The effect of J2 on equatorial and halo orbits around a magnetic planet

We calculate equatorial and halo orbits around a non-spherical (both oblate and prolate) magnetic planet. It is known that circular equatorial and halo orbits exist for a dust grain orbiting a spherical magnetic planet. However, the frequency of the orbit is constrained by the charge–mass ratio of the particle. If the non-sphericity of the planet is taken into account this constraint is modified or, in some cases, it disappears.