Generalizations of the Stِrmer problem for dust grain orbits

We investigate the generalized Störmer problem, which includes electromagnetic and gravitational forces on a charged dust grain near an axisymmetric planet. For typical charge-to-mass ratios neither force can be neglected. The effects of the different forces are discussed in detail. Thus, including the gravitational force gives rise to stable circular orbits lying in a plane entirely above/below the equatorial plane. A modified third Kepler’s law for these orbits is found and analyzed.