The restricted three-body problem

Abstract

Celestial mechanics has a long history, see for example the encyclopedic works of Hagihara [109] and Szebehely [231], or the Scholarpedia article on the threebody problem by Chenciner [53] or on Celestial Mechanics by Ferraz-Mello [83] and the references therein. The first basic problem in celestial mechanics going beyond the Kepler problem we have seen in Sections 3.3 and 3.5 is of course the three-body problem. Even the planar three-body problem is very complicated due to its high, twelve-dimensional phase space, although this can be reduced by using symmetries, and the presence of three-body collisions, which cannot always be regularized.