Hamilton, D.P. and J.A. Burns 1991. Orbital stability zones about
asteroids. Icarus 92, 118-131.
We have numerically investigated a three-body problem
consisting of the Sun, an asteroid, and an infinitesimal particle
initially placed about the asteroid. We assume that the asteroid has
the following properties: a circular heliocentric orbit at $R=2.55 \AU$,
an asteroid/Sun mass ratio of $\mu=5*10^{-12}$, and a spherical shape with
radius $R_A$=100 km; these values are close to those of the minor planet
29 Amphitrite. In order to describe the zone in which
circum-asteroidal debris could be stably trapped, we pay particular
attention to the orbits of particles that are on the verge of escape.
We consider particles to be stable or trapped if they remain in the
asteroid's vicinity for at least 5 asteroid orbits about the Sun, or
about 20 years. Applying this criterion to particles started on
circular orbits around the asteroid, we find that, as we vary the
starting distance from the asteroid, a fairly abrupt transition
between trapped and untrapped objects occurs. We define the distance
where the transition occurs to be the critical distance.
Our orbital plots for Amphitrite can be scaled for application
to other asteroids using the same functional dependence as the Hill
radius which is $r_H=(\mu/3)^{1/3}R$; for Amphitrite $r_H \sim 450
R_A$. We find empirically that initially circular prograde orbits
remain bound out to a critical distance of about $r_H/2 = 225 R_A$,
while initially circular retrograde orbits remain bound out to nearly
twice that distance. Particle orbits that start out circular and are
inclined with respect to the asteroid's orbital plane have critical
distances between these two extremes. Note that our choice of
initially circular orbits is arbitrary; different initial conditions
would generally lead to different critical distances.
This study explores the three-dimensional aspects of stability
more thoroughly than previous studies. To first order, particles that
are on stable orbits reside within a region that is approximately
spherical for angles $\theta < 35\dg$ ($\theta$ is the latitude in a
spherical coordinate system) such that $|z|< 285 R_A$, but is fairly
flat and parallel to the $xy$ plane at $z=\pm~285 R_A$ over the poles.
The radius of the spherical surface is roughly 480 $R_A$. These
distances would be reduced if the model included the asteroid's
orbital eccentricity or other perturbations such as those from
Jupiter. This result does not address whether any mechanisms exist to
populate such orbits.
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