomical Position Line will be incorrectly transferred, either because the course laid off on the chart may differ from the course actually made good, or the distance estimated to have been made good may differ from the correct distance made good. A full explanation of the procedures for constructing an Estimated Position (EP), a Probable Position Area (PPA) and the Most Probable Position (MPP) , and which allow for course and speed made good errors, may be found as follows:
• • •
BR 45 Vol 1 Chps 8 and 16 Estimated Position (EP) Probable Position Area (PPA) BR 45 Vol 1 Chps 8 & 16/16A and BR 45 Vol 4 Most Probable Position (MPP) BR 45 Vol 1 Chps 8 &16/16A and BR 45 Vol 4 9-5 Original
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0906.
The Cocked Hat formed by Astronomical Position Lines
a. Reasons for a Cocked Hat. In general, the Astronomical Position Lines obtained from three observations (which, for simplicity are considered as being taken simultaneously) are no more likely to pass through a common point than for three terrestrial Position Lines to do so, though for different reasons, as follows: •
With terrestrial Position Lines, the error is one of True Bearing , and if the same constant error applies to each True Bearing (ie the result of a compass error of lubber’s line misalignment) the bearing differences can be re-plotted with a station pointer and the constant error quantified and corrected (see BR 45 Vol 1 Chapter 9). The corrected True Bearing s may then be re-plotted and will result in a different fix position with True Bearing s ‘skewed’ slightly from the original ones.
•
With Astronomical Position Lines, the most likely reason for a Cocked Hat being formed is that the Zenith Distances are incorrect. Correction to the Zenith Distance displaces the Position Line parallel to itself.
b. Correction for Errors Causing A Cocked Hat. There are two general groups of errors in Astronomical Position Lines relating to the Observed (True) Altitude itself: •
Common Equal Error. If it is believed that there is a Common Equal Error in magnitude and sign for each sight (as in an incorrect Index Error), then simple constructions or iterations will allow the true Observed Position to be plotted. The most common use of this technique is among experienced and skilled Sextant users who consistently have a small ‘personal error’ caused by always ‘cutting’ the heavenly body deep (or shallow) on the horizon. See CAUTIONS at Para 0907.
•
Individual Random Errors. Unless individual errors for each sight are known and applied (which is most unlikely), then the true Observed Position cannot be found with certainty. However, assuming that any constant or systematic errors (eg incorrect Index Error ) have been removed, but that a Cocked Hat caused by normally distributed random errors in the Position Lines still remain, then a derivation of the Most Probable Position is possible using a Least Squares calculation. The Least Squares mathematical technique is explained in full at BR 45 Vol 1 Annex 16A (pages 494-496). Where there are three or more observations NAVPAC 2 employs a Least Square method of calculation to obtain the Most Probable Position (See BR 45 Vol 1 Annex 16A).
c. Methods of Applying Common Equal Error Corrections. If it is believed that there is a Common Equal Error in magnitude and sign for each sight, it is possible to re-plot the fix in two ways, as follows. See CAUTIONS at Para 0907. •
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Mathematical Construction. Re-plot the intercepts as if for a new Index Error. With a ‘new line’, join the original intersection of any two Position Lines to the intersection of their ‘adjusted’ Position Lines. Repeat this procedure with the same Index Error for each pair of sights. Produce each ‘new line’ so constructed until they meet; this is the true Observed Position. Care must be taken to plot ‘adjusted’ Position Lines in the correct Intercept (‘to’ or ‘from’) direction, otherwise serious errors will result. Examples of this method are at Figs 9-2 and 9-3 opposite.
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Fig 9-2. Applying Common Equal Error Corrections - Mathematical Construction (All intercepts ‘towards’ - True Obs Pos inside original Cocked Hat)
Fig 9-3. Applying Common Equal Error Corrections - Mathematical Construction (Mixed intercepts ‘from and ‘towards’ - True Obs Pos outside original Cocked Hat)
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•
Iterative Method. A similar but simpler method of achieving the same result as the ‘Mathematical Construction’ method above, is merely to re plot the intercepts as if for a different Index Error (taking care to plot the intercepts in the correct ‘to’ or ‘from’ direction). Having plotted all three ‘adjusted’ Position Lines, it can be determined by inspection whether this has made the fix better or worse. The process can be repeated on an iterative basis with different ‘adjustment’ values and signs until the true Observed Position is determined. See CAUTIONS at Para 0907.
•
NAVPAC 2 Version of the Iterative Method . With NAVPAC 2 the quickest way to achieve the Iterative Method is to alter the Index Error setting for each sight, re-calculate and observe the computer generated plot. See CAUTIONS at Para 0907.
0907.
Caution in Applying Common Equal Error Corrections to Cocked Hats The following important CAUTIONS should be borne in mind when considering the use of the above constructions (Para 0906c) for applying Common Equal Error corrections to Observed (True) Altitudes:
CAUTIONS 1. THE ABOVE CONSTRUCTIONS ARE VALID ONLY WHEN THE ERRORS IN THE ZENITH DISTANCES OBTAINED ARE EQUAL IN MAGNITUDE AND SIGN, AS THEY ARE WHEN THE INDEX ERROR IS INACCURATE. 2. THE ABOVE CONSTRUCTIONS CAN BE MADE WHETHER OR NOT OTHER ERRORS ARE TAKEN INTO CONSIDERATION AND MAY THUS GIVE A FALSE SENSE OF PRECISION. 3. FOR THESE REASONS, NO RELIANCE SHOULD BE PLACED ON SUCH CONSTRUCTIONS UNLESS IT IS FIRMLY BELIEVED THAT THE TOTAL ERRORS IN EACH INTERCEPT ARE EQUAL IN MAGNITUDE AND SIGN. 4. THE TRUE OBSERVED POSITION LIES OUTSIDE THE ORIGINAL COCKED HAT ONLY IF ALL THREE BEARINGS CAN BE ENCLOSED BY 180°.
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APPENDIX 1 THE SKY AT NIGHT 1.
An Overview of the Navigational Stars The 58 ‘Navigational Stars’ are shown at Fig App 1-1. The red line indicates the most convenient route for identifying one star from another, if observing the sta rs without instruments.
