Bifurcation Graphs for the CR3BP via Symplectic Methods

In this article, using the symplectic methods developed by Moreno and Frauenfelder (aimed at analyzing periodic orbits, their stability and their bifurcations), we will carry out numerical studies concerning periodic orbits in the Jupiter–Europa and Saturn–Enceladus systems. We will put emphasis on planar-to-spatial bifurcations, from deformation of the families in Hill’s lunar problem studied by Aydin. We will also provide an algorithm for the numerical computation of Conley–Zehnder indices, which are instrumental in practice for determining which families of orbits connect to which. As an application, we use our tools to analyze a well-known family of Halo orbits that approaches Enceladus at an altitude of 29 km, which bears interest for future space missions that visit the water plumes.