Analysis of the relative dynamics of a charged spacecraft moving under the influence of a magnetic field

We focus on the dynamical characteristics of the system as a function of its parameters, with special attention to the ratio of the leader's mean motion around the Earth to the rotating rate of the dipole. We study the critical points of the model and their stability, the admissible and forbidden regions of motion of the deputy using the zero velocity surfaces and the families of periodic orbits emanating from equilibria. In the normal case we pay special attention to the periodic orbits of elliptic type and to the families of 2D tori surrounding them that are computed by means of a parameterisation method. The result is a fine catalog of orbits together with an accurate dynamical description suitable to researchers interested in potential applications of satellite formation flight using this kind of technology.