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The trajectories of two point masses or spherically symmetric masses with respect to their center of mass are conic sections or Kepler orbits.

Consider that the bodies have finite size with respect to their separation and not necessarily uniform, or even spherically symmetric mass distributions.

In that case what are the constraints on their mass distributions and orientations such that their orbits are still Keplerian? Or does any deviation from spherical symmetry of one or both body immediately result in a non-Keplerian orbit?

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  • $\begingroup$ @Qmechanic thanks for the edit; can you help me understand why the classical-mechanics tag does not apply? I'm thinking that those following the tag might be able to answer this fairly simple mechanics problem, and they might not also be following celestial-mechanics. Thanks! $\endgroup$ – uhoh Jan 20 at 6:15
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    $\begingroup$ If there are a tag X and a subset tag Y that both apply, the general guideline is to use just the subset tag Y. $\endgroup$ – Qmechanic Jan 20 at 7:05
  • $\begingroup$ @Qmechanic It's not a very "celestial" question, just two masses with a 1/r^2 force (could as well be +/- charges), but I've got Kepler in there, so okay. $\endgroup$ – uhoh Jan 20 at 7:07

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