Fig App 1-1. The 58 Navigational Stars App 1-1 Original
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2.
The Navigational Planets The Declinations The Declinations of of the four navigational planets rarely exceed t he limits of 26°N and 26°S and therefore are seen near the the Ecliptic Ecliptic (the apparent path of the sun in the Celestial Sphere). Sphere). Nevertheless, against the backdrop of stars, the planet’s movements in the sky are relatively volatile. The mean distance of the 5 main planets from the Sun are:
Venus Earth Mars Jupiter Saturn
— 67,000,000 miles — 93,000,000 miles — 142,000,000 miles — 483,000,000 mi miles — 886,000,000 mi miles
a. Venus. Venus lies between the Earth and the Sun, and is therefore said to be an ‘inferior’ planet. To an observer on the Earth, it is never more more than 47° removed from the Sun, for which reason it cannot be seen throughout the night in temperate Latitudes temperate Latitudes.. It is thus a ‘morning or evening’ planet. Its magnitude varies slightly, but is on the average 3.4. No other star or planet is so brilliant. b. Mars Mars has an average magnitude of about 0.2, varies appreciably in brilliance, but may distinguished with with care by its reddish light. .
c.
Jupiter. Jupiter has an average magnitude of 2.2 and is next to Venus in brilliance. brill iance.
d. Saturn. Saturn has an average magnitude of 1.4, 1.4, is not readily identified. Saturn’s rings are not visible through the telescopes and binoculars normally used on the bridge. 3.
The Co Constellations Stars maintain an almost static position relative to each other and the bright ‘navigational’ stars appear mostly within certain well-defined constellations. Once these constellations have been memorised, it is i s possible with practice to identify the stars by eye eye from the relative positions which they maintain. The constellations still carry the fanciful names given to them by early (mostly Greek) astronomers, but these names require significant imagination to represent the objects described. The star charts in The Nautical Almanac Almanac show all the ‘navigational’ stars.
a. Ursa Major or The Great Bear. The constellation of Ursa Major is popularly known as ‘The Plough’, and it is important because a line drawn through its ‘Pointers’ directs one towards Polaris (the Pole Star). Fig App 1-1 shows the position of The The Plough in relation to other constellations. In the Latitude the Latitude of of UK, the entire constellation is circumpolar (that is, the heavenly body never sets) sets) and thus remains above the observer’s horizon; when the constellation is above the Pole it will look as in Fig App12 whereas when below the Pole it will appear as in Fig App 1-3. It can also be seen in Figs App1-2 and App1-3 why the stars Dubhe and Merak are referred to as ‘The Pointers’. b. Ursa Minor or The Little Bear. Ursa Minor is not unlike the Plough Plough in shape but is much smaller and fainter. Its stars form a saucepan sa ucepan shape reminiscent of the Plough though with the curve in its ‘handle’ reversed. Ursa Minor’s main claim to distinction lies in its possession of Polaris at its extreme end, nearest to the Celestial Pole. Pole. App 1-2 Original
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Fig App 1-2. The Plough (Above the Pole, Observer Looking North)
Fig App 1-3. The Plough (Below the Pole, Pole, Observer Looking Looking North) App 1-3 Original
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c. Cassiopeia. This constellation - sometimes known as ‘The as ‘The Chair’ - is found on the side of the pole opposite to Ursa Major, and about the same distance away. It does not contain any stars of first-magnitude, but it is fairly prominent in the sky, and is useful in identifying Pegasus (Fig App 1-4). d. Pegasus . This constellation (Fig App 1-4) - sometimes known as ‘The Square’ is useful to anybody wishing to obtain some idea of sidereal time, because the side formed by Alpheratz and Algenib lies almost on the Meridian the Meridian through through the First the First Point of Aries. Aries. e. Aries ( ). This constellation (Fig App App 1-4) is not is itself particularly significant except that it lends its name to a position where the Ecliptic once Ecliptic once cut the Celestial st Equator at at the Spring Equinox (21 Equinox (21 March). The name ‘First Point of Aries’ ( ( ) has been retained for this position, even though though Aries itself has apparently apparently moved away and no longer occupies this ‘prime site’ in the Celestial Sphere. See Para 0104.
Fig App 1-4 Pegasus or the Square ( Below the Pole, Observer Looking North)
App 1-4 Original
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f. Orion. This constellation (Fig App 1-5), contains stars of N. and S. Declination S. Declination and important ‘signposts’ to others. It is supposed to resemble a ‘giant’, and the three close stars in the centre of the constellation are referred to as Orion’s Orion’s Belt. The ‘belt’ points almost directly at Sirius (the Dog Dog star), in the constellation of Canis Major (The Great Dog); a line through Rigel and its centre ‘button’ leads to Castor in the constellati conste llation on of Gemini (The Twins). The constellations of Canis Minor (The Little Dog) which contains contains Procyon, Procyon, and of Taurus (The Bull) which contains Aldebaran, lie nearby. g. The Southern Cross (Crux) . This constellation (Fig App 1-6) forms a cross if the observer imagines diagonal lines joining the four stars. Its significance is more poetic poetic than navigational, and it is too far removed from the South Celestial Pole to Pole to be useful in finding the observer’s Latitude observer’s Latitude directly, directly, as may be done with Polaris in the northern hemisphere. Two bright stars in the constellation Centaurus help the observer to find it.
Fig App 1-5 Orion (Observer Looking South)
Fig App 1-6 The Southern Cross (Observer Looking South) App 1-5 Original
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4.
Specific Navigational St Stars From knowledge of the constellations, an observer should be able to pick out the navigational stars - if they are above the horizon - by referring them to imaginary lines in the Celestial Sphere. Sphere. (α Eridani, Mag. 0.6). This star lies midway between Canopus and a. Achernar (α Fomalhaut on the line joining them (Fig App 1-1)
b. Aldebaran (α (α Tauri, Mag. 1.1). This star can be fixed in relation to Orion’s belt, which points roughly at it in one direction and at Sirius in the other and lies almost midway between them (Fig (Fig App App 1-5). 1-5). Aldebaran Aldebaran is further further distinguis distinguished hed by by a reddish tint. c. Altair (α Aquilae, Mag. 0.9). A line from Capella through through Caph in Cassiopeia Cassiopeia points to Altair, which also lies between two less bright stars in a line with Vega (Fig App 1-1). d. Antares (α Scorpii, Mag. 1.2). This, another reddish star, lies at the centre of a small bow which which points points directly at another another bow bow (Fig (Fig App App 1-1). 1-1). e.
