Analytical solutions around planar equilibria of three dipole problem

Proceeding with our investigation into the motion of a particle influenced by the electromagnetic field of three celestial bodies of a magnetic-dipole nature we give here for the first time the analytical expressions of periodic solutions around a planar equilibrium point. These relations are expansions of the planar equations of motion in series of second order power of a parameter in the vicinity of equilibria. The above analytical expressions of periodic solutions give the first members of the family of periodic orbits which emanate from a stable equilibrium point. The whole family can then be calculated using a predictor-corrector algorithm.