Parabolic Orbits in the Elliptic restricted three-body problem

Abstract The main goal of this paper is to describe the parabolic orbits of the planar restricted elliptic three body problem. The method used is based on a standard blow up of the periodic orbits at the infinity and the perturbation of the integrable case corresponding to mass parameter equal to zero. We give an asymptotic formula for the distance between the stable and unstable manifolds of the infinity which allows us to describe how the heteroclinic orbits are created, changing the eccentricity of the primaries. Some conclusions of the quantitative study are given at the end.