Hamilton, D.P. and J.A. Burns 1992. Orbital stability zones about
asteroids II. The destabilizing effects of eccentric orbits and of
solar radiation. Icarus 96, 43-64.
The gravitational effects of the Sun on a particle orbiting another
massive body which itself moves on a circular path around the Sun have
been studied extensively. Most recently, Hamilton and Burns (1991)
characterized the size and shape of a stability zone around an
asteroid on a circular heliocentric orbit within which material could
remain bound for an extended period of time. We now consider two
additional effects analytically and numerically: the asteroid's
non-zero heliocentric eccentricity and solar radiation pressure. In
both of these cases, our numerical integrations apply directly to a
spherical asteroid, ``Amphitrite,'' with semimajor axis 2.55 $AU$,
radius $R_A=100 km$, and density $2.38 g/cm^3$. For an asteroid on an
eccentric orbit we argue, based on numerical integrations and
analytical approximations, that the stability zone scales roughly as
the size of the Hill sphere calculated at the asteroid's pericenter.
This scaling holds for large values of eccentricity and allows results
for one asteroid with a given mass, semimajor axis and eccentricity to
be used for another with different values of these parameters. We
compare predictions of the scaling law to numerical integrations for
an ``Amphitrite'' with various orbital eccentricities and find good
agreement for prograde orbits and for those with orbital planes nearly
normal to the asteroid's heliocentric path, but not for retrograde
orbits. We apply our results to the minor planet 951 Gaspra.
We also determine that solar radiation pressure is a very efficient
mechanism for removing relatively small particles from the
circum-asteroidal zone. Radiation pressure acting on an orbiting
grain can cause large oscillations in the grain's orbital eccentricity
which in turn can lead to either escape from the system or impact with
the asteroid. We find numerically that particles with radius 0.1
millimeter started on circular orbits escape from ``Amphitrite'' at
all distances beyond 130 \RA. Grains of this size started anywhere
between the asteroid's surface and 130 \RA are forced to crash into
the minor planet. Smaller grains are even more severely affected; we
find that all particles with radii ranging from $<1$ micron to tenths
of millimeters are swept from the circum-asteroidal environment on
timescales comparable to the asteroid's orbital period. The orbits of
millimeter-sized grains are also strongly perturbed. Planar paths
bound for twenty years are found to extend to only $\sim40\%$ of the
critical distance found by Hamilton and Burns (1991); orbits with
inclinations near $90\deg$ are somewhat more resilient. Particles
larger than a few centimeters are only slightly affected by radiation
pressure. These results can be applied to ``Gaspra'', an asteroid
only one-thousandth as massive as ``Amphitrite'', by increasing all
particle sizes by a factor of $\sim$ ten.
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