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My friend presented a bit of a puzzle to me, and I can't remember enough physics to say whether it would work, and more importantly, why. It goes like this:

Imagine you are an extremely dexterous astronaut equipped with a ball on a string. If the ball is swinging around you and you pull the ball to yourself, tightening the orbit, do you experience a force moving you toward the ball? If so, could you then slowly widen the orbit, and repeat the process to move yourself (and the ball) in a desired direction?

It seems strange to me that a closed system (even one with an internal energy source) would be able to move through space, but I can't think of why it wouldn't work.

Some questions around this:

  • What happens to the astronaut force-wise when widening the orbit?
  • What happens to the astronaut force-wise when tightening the orbit?

One other note: this is not an attempt to create a perpetual motion machine. Obviously energy is expended changing the orbit of the ball.

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I'll assume that you start with the ball already rotating around the astronaut - there is no way to get it started without outside forces, as the angular momentum of the system is constant.

The ball and the astronaut are both rotating around their common CoM (center of mass) - not 'around the astronaut'. With the astronaut being significantly heavier, that point will probably be still inside the astronaut, but it is not in his middle = his personal center of mass.

When the astronaut pulls the ball in, he moves a bit (and the ball a lot), but the CoM doesn't move. No matter when and how fast the astronaut shortens and lengthens the line, the common CoM never moves.

Not that that does not preclude the astronaut from travelling quite some distance - but to achieve that, he could simply let the ball out several light years right away, and he would move in the opposite direction by the respective fraction (ball mass divided by astronaut mass)

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  • $\begingroup$ I would add that, due the conservation of angular momentum, even the rotation around a common COM would not be possible to achieve without external help. $\endgroup$ – V.F. Oct 27 '18 at 20:53
  • $\begingroup$ If there are no external forces the total angular momentum of the system is constant. But this does not prevent the astronaut or ball from spinning about its own axis while the both rotate around their common COM. $\endgroup$ – sammy gerbil Oct 29 '18 at 14:04

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