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Does the Roche limit apply also to two satellites orbiting each other or only to individual satellites held together by gravity?

For example, I have a tungsten little ball (10 cm in diameter) around which a penny orbits about every hour. Both the ball and the penny are orbiting Earth.

Will the penny's orbit be destroyed as soon as the two objects reach Earth's Roche limit or is there another limit to look for for destroying such a configuration?

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  • $\begingroup$ I'm pretty sure I can place a penny right next to a tungsten ball and have both retain their mechanical integrity, whether orbiting each other or not. So, what are you really asking? $\endgroup$
    – Jon Custer
    Dec 21, 2021 at 16:45
  • $\begingroup$ I am asking whether a penny that is already orbiting a tungsten ball will stop orbiting the tungsten ball after both objects approach Earth's Roche limit or instead another limit (not Roche) will determine the disruption of the penny's orbit around the ball. $\endgroup$
    – moonblink
    Dec 21, 2021 at 17:23

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I think the Roche limit doesn't apply to your configuration. The Roche limit assumes that the satellite consists of an incompressible material and is held together by gravity, and itself is rotating so slowly that the effect of centrifugal force can be ignored.

Your configuration is different. The "satellite" consists of two unconnected bodies, not only orbiting Earth, but also one another, and this local orbiting means that centrifugal force is enough to compensate the inner gravity force between the two satellites, so surely the centrifugal force can't be ignored in this situation.

Something like the Roche limit would apply to a different (fragile) configuration, if your tungsten ball and your penny were held at distance by a rigid rod between them (and held together by their mutual gravity). Then the Roche limit (or something similar) would denote the Earth distance where this configuration desintegrates because the differences in Earth gravity exceed the inner gravity forces.

The situation you are asking about, is in fact an instance of the Three Body Problem, and there is no simple solution. So, any external gravitational force will to some degree disturb the orbit of the penny and the tungsten ball, no matter whether this happens inside or outside of the third body's Roche limit.

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