Hamilton, D.P. 1993. Motion of dust in a planetary magnetosphere:
Orbit-averaged equations for oblateness, electromagnetic, and
radiation forces with application to Saturn's E ring. Icarus
101, 244-264. Erratum: Icarus 103, 161.
In this paper, we apply orbital perturbation theory to the
circumplanetary motion of micron-sized dust grains subject to
gravitational, electromagnetic, and radiation forces. We extend the
orbit-averaged radiation pressure equations of Mignard (1982) 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.
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