Horseshoe orbits in the restricted four-body problem

Abstract

The circular restricted four-body problem studies the dynamics of a massless particle under the gravitational force produced by three point masses that follow circular orbits with constant angular velocity, the configuration of these circular orbits forms an equilateral triangle for all time; this problem can be considered as an extension of the celebrated restricted three-body problem. In this work we investigate the orbits which emanate from some equilibrium points. In particular, we focus on the horseshoe shaped orbits (rotating frame), which are well known in the restricted three-body problem. We study some families of symmetric horseshoe orbits and show their relation with a family of the so called Lyapunov orbits.