0.2). This is one of the brightest stars, and is found by Arcturus (α Bootis, Mag. 0.2). continuing the curve of the Great Bear’s ‘tail’ (Fig App 1-1).
f. Bellatrix (γ Orionis, Mag. 1.7). This is one of the three bright stars that mark corners of the quadrilateral in the constellation of Orion (Figs App 1-1 and App 1-5). g. Betelgeuse (α Orionis, Mag. 0.5 - 1.1). This is another of the three bright bright stars that mark corners of the quadrilateral in the constellation of Orion. It may be identified by its reddish colour (Figs App 1-1 and App 1-5). h. Canopus (α Carinae, Mag. 0.9). Next to Sirius, Canopus Canopus is the brightest brightest star. It lies about half-way between Sirius and the South Celestial Pole, Pole, and on the line joining Fomalhaut and Achernar (Fig App 1-1). i. Capella (α Aurigae, Mag. 0.2). This bright star forms a rough rough equilateral triangle with Betelgeuse and Castor, about half-way between Orion and Polaris (Fig App 1-1). j. Castor ( α Geminorum, Mag. 1.6). A line from Rigel through the middle star of Orion’s Belt points to Castor (Figs App 1-1 and App 1-5). k. Rigil Kent (α Centauri, Mag. 0.1), and Hadar (β (β Centauri, Mag. 0.9). These are two bright stars on the line joining Antares and Canopus (Fig App 1-1). l. Fomalhaut (α Piscis Australis, Mag. 1.3). The line joining Scheat and a nd Markab in Pegasus, produced away from Polaris, passes pass es through Fomalhaut (Fig App 1-1). m. Polaris or The Pole Star (α Ursae Minoris, Mag. 2.1). A line through ‘the Pointers’ of the Plough (Ursa Major or the Great Bear) leads to this star and the observer can easily verify that he has chosen the correct star by measuring its altitude, which is roughly his Latitude his Latitude (Figs (Figs App 1-1, App1-2 and App1-3).
App 1-6 Original
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n. Pollux (β Geminorum, Mag. 1.2). This as the name of the constellation suggests, will be seen close to Castor (Figs App 1-1 and App 1-5). o. Procyon ( α Canis Minoris, Mag. 0.5). 0.5). Procyon, Betelgeuse and Sirius form an equilateral triangle (Figs App 1-1 and a nd App 1-5). p. Regulus (α Leonis, Mag. 1.3). A line from Bellatrix through through Betelgeuse points to Regulus, which is about 60° from Betelgeuse (Fig App 1-1). q. Rigel (β Orionis, Mag. 0.3). This is the third of the three bright bright stars that, together with κ Orionis Orionis, form the quadrilateral in the constellation of Orion (Figs App 1-1 and App 1-5). r. Sirius (α Canis Majoris, Mag. 1.6). Sirius is the brightest star. It lies to the southeast of Orion, approximately in a line with the ‘Belt’ (Figs App 1-1 and App 1-5). s. Spica (α Virginis, Mag. 1.2). This bright star may be found by continuing the curve of the Great Bear’s ‘tail’ ‘tail ’ through Arcturus, which lies about midway between the ‘tail’ and Spica (Fig App 1-1). t. Vega (α Lyrae, Mag. 0.1). Vega is found found by extending the line joining Capella to Polaris about an equal distance on the opposite side of the pole. Near Vega is a distinct ‘W’ of small stars (Fig App 1-1).
App 1-7 Original
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APPENDIX 2 EXTRACTS FROM THE NAUTICAL ALMANAC (1997)
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INDEX 1. Paragraph numbers in BOLD TYPE indicate the primary references, which give the main definition and/or explanation, including definitions / explanations at Para 0401. 2. Paragraph numbers in ORDINARY TYPE indicate other occurrences of the term. Where appropriate, cross references to other variants of the term are given. Paragraph NUMBERS IN BRACKETS indicate associated information. 3. Software commands and terms used exclusively within NAVPAC 2 are NOT INCLUDED in this Index, although they will be found in the text of Chapter 3 and Annex 3A. Terms used in the verbatim extracts from The Nautical Almanac at Paras 0545 and 0546 are NOT INCLUDED in this Index, unless found elsewhere in the book. Abnormal Refraction. Paras 0339j, 0401, 0560, 0804, 0807, 0902. Altitude (of a heavenly body) . Paras 0118, 0132, 0324, 0350, 0351, 0401, 0501, 0521, 0524, 0542, 0551, Anx 5A, 0604, 0605, 0723, 0741, 0742. See also separate entries for: Apparent Altitude Calculated (Tabulated) Altitude ‘d’ (Altitude Difference (d) from NP 401) Observed (True) Altitude Sextant Altitude Tabulated Altitude Very High Altitude (Tropical) Sights Altitude Difference (d). See separate entry for ‘d’ (Altitude Difference (d) from NP 401). Angle of Incidence (). Paras 0401, 0802.
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Angle of Refraction (θ). Paras 0401, 0802. Angular Distance. Paras 0102, 0104, 0105, 0106, 0401, 0420, 0422, 0436, 0442, 0443, 0501, 0522, 0601, 0621. Apparent Altitude. Paras 0107, 0118, 0348, 0401, 0560, 0720, 0721, 0723, 0730, 0741, 0742, 0803, 0805, 0806. Apparent Solar Day / Time. Paras 0401, 0432, 0439, 0441, 0442. Aries ( ). Paras 0104, 0106, 0420, 0401, 0421 / Fig 4-1 , 0441, 0443, 0444, 0450, 0453, 0501, 0543, 0544, Anx 5A, 0608, 0609, 0622, App 1. Astronomical Day. Paras 0401, 0434, 0435. Astronomical Position Line / Position Line. Paras 0345, (0346), 0350, 0351, 0401 , 0520, 0521, 0524, 0525, 0526, 0530, 0544, 0550, 0551, 0560, 0561, 0562, 0601, 0801, 0807, 0901, 0902, 0903, 0905, 0906. Brackets indicate associated information. Index-1 Change 1
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Astronomical Twilight (AT). Paras 0108, 0401, 0724, 0725, 0726 , 0741, 0742. Atmospheric Refraction. Paras 0107, 0502 (Note 5-1), 0401, 0702, 0802, 0803, 0804, 0806, 0807, 0808.
