Burns, J.A. and D.P. Hamilton 1992. Debris about asteroids: Where and how much? In Asteroids, Comets and Meteors 1991 , (A.W. Harris and E. Bowell Eds.), pp. 101-108. Lunar and Planetary Institute, Houston, Texas.

We summarize several recent findings on the size and shape of the region within which material can stably orbit an asteroid. If the asteroid (with assumed density 2.38 g/cm3) circles the Sun at 2.55 AU, co-planar prograde material will remain trapped whenever started on unperturbed circular orbits at less than about 220 RA (asteroid radii); co-planar retrograde particles are stable out twice as far. Our 3-D stability surface, which encloses several hundred numerically calculated orbits that start with various inclinations, is shaped like a sphere with its top and bottom sliced off; its dimensions scale like the Hill radius =(m/3)1/3R, where m is the asteroid-to-solar mass ratio and R is the asteroid's orbital radius. If the asteroid moves along an elliptical orbit, a fairly reliable indicator of the dimensions of the hazard zone is the size of its Hill sphere at the orbit's pericenter. Grains with radii less than a few mm will be lost through the action of radiation forces which can induce escape or cause collisions with the asteroid on time scales of a few years; interplanetary micrometeoroids produce collisional break-up of these particles in ~104 yrs. The effects of Jupiter and of asteroids that pass close to the target asteroid allow particles to diffuse from the system, again shrinking the hazard zone.
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