A Note on the Existence of Heteroclinic Orbits in the Planar Three-Body Problem

Abstract

The existence and transversality of orbits of the planar three-body problem such that one of the masses escapes to infinity for positive and negative time with zero limit velocity is obtained. An asymptotic expression for the parameters which define the limit periodic orbits for the other two masses at infinity is also given. The problem is considered as a perturbation of two two-body problems, an elliptic one and a parabolic one. The results obtained and the methods used are natural modifications of the corresponding ones for the planar restricted elliptic three-body problem, recently studied in [M-P].