# Asteroidal Satellites

Friday, November 2, 2001 - 9:30am - 10:30am

Keller 3-180

James Howard (University of Colorado)

t is now well established that many asteroids are actually binary systems - in some cases of comparable mass, in others a small body orbiting a much larger mass perhaps 100 km in diameter. The satellite may of course be a spacecraft, e. g. the NEAR-Shoemaker orbiter which landed on 433 Eros. Thus the system Sun-Asteroid-Satellite forms a three body problem, with Msun >>Mast >>m. When the satellite is relatively distant, but within the Hill sphere of the asteroid, we may neglect solar gravity and treat the system as a two body problem, with two interesting complications: (i) the central mass is highly nonspherical, (ii) it is also rotating.

Most asteroids rotate about the axis of maximum moment of inertia (pencil-on-the-table mode) with a period of 5-10 hours. There is also a significant and mysterious population of slow rotators with much longer periods.

In this talk we will focus on orbital stability about axisymmetric bodies, such as prolate ellipsoids or peanut-shaped bodies represented by Cassini ovals. We consider two classes of orbits, those encircling the axis of symmetry (thus crossing the plane of rotation) and those lying within this plane. The motion of the transverse class is governed by an effective potential for nonrotating bodies, which becomes an averaged effective potential for slow rotators. The coplanar orbits may be further classified as prograde or retrograde and are described by zero-velocity curves and Poincaré sections. Preliminary conclusions about the stability of the various orbital classes will be ventured.

Most asteroids rotate about the axis of maximum moment of inertia (pencil-on-the-table mode) with a period of 5-10 hours. There is also a significant and mysterious population of slow rotators with much longer periods.

In this talk we will focus on orbital stability about axisymmetric bodies, such as prolate ellipsoids or peanut-shaped bodies represented by Cassini ovals. We consider two classes of orbits, those encircling the axis of symmetry (thus crossing the plane of rotation) and those lying within this plane. The motion of the transverse class is governed by an effective potential for nonrotating bodies, which becomes an averaged effective potential for slow rotators. The coplanar orbits may be further classified as prograde or retrograde and are described by zero-velocity curves and Poincaré sections. Preliminary conclusions about the stability of the various orbital classes will be ventured.