Accuracy of epicyclic description of dust grain orbits about Saturn

Abstract

We investigate the metamorphosis of charged dust grain orbits in a planetary magnetosphere, the so‐called gravito‐electrodynamic problem. Our primary aim is to determine practical limits to the validity of an epicyclic model. We assume an axisymmetric planet with a centered dipole magnetic field aligned with the planetary spin axis, a good approximation for Saturn and a fair approximation for Jupiter. Nonideal forces, such as planetary oblateness, solar radiation pressure, plasma drag, and the effects of time‐dependent charging are neglected. A standard epicyclic expansion is used to calculate the mean motion and the aspect ratio of the epicyclic ellipse. For gravitationally dominated grains the mean motion is accurately given by the standard expression, but for magnetically dominated grains it can differ significantly even for small excursions from the equilibrium orbit. In some cases this finite gyroradius effect can even cause the mean motion to change direction. Previous studies are extended by examining a wide range of charge‐to‐mass ratios, for positively and negatively charged grains in prograde or retrograde equatorial orbits about Saturn, inside and outside of the synchronous radius. The results show that the epicyclic model is reasonably accurate for the majority of physically interesting orbits about Saturn. For grains suffering large radial excursions, however, major topological changes were often seen which defy an epicyclic description.