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Can anyone describe the mathematics behind the calculation of a resonance keyhole (for a two-body model)? It seems like the size and position of the keyhole should be a function only of mass and relative velocity, but I'm having difficulty deriving a formulaic solution.

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I don't think that a two-body system would have a gravitational keyhole: you need to change the angular momentum of one object relative to its orbit with the other, in order to generate the possibility of a "future collision". The only way you can do that is with a non-central force, which I believe implies the presence of a third body.

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