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Autumn Equinox. See separate entry for Equinoxes - Spring and Autumn. Axis (of the Earth). Para 0401 “Axis (of the Earth)” , Anx 5A. Azimuth (of a heavenly body) . Paras 0117, 0324, 0345, 0348, 0351, 0401, 0501, 0524, 0533, 0534, 0535, 0536, 0542, Anx 5A, 0622, 0742, 0903. See also separate entries for: Azimuth Angle (of a heavenly body) Calculated (Tabulated) Azimuth Supplementary Azimuth True Bearing (of a heavenly body) Azimuth Angle (of a heavenly body). Paras 0401, 0536, 0542, 0543, 0741. Bearing. See separate entry for True Bearing (of a heavenly body). Calculated (Tabulated) Altitude. Paras 0118, 0345, 0351, 0401, 0531, 0521, 0524, 0530, 0531, 0532, 0533, 0542, 0741, 0903. See also separate entry for Tabulated Altitude. Calculated (Tabulated) Azimuth. Paras 0401, 0530, 0531 , 0535, 0536, 0741. Calculated (Tabulated) Co-Declination. Paras 0401, 0531. See also separate entry for Co Declination (also known as ‘Polar Distance’). Calculated (Tabulated) LHA. Paras 0401, 0531. Calculated (Tabulated) Position Circle. Paras 0401, (0522), 0524. See also separate entry for Position Circl e. Brackets indicate associated information. Calculated (Tabulated) Zenith Distance (CZD). Paras 0401, 0524, 0532, 0533. Calculated Zenith Distance . See separate entry Calculated (Tabulated) Zenith Distance (CZD). Celestial Equator. Paras 0101, 0103, 0104, 0105, 0106, 0401, 0421 / Fig 4-1 , 0433, 0444, 0501 (Note 5-1), 0503, 0544f, Anx 5A, 0612d/e, App1. Celestial Horizon. Paras 0107, 0108, 0115, 0119, 0401, 0501 (Note 5-1), 0612d, 0621, 0702, 0721, 0724, 0725, 0730, 0741. Celestial Latitude. Paras 0105 (Note 1-1), 0401. Celestial Longitude. Paras 0106 (Note 1-2), 0401. Celestial Meridian. Paras 0401, 0421 / Fig 4-1, Anx 5A. Index-2 Change 1
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Celestial Poles. Paras 0101, 0401, 0421 / Fig 4-1 , Anx 5A, 0620, 0621, 0723, 0727. Celestial Sphere. Paras 0101, 0102, 0105, 0106, 0114, 0115, 0120, 0401, 0420, 0421 / Fig 4-1 , 0430, 0431, 0444, 0453, 0501, 0502, 0503, 0524, 0741, App 1. Chosen Declination. Paras 0401, 0542, 0542g, 0543, 0544, App 1. Chosen Latitude. See separate entry for Chosen Position. Chosen Longitude. See separate entry for Chosen Position. Chosen Position. Paras 0401, 0524, 0525, 0531, 0542, 0542f , 0543, 0544, 0561, 0562. Circumpolar. Paras 0401, 0727. Civil Day. Paras 0401, 0434, 0435. Civil Twilight (CT). Paras 0108, 0401, 0724, 0725 , 0741, 0742. See also separate entries for: Evening Civil Twilight (ECT) Morning Civil Twilight (MCT) Cocked Hat. Paras 0401, 0906, 0907, and BR 45(1) Chapter 9 and Appendix 7. Co-Declination (also known as Polar Distance). Paras 0401, 0534b, 0542, 0620. See also separate entry for Calculated (Tabulated) Co-Declination. Co-Latitude. Paras 0401, 0501, 0531, 0534, 0542. Collimation Error. See separate entry for Sextant: Collimation Error. Common Equal Error (corrections). Paras 0401, 0906, 0907. Confidence Ellipse. Para 0346c, 0401, 0902. See also separate entry for Error Ellipse. CONTRARY (name). Paras 0401, 0542b, 0542, 0543, 0602, 0603, 0612, 0741, 0742. Co-ordinated Universal Time (UTC). Paras 0211, 0401. Corrected Tabulated Altitude (Corr Tab Alt). Paras 0401, 0542g, 0543, 0544g. ‘d’ (Altitude Difference (d) from NP 401). Paras 0401, 0542, 0542d, 0542g, 0543a. “d” / “d corrn” (Declination correction from The Nautical Almanac). Paras 0401, 0543b. Daily Difference (suffixed with MP, MR or MS as appropriate). Paras 0401, 0607c (Note 6-1), 0731 (Note 7-1).
