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?