Some Examples You Could Try

These are completely optional, will not be marked and I'll put the answers on the web page http://www.physics.drexel.edu/ hoyle/teach.html

1. A planet orbits around a 5 $\rm M_{\odot}$ star at a distance of 5 AU's. What is its period?

2. A planet orbits a star in a period of 3 years at a distance of 2 AU's. What is the star's mass?

3. A satellite orbits an 'earth' at a distance of 1000000 km in 30 hours. If we double the distance, what is the new period?

4. A satellite orbits a planet at a distance of 1000000 km in 30 hours. If we double the mass of the planet and keep the period the same as in (3), what distance does the satellite orbit at?

5. (Harder) What is the value of the acceleration produced by a planet that is twice as massive and twice as large as Earth (hint F = m1a = G(m1m2/r²) remembering that the force is felt by you and relate the value of a to the value of g). What would you weigh on this planet (assuming mass = 100kg).

6. (Sneaky one) Mercury orbits the Sun with semi major axis 0.4 AU in 0.25 years. If the mass of Mercury was doubled, what would the period be if the distance was kept at 0.4 AU (Think of the assumptions we make).

7. (Using small angle formula but same proportionality idea). At a distance of 12,000km, a planet appears to have an angular size of 4.4''. If the object is moved to 24,000km, what would the angular size be? Do this without calculating the linear size D by treating D*206265 as a constant (which it is as the planet is unchanged.)

8. A planet is orbiting a star with semi-major axis a. Does it have a larger period if we double the semi-major axis or halve the semi-major axis?