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Day. Paras 0401, 0431, 0441. See also separate entries for: Apparent Solar Day / Time Astronomical Day Civil Day Lunar Day / Month Mean Solar Day Sidereal Day / Time Solar Day Daylight Saving Time (DST). Paras 0202, 0204, 0401, 0438. Deck Watch. Paras 0401, 0903. Deck Watch Error (DWE). Paras 0211, 0327, 0340, 0350, 0351, 0401, 0543, 0544g, 0551, 0561, 0903. Deck Watch Time (DWT). Paras 0327, 0339, 0340, 0348, 0350, 0351, 0401, 0501, 0542h, 0543, 0544g, 0551, 0561. Declination. Paras 0105, 0114, 0348f, 0348g, 0348h, 0401, 0421 / Fig 4-1 , 0501, 0502, 0532, 0534, 0542, 0543, 0551, Anx 5A, 0602, 0603, 0605, 0612, 0620, 0725, 0726, 0730, 0741, 0742, App 1. See also separate entries for: Chosen Declination Parallels of Declination Tabulated Declination. Declination Increment (Dec Inc). Paras 0401, 0542g, 0543, 0544f. Depressed Pole. Paras 0401, 0741. Diamond of Error. Paras 0401, 0902. Difference “d” . See separate entry for “d”(Altitude Difference from NP 401). Difference of Time for Longitude (suffixed MP, MR or MS as appropriate). Paras 0401, 0607d, 0731c. Dip. Paras 0118, 0339r, 0348, 0401, 0543, 0560, 0741, 0742, 0802, 0806, 0902. Double Second Difference Correction (from NP 401). Paras 0401, 0542g, 0543. Earth’s Axis. See separate entry for Axis (of Earth). Ecliptic. Paras 0103a, 0104, 0105, 0106, 0120, 0401, 0431, 0433, 0544f, Anx 5A, App1. Elevated Pole. Paras 0401, 0535, 0542, Anx 5A, 0741. EP (Estimated Position). Paras 0401, 0905. See also BR 45(1) Chapters 8 and 16. Index-4 Original
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Epoch. Paras 0401, 0544e, 0544f. Equation of Time. Paras 0401, 0439. Equator. Paras 0401, 0903. See also BR 45(1) Chapter 1. Equinoxes - Spring and Autumn. Paras 0103b, 0104, 0401, 0452, 0544f, App 1. Error Ellipse. Para 0902. See also separate entry for Confidence Ellipse and BR 45(1) Chapters 8 and16. Estimated Position (EP). See separate entry for EP (Estimated Position). Evening Civil Twilight (ECT). Paras 0108, 0320, 0321, 0322, 0323, 0339, 0401, 0724, 0725 , 0741, 0742. Evening Nautical Twilight (ENT). Paras 0108, 0320, 0321, 0322, 0323, 0339 0401, 0724, 0725, 0741, 0742. First Difference Correction (FDC) (from NP401). Paras 0401, 0542g, 0543. First Point of Aries (
). See separate entry for Aries ( ).
First Point of Libra. See separate entry for Libra. First Quarter (of the Moon). Para 0401, 0452. Full Moon. Paras 0339s, 0401, 0452. Geographic Position. Para 0109, 0401, 0521, 0525, 0550, 0551, 0552. Great Circle. Paras 0103, 0110, 0111, 0115, 0119, 0301, 0401, 0525,0562, 0741. Greenwich Celestial Meridian. Paras 0401, 0421 / Fig 4-1. Greenwich Hour Angle (GHA). Paras 0106, 0401, 0420c , 0421 / Fig 4-1, 0422, 0435, 0444, 0450, 0452, 0453, 0501, 0542, 0543, 0544, 0551, Anx 5A, 0606, 0607, 0608, 0609, 0725, 0730, 0742. Greenwich Hour Angle Increment (GHA Increment) . Para 0401, 0543b. Greenwich Mean Time (GMT). Paras 0201, 0210, 0350, 0401, 0434, 0435, 0436, 0437, 0450, 0560, 0606, 0607, 0608, 0609, 0611, 0731, 0903. See also separate entry Universal Time (UT). Greenwich Meridian. Paras 0112, 0322, 0325, 0401, 0420, 0422, 0435, 0607, 0608, 0611, 0722, 0730, 0731. Height of Eye (HE). 0116, 0118, 0344, 0348, 0401, 0551, 0561, 0720, 0721, 0730, 0742, 0806. See also separate entry for Dip. Index-5 Original
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High Latitude (Polar) Sights. Paras 0401, 0560, 0561, 0562. High Altitude (Tropical) Sights. See separate entry for Very High Altitude (Tropical) Sights. Horizon. See separate entries for: Celestial Horizon Plane of the Celestial Horizon Visible Horizon Horizontal Parallax. Paras 0348d (Note 3-8) , 0401, 0543, 0702, 0730, 0741, 0742, 0902. Hour Angles. Paras 0106, 0401, 0420, 0421 / Fig 4-1 , 0433, 0443, 0452, 0453, 0534, 0542, 0725, 0903. See also separate entries for: Greenwich Hour Angle (GHA) Local Hour Angle (LHA) Right Ascension (RA) Sidereal Hour Angle (SHA) Index Error (IE). See separate entry for Sextant: Index Error. Index of Refraction (µ). See separate entry for Refractive Index. Intercept. Paras 0345, 0346, 0351, 0401, 0521, 0524 / Fig 5-3, Fig 5-4 , 0525, 0526, 0542h, 0543, 0544g, 0550, 0561, 0562, 0902, 0906. International Atomic Time (TAI). Paras 0211b, 0401. International Date Line (IDL). Paras 0201, 0206, 0401. Last Quarter (of the Moon). Paras 0401, 0452. Latitude. Para 0401 and BR 45(1) Chapter 1. Least Square (method of calculation). Paras 0401, 0904, 0906 and also BR 45(1) Annex 16A Legal Time. See separate entry for Standard Legal Time. Libra. Para 0104, 0401, 0544f. Local Hour Angle (LHA). Paras 0106, 0132, 0348j, 0401, 0420d , 0421 / Fig 4-1, 0422, 0435, 0436, 0452, 0453, 0501, 0532, 0535, 0542, 0543, 0544, Anx 5A, 0601, 0602, 0603, 0608, 0609, 0610, 0611, 0621, 0622, 0723, 0741, 0742. Local Mean Time (LMT). Paras 0133, 0205, 0322, 0325, 0401, 0435, 0436, 0437, 0606, 0607, 0608, 0609, 0611, 0722, 0731, 0742. Local Sidereal Time (LST). Paras 0401, 0443. Index-6 Original
