Motion of Dust in a Planetary Magnetosphere: Orbit-Averaged Equations for Oblateness, Electromagnetic, and Radiation Forces with Application to Saturn's E Ring

Abstract

In this paper, we apply orbital perturbation theory to the circumplanetary motion of micrometer-sized dust grains subject to gravitational, electromagnetic, and radiation forces. We extend the orbit-averaged radiation pressure equations of Mignard (1982, Icarus 49, 347-366) to include planetary obliquity. We also derive new equations for the Lorentz force arising from the aligned dipolar and quadrupolar components of the planetary magnetic field. Following these derivations, we provide a framework for combining all perturbations and demonstrate the validity of the resulting expressions by comparing numerical integrations of them to integrations of the full Newtonian equations; typically the orbit-averaged equations can be integrated several hundred times faster. Finally, we analytically and numerically apply the newly derived equations to particles moving through the Saturnian E ring and discuss implications for that ring's azimuthal and vertical structure. It is argued that the behavior of orbital precession rates at large eccentricities leads to azimuthal asymmetry in the E ring. Furthermore, a peculiar locking of orbital pericenters out of the equatorial plane is shown to have implications for the E ring's vertical structure. We show analytically that the locking is caused by small vertical forces arising from radiation pressure and from the planet's aligned quadrupolar field. Because the normal component of radiation pressure varies over Saturn's orbital period, we suggest that the vertical structure of the E ring varies with time.