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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