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Longitude. Para 0401 and BR 45(1) Chapter 1. Looming (Mirage). Paras 0401, 0808b. Lower Hemisphere. Paras 0401, 0502(Note 5-1). See also separate entry for Visible Hemisphere. Lower Limb (LL). Paras 0170b, 0348d, 0401, 0702, 0704, 0723. Lower Mer Pass / Lower Meridian Passage (of a heavenly body), (also known as Meridian Passage Below the Pole). Paras 0348i, 0401, 0602, 0603, 0610, 0612e. Lunar Day / Month. Paras 0401, 0450, 0451, 0607. Lunar Units. Paras 0401, 0450. Lunation. Paras 0401, 0451. Mean Refraction. Paras 0401, 0803, 0805. Mean Solar Day. Paras 0401, 0434, 0442, 0443, 0441, 0450, 0451, 0607. Mean Solar Hour / Minute / Time. Paras 0209, 0401, 0434, 0439, 0443, 0451. Mean Sun. Paras 0401, 0433, 0434, 0435, 0436, 0439, 0444, 0452, 0608. See also separate entry for True Sun. Meridian. Paras 0107, 0111, 0112, 0132, 0201, 0206, 0320, 0325, 0326, 0339, 0401, 0420, 0422, 0431, 0432, 0434, 0435, 0436, 0438, 0441, 0450, 0501, 0526, 0535, 0542, 0562, Anx 5A, 0601, 0602, 0603, 0606, 0608, 0609, 0611, 0702, 0722, 0903. See also separate entries for: Celestial Meridian Greenwich Meridian Greenwich Celestial Meridian Lower Mer Pass / Lower Meridian Passage (of a heavenly body), (also known as ‘Meridian Passage below the Pole’) Mer Pass / Meridian Passage (of a heavenly body),(also known as ‘Upper Mer Pass / Upper Meridian Passage’) Observer’s Meridian Prime Meridian Meridian Passage Below the Pole. See separate entry for ‘Lower Mer Pass / Lower Meridian . Passage (of a heavenly body)’ Mer Pass / Meridian Passage (of a heavenly body), (also known as ‘Upper Mer Pass / Upper Meridian Passage’). Paras 0133, 0320, 0325, 0326, 0348f-g, 0348i, 0401, 0452, 0540, 0550, 0551, 0601, 0602, 0603, 0604, 0605, 0606, 0607, 0608, 0609, 0610, 0611, 0612, 0731, 0741, 0742. Midnight Sun. Para 0726. Index-7 Original
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Mirage. Paras 0401, 0808. See also separate entries for: Looming Stooping Sinking Towering Month. See separate entry for Lunar Day / Month. Moonrise, Moonset. See separate entries (which co-ordinate all variants) for: True (Theoretical) Rising and Setting (Sun and Moon) Visible Rising and Setting (Sun and Moon) Morning Civil Twilight (MCT). Paras 0108, 0320, 0321, 0322, 0323, 0339, 0401, 0724, 0725 , 0741, 0742. Morning Nautical Twilight (MNT). Paras 0108, 0320, 0321, 0322, 0323, 0327, 0339, 0401, 0724, 0725, 0741, 0742. Most Probable Position (MPP). Paras 0401, 0904, 0905 , 0906. See also BR 45(1) Chapter 16 / Annex 16A, and BR 45(4). Nautical Twilight (NT). Paras 0108, 0401, 0724, 0725 , 0741, 0742. See also separate entries for: Evening Nautical Twilight (ENT) Morning Nautical Twilight (MNT) NAVPAC 2 / NAVPAC 1. Paras 0131, Chapter 3, 0401, 0502, 0525, 0540, 0541, 0561, 0604, 0624, 0725, 0740, 0742, 0902, 0904, 0906. New Moon. Paras 0401, 0451, 0452. Nutation. Paras 0401, 0544b, 0544e, 0544f, 0544g. Obliquity of the Ecliptic. Paras 0103a, 0401. Observed Position (Obs. Pos). Para 0346d, 0401, 0525, 0526, 0540, 0542h, 0543, 0544, 0551, 0904, 0906. See also separate entry for Observed (True) Position. Observed (True) Altitude. Paras 0118, 0345, 0348d, 0401, 0351, 0521, 0522, 0524, 0543, 0550, 0551, 0612, 0620, 0621, 0721, 0730, 0741, 0901, 0902, 0906, 0907. Observed (True) Position. Paras 0401, 0524b. See also separate entry Observed Position. Observed (True) Position Circle . Paras 0401, (0522), 0524, 0525. See also Position Circle. Observed (True) Zenith Distance (TZD). Paras 0401, 0524, 0525, (0551f), (0552), (0702, (0721), (0723), (0725). Brackets indicate associated information. Index-8 Original
BR 45(2)
