Chapter 4, Problem 57EAP

Using Newton’s Version of Kepler’s Third Law.

1. Calculate Earth’s approximate mass from the fact that the Moon orbits Earth every 27.3 days at an average distance of 384,000 kilometers.
2. Calculate Jupiter’s approximate mass from the fact that its moon Io orbits every 42.5 hours at an average distance of 422,000 kilometers.
3. Calculate the orbital distance for a planet that has an orbital period of 63 days around a star with the mass of the Sun.
4. Calculate the combined mass of Pluto and its moon Charon from the fact that Charon orbits Pluto every 6.4 days with a semimajor axis of 19,700 kilometers.
5. Calculate the orbital period of a spacecraft in an orbit 300 kilometers above Earth’s surface.
6. Calculate the approximate mass of the Milky Way Galaxy from the fact that the Sun orbits the galactic center every 230 million years at a distance of 27,000 light-years. (As discussed in Chapter 19, this calculation tells us only the mass of the galaxy within the Sun’s orbit.)