Manager: Adnan Ismail
Recorder: Investigating the Parameters of Circular Orbits
Skeptic(s):
Objectives Determine the relationship between orbital speed and orbital radius for circular orbits.
Determine the relationship between orbital speed and mass of system objects for circular orbits. Describe the characteristics of orbits than don’t follow this relationship.
Calculate how changing various parameters in the Earth-Sun system (me, ms, res, or ve ) affects the orbit of the Earth
Directions 1. Go to https://phet.colorad https://phet.colorado.edu/en/simulation o.edu/en/simulation/gravity-and/gravity-andorbits. Click the Play arrow. Choose “To Scale”. 2. Select Sun and Earth (top choice). Make sure Velocity, Grid, and Measuring Tape are selected (like the diagram to the right). Earth should be two boxes from the Sun. 3. Click the big blue Play arrow arrow
. Click the Fast Motion and and Slow Motion arrows to see what affect they have. have. Use
these two buttons as needed. Click Click the big big blue stop button. button. Click the grey reset button in the upper right. right. (This is the only reset button you will ever use.) 4. Determine the speed of the Earth in m/s when it is in this initial orbit of two boxes from the Sun. Describe your your plan and show your work below.
=2 2× 1010×3.162 = = 29,29,244.44.03 / / One Box
5. Click Reset . Move the Earth so it is one box from the Sun. Sun. (Note: one box side equals equals about 46,000,000 miles.) Do not change the length of the velocity vector. Predict what will happen to the Earth and Sun when you hit Play.
I predict that the Ear th will move in an elliptical pattern and get faster as the Earth approaches closer to the Sun.
6. Click Play way?
. What do you observe about the the motions motions of the Earth and Sun? Sun? Why Why does does the Earth move move in this
The Earth moved in an elliptical pattern and got faster as it went closer to the Sun. This is because the attractive force becomes greater, meaning that the t he speed also increases. The Sun is also slightly attracted to other smaller bodies, meaning that they have very small orbits as well.
7. Click Reset . Stretch or shrink the velocity vector so, when you click Play and error. How can you quickly tell if the orbit is circular?
, the orbit is circular. First use trial
We can tell if the orbit is circular because the orbital radius is the same all throughout the entire orbit.
8. Use the general formulas for gravitational force and centripetal force to derive the relationship between speed (v) and orbital radius (r) for circular orbits. Show the relationship you derived to your instructor before going on.
× = = = √
Instructor or LA approval: 9. Use this formula to determine the speed in m/s that will result in a circular orbit when Earth is one box from the Sun.
− ( 6. 6 7 ×10 ×1. 9 88×10 √ = 4.6×10 =1,697,822 / Three Boxes 10. Click Reset . Move the Earth so it is three boxes from the Sun. Do not change the length of the velocity vector. Predict what will happen to the Ear th and Sun when you hit Play. If the Earth is too far away, the Earth may be out of the gravitational plane of the Sun and go out o f orbit.
11. Click Play . What do you observe about the motions of the Earth and Sun? Compare what you observed with the one box motion you observed above.
The planet does fly out of the orbit of the Sun and the Sun doesn’t move either, which is contrary to the prior instance
12. Click Reset . Stretch or shrink the velocity vector so, when you click Play , the orbit is circular. First use trial and error. Use the formula you derived in item 8 to determine the speed in m/s that will result in a c ircular orbit when the Earth is three boxes from the Sun.
− (6. 6 7 ×10 ×1. 9 88×10 √ = 3(4.6×10) =986,238.0061 / More massive Sun 13. Click Reset . Change the mass of the Sun to 2.0 Solar masses. Predict what will happen to the Earth and Sun when you hit Play.
The Earth will be significantly more attracted to the Sun because it has a greater mass now, so it will move faster.
14. Click Play way?
. What do you observe about the motions of the Earth and Sun? Why does the Earth move in this
The Earth still maintains an elliptical orbit, but the greater mass of the Sun brings the Earth closer to it and makes it faster.
15. Click Reset . Stretch or shrink the velocity vector so, when you click Play , the orbit is circular. Use the formula you derived in item 8 to determine the speed that will result in a circular orbit when the Sun is 2.0 Solar masses.
−)×2(1.9 88×10) =1,697,822 / = √ (6.67 ×102(4. 6×10) Less massive Sun 16. Click Reset . Change the mass of the Sun to 0.5 Solar masses. Predict what will happen to the Earth and Sun when you hit Play. The force from the Sun is smaller now that the mass is smaller, so it won’t be able to maintain a stable orbit of the Earth’s. If anything it will be farther away.
17. Click Play . What do you observe about the motions of the Earth and Sun? Compare what you observed with the more massive Sun motion you observed above.
While the Sun doesn’t move, the Earth also moves out of the gravitational field of the Sun because the Sun isn’t strong enough to hold onto the Earth
18. Click Reset . Stretch or shrink the velocity vector so, when you click Play , the orbit is circular. Use the formula you derived in item 8 to determine the speed that will result in a circular orbit when the Sun is 0.5 Solar masses.
5(1.9)88×10) =848,911 / = √ (6.67 ×102(4.−).6×10 More massive Earth 19. Click Reset . Change the mass of the Earth to 2.0 Earth masses. Predict what will happen to the Earth and Sun when you hit Play. Nothing will happen to the Ear th’s orbit because our equation doesn’t revolve around the mass of the Earth. The Sun might move slightly however closer towards the earth because it has a stronger attractive force.
20. Click Play way?
. What do you observe about the motions of the Earth and Sun? Why does the Earth move in this
There is no discernable impact of the mor e massive Earth because the equations are not reliant upon it.
21. Click Reset . Stretch or shrink the velocity vector so, when you click Play , the orbit is circular. Use the formula you derived in item 8 to determine the speed that will result in a circular orbit when the Earth is 2.0 Earth masses. It remained at the same speed at 29,244 m/2
Less massive Earth 22. Click Reset . Change the mass of the Earth to 0.5 Earth masses. Predict what will happen to the Earth and Sun when you hit Play. Nothing will happen to the Earth’s orbit because our equation doesn’t revolve around the mass of the Earth. The Sun might move slightly however further away from the earth because it has a weaker attractive force.
23. Click Play . What do you observe about the motions of the Earth and Sun? Compare what you observed with the more massive Earth motion you observed above. There were no discernable differences betwee n the motion between the earlier motion and this motion.
24. Click Reset . Stretch or shrink the velocity vector so, when you click Play , the orbit is circular. Use the formula you derived in item 8 to determine the speed that will result in a circular orbit when the Earth is 0.5 Earth masses.
It remained at the same speed at 29,244 m/2
Application 25. Which of the tested parameters affect the speed of the orbiting object? The Mass of the star and the distance between the star and the satellite affected the speed of the orbiting object.
26. Describe the main condition(s) for circular orbits.
-Velocity -A constant orbit radius -The mass of a star (Gravitational attraction) -the distance between the satellite and the star.
27. Suppose someone showed you the orbital speed and orbital radius of something orbiting the Sun. How could you determine if the object had a circular (or very close to circular) orbit?
When the orbit speed and the r adius of the satellite are constant, we would be able to figure out if the object has a circular orbit if it fits with the equations.
