The motion of Saturn coorbital satellites in the restricted three-body problem

Abstract

This paper provides a description of the motion of Saturn coorbital satellites Janus and Epimetheus by means of horseshoe periodic orbits in the framework of the planar restricted three-body problem for the mass parameter . The mechanism of existence of such orbits for any value of and the Jacobi constant C close to C(L3), L3 being an adequate collinear equilibrium point, is analyzed from two different points of view and a systematic way to compute the horseshoe periodic orbits is also described.