I know that three-body problem in celestial mechanics can't be solved analytically in general. But suppose that the 3rd body is much smaller than the others, so it does not perturb their orbits. This is known as the reduced three-body problem. Can the problem be solved analytically in that special case?

If not, then maybe another assumption that two major bodies move in circular orbit (circular restricted three-body problem) would allow analytic solution?

  • $\begingroup$ See "Lagrange Points." $\endgroup$ – Carl Witthoft Jan 8 '15 at 19:25
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    $\begingroup$ @CarlWitthoft Lagrange Points are only a few analytical solutions for the restricted three-body problem. Or where you referring to the potential in the rotating reference frame? I believe that this approach would allow to describe trajectories around those points, such as horse shoe orbits, however I do not know if this can be done in a more general way for example when the two dominant bodies in a elliptical orbit around each other. $\endgroup$ – fibonatic Jan 8 '15 at 19:57
  • $\begingroup$ I meant not orbits around Lagrange points, but a general case with the assumption stated in my question. Thanks! $\endgroup$ – Alexandr Zarubkin Jan 8 '15 at 20:01

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