Periodic Solutions Close to Commensurabilities in the Three-Body Problem

Abstract

Various families of periodic solutions are shown to exist in the three-body problem in which the two secondary bodies are close to a commensurability in mean motions. Both the restricted problem and the planar non-restricted problem are considered. In the restricted problem the disturbing body has either an eccentric orbit in the plane of the disturbed body's orbit, or a circular orbit inclined to this plane. The existence of some of these solutions is verified numerically.