Periodic orbits branch into three dimensions at the plane periodic orbits of indifferent vertical stability. These vertical-critical orbits are doubly important since they also specify the vertically stable segments of the families of plane periodic orbits. We determine sample vertical-critical orbits, namely those of the basic family i, of the restricted three-body problem with the larger primary oblate, for the entire range of the mass parameter mu. Their horizontal stability is also examined and this leads to predictions of where in the range of mu and A_1 (the oblateness coefficient) stable 3D periodic orbits may not branch from the plane.
Joint European and National Astronomical Meeting
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