Study of the ejection/collision orbits in the spatial RTBP using the McGehee regularization

Abstract

In this paper we analyse the McGehee regularization of the collision in the spatial Restricted three-body problem (3D RTBP). As a particular application, we study the ejection (collision) orbits. The parameterization method is applied up to high order to obtain suitable initial conditions of ejection (collision) orbits. Moreover, assuming ejection orbits, different methods are discussed to detect which of them are also collision orbits. Finally we explore the so called ejection-collision (EC) orbits, that is, orbits where the particle ejects from one primary, reaches a maximum in the distance with respect to the same primary, and ends at collision with that primary. Some results concerning the existence of spatial EC orbits are described.