Observed Zenith Distance. See separate entry for Observed (True) Zenith Distance (TZD). Observer’s Meridian. Paras 0320, 0325, 0326, 0348, 0401, 0421 / Fig 4-1 , 0422, 0431, 0432, 0434, 0442, 0443, 0450, 0451, 0535, 0551, Anx 5A, 0601, 0602, 0603, 0604, 0605, 0607, 0621, 0731, 0742. Observer’s Zenith (Z). Paras 0109, 0114, 0115, 0118, 0119, 0401 , 0421, 0501, 0502 (Note 5-1), 0503, Anx 5A, 0803. Parallax. See separate entry for Horizontal Parallax. Parallels of Declination. Paras 0105, 0401. Parallels of Latitude. See BR 45(1) Chapter 1. Perpendicularity (error). See separate entry for Sextant: Perpendicularity (error). Plane of the Celestial Horizon. Paras 0401, 0503 (Note 5-2). Polar Distance (PX). See separate entry for alternative title of ‘Co-Declination’ . Polaris. Paras 0348j, 0401, 0540, 0620, 0621, 0622, 0623, 0624. Polar Variation. Para 0401. Poles (of the Earth). Paras 0111, 0401, 0561, 0562, 0602, 0603, 0741. See also separate entry for Celestial Poles. Position Circle. Paras 0401, 0522, 0523, (0524) 0525, 0550, 0561. Brackets indicate associated information. See also separate entries for: Observed (True) Position Circle Calculated (Tabulated) Position Circle Position Line. See separate entry for Astronomical Position Line. Precession. Paras 0104, 0401, 0544b, 0544f , 0544e, 0544g. Precession of Equinoxes. Paras (0104), 0401, 0544f. See also separate entry for Equinoxes Spring and Autumn. Prime Meridian. Paras 0112, 0209, 0401. Probable Position Area (PPA). Paras 0401, 0905. See also BR 45(1) Chapter 16 / Annex 16A, and BR 45(4). PZX Triangle. Paras 0401, 0501, 0531, 0532, 0533, 0534, 0542, 0741. P'Z'X Triangle. Paras 0401, 0741. Index-9 Original
BR 45(2)
Refraction. Paras 0348d, 0349, 0401, 0543, 0551, 0612, 0723, 0730, 0741, 0742, 0801, 0802, 0803, 0804, 0805, 0806, 0807, 0808 , 0902. See also separate entries for: Abnormal Refraction Angle of Incidence Angle of Refraction Atmospheric Refraction Mean Refraction Refractive Index (also known as Index of Refraction) Terrestrial Refraction Refractive Index (µ) . Paras 0401, 0802, 0805. Rhumb Line. Para 0113, 0301, 0401, 0524, 0525. Right Ascension (RA). Paras 0106, 0133, 0401, 0420a/b, 0421, 0501, Anx 5A. Run / Run-on, Run-back. Paras 0345, 0346, 0350, 0351 and Note 3-9 , 0401, 0525, 0524h, 0543, 0544g, 0551. SAME (name). Paras 0401, 0542b, 0542, 0543, 0602, 0603, 0612, 0725, 0741, 0742. Semi-Diameter. Paras 0107, 0401, 0551, 0702, 0704, 0721, 0723, 0730, 0741, 0742, 0803, 0902. Sextant. Paras 0330-0339, 0401, 0542g, 0550, 0551, 0552, 0620, 0622, 0806 and entries for: Sextant: Altitude. See separate entry “Sextant Altitude” on following page. Sextant: Arc. Paras 0331, 0332, 0333, 0336, 0338, 0339. Sextant: Arc of Excess. Para 0332. Sextant: Clamp (Index Bar). Paras 0331, 0333, 0338. Sextant: Collar. Paras 0331, 0334, 0338. Sextant: Collimation Error. Paras 0335, 0336d/e. Sextant: Horizon Glass. Paras 0331, 0332, 0334, 0336, 0339. Sextant: Index Bar. Paras 0331, 0332, 0333, 0336, 0338. Sextant: Index Error. Paras 0118, 0332, 0336c, 0336g, 0337, 0339, 0340, 0344, 0348, 0543, 0544g, 0551, 0561, 0720, 0807, 0902, 0906. Sextant: Index Glass. Paras 0332, 0334d, 0336, 0339. Sextant: Index Mark. Paras 0331, 0332. Sextant: Main Frame. Paras 0331, 0334, 0338. Sextant: Micrometer Drum. Paras 0331, 0332, 0333, 0336f , 0339. Sextant: Milled Head . Paras 0334b. Sextant: On the Arc. Paras 0332, 0336. Sextant: Off the Arc. Paras 0332, 0336. Sextant: Perpendicularity (error). Paras 0336a, 0337, 0339, 0902. Sextant: Reading Lamp. Paras 0331, 0334, 0339. Sextant: Shades. Paras 0331, 0334, 0338, 0339. Sextant: Side Error. Paras 0336b, 0337, 0339. Sextant: Star Telescope. Paras 0335, 0336, 0339, 0902. Sextant: Sun Telescope. Paras 0335, 0336, 0339. Sextant: Telescope. Paras 0331, 0334, (0335), 0336, 0338. Index-10 Original
BR 45(2)
Sextant Altitude. Paras 0118, 0336, 0339h, 0340, 0348, 0401, 0542h, 0543, 0544g, 0550, 0551, 0561, 0605, 0612, 0702, 0807, 0902. Side Error. See separate entry for Sextant: Side Error. Sidereal Day / Time. Paras 0401, 0441, 0442, 0443. Sidereal Hour Angle (SHA). Paras 0106, 0133, 0401, 0420a/b, 0421 / Fig 4-1 , 0422, 0444, 0450, 0453, 0501, 0502, 0543, 0544f, Anx 5A, 0609, 0730. Sidereal Hour / Minute. Paras 0401, 0443. Sinking (Mirage). Paras 0401, 0808c. Small Circle. Paras 0110, 0351, 0401, 0521, 0522, 0562, 0620, 0621. Solar Day. Paras 0401, 0431. Solar Time. Paras 0209, 0401, 0431. See also Mean Solar Hour / Minute / Time. Solstice. Paras 0103b, 0401. Spring Equinox.
See separate entry for Equinoxes - Spring and Autumn.
