Question

ii. A moon of mass ‘m’ orbits a planet of mass ‘M’ in a perfectly circular orbit of radius R, with a force of gravitational attraction between the two bodies of Fg. How much work is done on the moon by the planet during a single orbit of the moon?

Answer 1

Answer:

Zero.

In a circular orbit that’s easy to see. The moon would never get closer to or farther from the Earth, and when gravity does work, it does so by moving the object closer to the Earth.

But even in its actual elliptical orbit, where both distance and speed vary, the symmetry of the orbit ensures that for all the positive work that gravity does during one part of the orbit, there is a corresponding part of the orbit where the work done is negative. So no matter where on the orbit you start, if you come back to that same spot, the net work over the entire orbit will be zero.