Generalizations of the St\"ormer Problem for Dust Grain Orbits

We consider the generalized St\"ormer Problem that includes the electromagnetic and gravitational forces on a charged dust grain near a planet. For dust grains a typical charge to mass ratio is such that neither force can be neglected. Including the gravitational force gives rise to stable circular orbits that encircle that plane entirely above/below the equatorial plane. The effects of the different forces are discussed in detail. A modified 3rd Kepler's law is found and analyzed for dust grains.