Variational proof of the existence of brake orbits in the planar 2-center problem

Abstract

The restricted three-body problem is an important subject that deals with significant issues referring to scientific fields of celestial mechanics, such as analyzing asteroid movement behavior and orbit designing for space probes. The 2-center problem is its simplified model. The goal of this paper is to show the existence of brake orbits, which means orbits whose velocities are zero at some times, under some particular conditions in the 2-center problem by using variational methods.