IAO 1999 Problems

IV International Astronomy Olympiad Crimean Laboratory of SAI MSU and Crimean Astrophysical Observatory, s. Nachny!, September "# $ October ", %&&&.

'roblems to solve (heoretical rond Text of these problems is available also in other languages. languages. To solve every problem you may use constants and well-known values you know by heart.

)rop A *!niors, + % years old-. %. The apparent diameter of the Moon, as seen from the Earth, is 31'. hat is the ima!e diameter in the ob"ective focal plane if its focal len!th is #$% cm and the ob"ective diameter is %& cm (raw a fi!ure )a few fi!ures* to e+plain your calculations. ".  photometer is mounted on a 1#$ cm )focal len!th* telescope. an you observe a star with ma!nitude

a. $m  b. 1&m c. 1$m in a cluster if a count from a star of a similar spectral type with ma!nitude m !ives %&&& counts/second The level of white noise of the photometer )instrumental noise* is $&& counts/second0 the upper limitin! value for observations is #&&&&& counts/second. E+plain your calculations. )rop  *seniors, / % years old-. %. ne star peaks at #&&& . nother peaks at 1&&&& . hich one emits more radiation at #&&&  hich one emits more radiation at 1&&&&  hat is the ratio of the total radiation emitted by the two stars onsider the stars as black bodies. ". En!ineers from the 2imferopol niversity describe a new method to utili4e old military ships5 to construct very small black holes from their material )patent y4arc&%6*. Estimate the diameter of a black hole constructed usin! this patent from a ship with the mass of $&&& tn )1 tn 7 1&&& k!*. hat physical ob"ect o b"ect has a si4e of the same order of ma!nitude (escribe propa!ation of visible li!ht near this black hole.

Other problems *0$&- are for the both *A and - 1rops2

(heoretical rond wh en is it possible to observe the sunrise with the lon!est 0. here )on the Earth* and when duration Estimate its duration. 3. sually we consider that there are about a bout 8&&& stars in the whole sky which are visible  by our eyes. Estimate, how many visible stars are circumpolar )which means means that they never set*5

a. if you you are are pl placed aced 1° from the 9orth :ole.  b. if you are placed 1° from the E;uator )to the 9orth*. 1

 9ote5 formula for sphere's area calculation5 2 7 %π< #. #. n airship started from a cosmodrome located nea r the e;uator of the earth at the moment of a sunset.  pilot of the airship wants to continue to observe the sun on o n the hori4on. hat should the speed of movin! of the airship be (escribe in detail the motion of the air ship.

e;u ator when the sun . 2uppose that a total solar eclipse is observed from a place at the e;uator is in 4enith. lso, suppose that the shadow of the moon moves alon! the e;uator. alculate the speed of the shadow relative to the observer.

'ractical rond 4. rite the observational pro!ram for this ni!ht on a %&-cm telescope. hat stars would you observe this ni!th rite se;uence of the observations. 2tars to observe5

 V (mag)

m

 (1950)

h

m

1

 Aql

3 .5

19  49 .9

2

Per

2.1

3 04.9

40 46

3

 Cyg

14.2

19 48.6

32 47

4

R Aqr

12.4

23 41.2

-15 34

5

Ori

1.3

5 52.4

7 24

6.7

12 04.7

-6 29

6

RW Vir

0° 53′

Moon rise5 #15165#8, phase &.66 2ideral time for &h s& 7 &5315&% =ou may use all observational time )since #&h till $h 3& min*. >ocal time >T7T?3 oordinates of observatory λ 7 #h18m ϕ 7 %%°%3′ :ut your result into the table5 S ta r

In t e r va l o f o b  e rv a ti o n

2tars that could not be included in the pro!ram5 E+planations and notes5

#

5.  li!th curve of eclipsin! binary is shown in the fi!ure. Estimate the ratio of
Observational rond &.%. 9ame the distance between the Moon and @upiter in de!ree. 2how how did you find the result. &.". Aind and name the five bri!htesr stars of autumn sky. hich one is the bri!htest &.0. (efine the period since new moon for today.

3