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A station situated somewhere like EML-2 is really at an unstable point. I've heard of crafts using rocket firing to maintain that position in response to small deviations. Could you do this without using propellant?

I wonder if this could be done by moving a long pole back and fourth, like a tightrope walker.

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    $\begingroup$ Lissajous orbits usually win hands-down. The limits of orbit control authority with poles are quite tight, not really suitable when larger perturbations (or a craft shutdown) come along. $\endgroup$ – Deer Hunter Sep 13 '13 at 6:26
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No, unless you have a rather massive and long pole. To be in a stable orbit, your center of mass1 must be at a particular point with a particular velocity. Rearranging your own mass without expelling any will not work as you cannot move your own center of mass.

However, with a long enough pole, the inverse square effects come into play, so one can change the net gravitational attraction by moving a pole back and forth, and thus regain the orbit.

1. The mass distribution will change your rotational properties, but not the revolutionary ones which depend on the position and velocity of the COM, assuming a near-homogeneous gravity field..

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