Standard Deviation (method of calculation). Paras 0401, 0902. See also BR 45(1) Chapter 16 and Annex 16A. Standard Legal Time. Paras 0201, 0202 / Fig 2-1, Fig 2-2, 0203, 0204 , 0206, 0401, 0438. Standard (or Zone) Time. Paras 0201, 0202, (0203), 0204, 0206 , 0322, 0325, 0401, 0438, Anx 5A, 0606, 0607, 0608, 0609, 0611, 0722, 0724, 0731, 0742. Brackets indicate associated information. Standard Time Zones / Time Zones. Paras 0201, 0202 / Fig 2-1, Fig 2-2 , 0204, 0206, 0208, 0322, 0325, 0401, 0438, 0560, 0606. Stooping (Mirage). Paras 0401, 0808b. Summer Solstice. See separate entry for Solstice. Sun. See separate entries for: Mean Sun True Sun Sunrise, Sunset. See separate entries (which co-ordinate all variants) for : True (Theoretical) Rising and Setting (Sun and Moon). Visible Rising and Setting (Sun and Moon). Index-11 Original
BR 45(2)
Supplementary Azimuth. Paras 0401, 0741, 0742. Tabulated Altitude (from NP 401 / NP 303). Paras 0401, 0542d, 0542g, 0543, 0544. See also separate entries for: Calculated (Tabulated) Altitude Corrected Tabulated Altitude (Corr Tab Alt) Tabulated Declination (used with NP 401 / NP 303). Paras 0401, 0543b Tabulated Zenith Distance. See separate entry Calculated (Tabulated) Zenith Distance (CZD). Terrestrial Refraction. Paras 0401, 0802, 0806, 0807. Time. See separate entries for: Apparent Solar Day / Time Astronomical Day Civil Day Coordinated Universal Time (UTC) Daylight Saving Time (DST) Deck Watch Time Equation of Time Greenwich Mean Time (GMT) International Atomic Time (TAI) International Date Line (IDL) Legal Time - see separate entry for Standard Legal Time Local Mean Time (LMT) Local Sidereal Time (LST) Lunar Day Mean Solar Day Mean Solar Hour / Minute / Time Sidereal Day / Time Sidereal Hour / Minute Solar Day Solar Time Standard Legal Time Standard (or Zone) Time Standard Time Zones / Time Zones Summer Time - see separate entry for Daylight Saving Time (DST) Time Errors Time Zones - see separate entry for Standard Time Zones / Time Zones Uniform Time System ‘Universal Coordinated Time’ - see Coordinated Universal Time (UTC) Universal Time (UT or UT1) Zone Time - see separate entry for Standard (or Zone) Time Note: All variations of ‘Hour Angle’ will be found listed separately under ‘Hour Angles’ . Time Errors. Paras 0401, 0901, 0903. Index-12 Original
BR 45(2)
Time Zones. See separate entry for Standard Time Zones / Time Zones Total Darkness. Paras 0108, 0401, 0725. Towering (Mirage). Paras 0401, 0808b. Transferred Position Lines. See separate entry for Run / Run-on, Run-back . True Altitude. See separate entry for Observed (True) Altitude. True Bearing (of a heavenly body). Paras 0117, 0324, 0348, 0401, 0501, 0502, 0521, 0524, 0525, 0530, 0531, 0533, 0534, 0535, 0536, 0542, 0543, 0544, 0551, 0562, Anx 5A, 0602, 0622, 0741, 0742, 0906. True Sun. Paras 0401, 0433, 0439. See also separate entry for Mean Sun. True (Theoretical) Moonrise and Moonset. See separate entry for True (Theoretical) Rising and Setting (Sun and Moon). True (Theoretical) Rising and Setting (Sun and Moon). See detailed entries for: Moon. Paras 0401, 0702, 0730. Sun. Paras 0401, 0107, 0702, 0721, 0723, 0725. True (Theoretical) Sunrise and Sunset. See separate entry for True (Theoretical) Rising and Setting (Sun and Moon). True Zenith Distance (TZD). See separate entry for Observed (True) Zenith Distance (TZD). Twilight. Paras 0108, 0322, 0401, 0722, 0724, 0725, 0740. See also separate entries for: Astronomical Twilight (AT) Evening Civil Twilight (ECT) Evening Nautical Twilight (ENT) Midnight Sun Morning Civil Twilight (MCT) Morning Nautical Twilight (MNT) Total Darkness Uniform Time System. Paras 0201, (0202 / Fig 2-1, Fig 2-2), (0203), (0204), (0205), (0206), 0401. Brackets indicate associated information. Universal Time (UT or UT1). Paras 0201, 0205, 0209, 0210, 0211, 0321, 0322, 0325, 0327, 0350, 0351, 0401, 0434, 0435, 0436, 0437, 0439, 0444, 0450, 0451, 0452, 0453, 0551, 0560, Anx 5A, 0606, 0607, 0608, 0609, 0611, 0722, 0731, 0742, 0903. Upper Limb (UL). Paras 0107a, 0345, 0348d, 0401, 0703, 0704, 0720, 0721, 0730.
Index-13 Original
BR 45(2)
Upper Mer Pass / Upper Meridian Passage (of a heavenly body). Paras 0401, 0602, 0603, 0610, 0612. See also separate entry for Mer Pass / Meridian Passage (of a heavenly body). “v corrn” / “v” (velocity correction from The Nautical Almanac). Paras 0401, 0543b. Vertical Circles. Paras 0118, 0119, 0401, 0535. Very High Altitude (Tropical) Sights. Paras 0401, 0523, 0525, 0550, 0551, 0552. Visible Hemisphere. Paras 0401, 0502 (Note 5-1), Anx 5A. See also separate entry for Lower Hemisphere. Visible Horizon. Paras 0107, 0115, 0116, 0118, 0401, 0503, 0702, 0703, 0704, 0721, 0723, 0726, 0727, 0730, 0802, 0806, 0808. Visible Moonrise and Moonset. See separate entry for Visible Rising and Setting (Sun and Moon). Visible Rising and Setting (Sun and Moon). See detailed entries for: Moon. Paras (0320, 0321, 0322 - non specific with NAVPAC 2), 0401, 0703, 0730, 0731, 0740, 0741, 0742. Sun. Paras 0107, 0320, 0321, 0322, 0401, 0702, 0703, 0720, 0721, 0722, 0725, 0740, 0741, 0742. Visible Sunrise and Sunset. See separate entry for Visible Rising and Setting (Sun and Moon). Waning (of Moon). Para 0401, 0452. Waxing (of Moon). Para 0401, 0452. Winter Solstice. See separate entry for Solstice. Zenith. See separate entry for Observer’s Zenith (Z). Zenith Distance. Paras 0401, 0524, 0803, 0906, 0907. See also separate entries for: Calculated (Tabulated) Zenith Distance (CZD) Observed (True) Zenith Distance (TZD) Zone Time. See separate entry for Standard (or Zone) Time.
Index-14 Original
BR 45(2)
LIST OF EFFECTIVE PAGES
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DIVIDER CHAPTER 1 1-1 / 1-2 1-3 to 1-8 1-9 to 1-12
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DIVIDER CHAPTER 2 2-1 / 2-2 2-3 to 2-6 2-7 to 2-8
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DIVIDER CHAPTER 3 3-1 to 3-38 3A-1 to 3A-46
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DIVIDER CHAPTER 4 4-1 / 4-2 4-3 / 4-4 4-5 to 4-32 4-33 / 4-34 4-35 to 4-38 4-39 / 4-40 4-41 to 4-44
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DIVIDER CHAPTER 5 5-1 / 5-2 5-3 to 5-14 5-15 to 5-18 5-19 to 5-48 5A-1 to 5A-2
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DIVIDER CHAPTER 6 6-1 to 6-14 6-15 / 6-16 6-17 to 6-20
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DIVIDER CHAPTER 7 7-1 to 7-12 7-13 / 7-14 7-15 / 7-16
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