Dynamics of micron-sized circumplanetary dust grains

A.V. Krivov, K.V. Kholshevnikov, L.L. Sokolov

Astronomical Institute, St. Petersburg University,
Stary Peterhof, 198904 St. Petersburg, Russia.
E-mail: krivov@aispbu.spb.su

Giant planets are known to be surrounded by complicated dust
structures, and similar (less dense but not less intricate) dust
configurations are expected to exist around Mars and Earth.  Further
investigation of these dust complexes strongly requires a careful
study of circumplanetary dust grain dynamics which is as yet poorly
understood.  We suggest an analytical model for micron-sized and
larger debris (which is likely to be most abundant near planets).
The model includes two disturbing forces being of major importance in
this size regime: direct sunlight pressure and planetary oblateness.
In planar case and neglecting the eccentricity of a planet's orbit,
the problem reduces to a semicanonical system with one degree of
freedom, and we present an exhaustive qualitative analysis in the
phase space.  The results provide the evolution of eccentricity and
apses line of a particle's orbit.  We show the possibility of
surprisingly complicated nonlinear dynamical effects, such as a
parametric bifurcation of separatrices and ``stochastic'' motion.
These phenomena, though never realized for tiny moons of the Jupiter
planets, are just the case for the Phobos ejecta orbiting Mars.
Furthermore, we predict similar effects for some mid-altitude Earth
satellites with large area-to-mass ratio.  By numerical integration,
we then check how the solutions of the simplified planar problem are
modified in a spatial case and with a more realistic force model.