Periodic collision orbits in the elliptic restricted three-body problem

Abstract

This article considers the two-dimensional elliptic restricted three-body problem, and in particular some of its aspects related to regularization and periodic collision orbits. The mechanism of regularization with Birkhoff coordinates and with theenergy differential equation is described. Then the initial conditions for collision orbits are established. The theory is illustrated with the description of a new family of symmetric periodic collision orbits. It is shown how this family is related to the work of Moulton, Darwin and Stromgren in the circular restricted problem, and also to the Earth-Moon mass ratio. In the high eccentricity ranges, some relations with the triple collision problem are pointed out. The differential corrections have been made with an automatic search technique which is described in the appendix.