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Question edited:

If you dig a tunnel through a large asteroid like Ceres along its axis of rotation and jumped in then what would be the first thing to stop you from falling back and forth along the tunnel length ?

Possibilities include:

Dmitry Brant mentions gravitational waves and charged particles. John Rennie mentions drag from impure vacuum.

Perturbations from other planets could shift axis of rotation causing you to hit the side.

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You would fall back and forth for a long time, but you will eventually stabilize in the center, because the two-body system (composed of you and Ceres) emits gravitational waves, hence you will gradually lose energy. (This is assuming that the vacuum is perfect, and there aren't any charged particles that might cause slight deviations in your free-fall) – Dmitry Brant Sep 18 '12 at 15:05
Related: and links therein. – Qmechanic Sep 18 '12 at 16:14

Yes. Well, you wouldn't fall back and forth forever because space in the asteroid belt isn't a true vacuum. The density is very low, but there would be some drag and it would bring you to a halt eventually. However you would oscillate for a very long time.

But then you could argue that wouldn't Ceres orbit the Sun forever (assuming it doesn't get hit by another asteroid), so isn't this just as much perpetual motion as the object oscillating within Ceres? Likewise the Solar system orbiting the Milky way, and so on.

Generally speaking when we talk about a perpetual motion machine we mean something that does work perpetually, even if that work is just overcoming internal friction. An object oscillating in a perfect vacuum doesn't really fit into this category.

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