Hamilton, D.P. 1996. The Asymmetric Time-Variable Rings of Mars.
Icarus 119, 153-172.
In this paper, we investigate the dynamics and steady-state behavior
of the hypothetical circumplanetary dust rings associated with the two
tiny satellites of Mars, Phobos and Deimos. These moonlets are subject
to a flux of micrometeoroids which erodes their surfaces and ejects
material into orbit around Mars. We study the detailed orbital
dynamics of ejected material between a micrometer and a millimeter in
radius and find that these grains are significantly perturbed by solar
radiation pressure and Mars' oblateness. The coupling between these
two forces forms rings that are vertically and azimuthally asymmetric
as well as time-variable. Our analytic and numerical results show that
material of all sizes launched from Deimos forms a ring that is
displaced {\it away} from the Sun. Grains with radii smaller than
$\sim$270\mic launched from Phobos, however, form a ring that is
displaced {\it toward} the Sun. This effect, as well as surprisingly
large orbital changes for Phobos grains, is due to a near resonance
between Mars' orbital motion and the precession of pericenter due to
the oblateness force. When viewed from along Mars' vernal equinox (the
intersection between Mars' orbital and equatorial planes), the ring
formed by Deimos grains smaller than $\sim$100\mic is tilted out of
the equatorial plane. We present a new analytical solution describing
this vertical asymmetry and interpret it in terms of the Laplace
Plane. Finally, we suggest that the martian rings may be sustained
through the ejecta produced by energetic collisions between ring
particles in the 20-50\mic range and the small moonlets Phobos and
Deimos.
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