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D.J. Scheeres (University of Michigan)
Particle motion about asteroid binaries is a topic of interest for understanding ejecta dynamics in binary systems, transient dynamics following formation of a binary system, and for the motion of spacecraft in the vicinity of binary asteroids. The problem, in its most general form, is difficult and requires modeling of the non-spherical mass distributions of the bodies, the mutual orbital and rotational motion of the bodies, and the perturbative influence of the sun on the system. Particle motion in these systems can be very complex, and may consist of orbits bound to either of the asteroid bodies, exchange trajectories between the bodies and with the exterior region, and orbits isolated in the exterior region about both bodies.
When properly formulated, the binary environment integrates 4 classical problems of celestial mechanics into a single environment: the Hill problem, the restricted 3-body problem, the non-spherical orbiter problem, and the full 2-body problem. In this talk we focus on the effect of the solar perturbation, and show how this creates an environment that modifies the restricted 3-body problem and leads to instability for particle motion over a wide range of parameter space. In particular, we find a simple parameter condition for stability in the vicinity of the triangular libration points. {To\over Th} < {27\over 8} m (1- m) < {1\over 8} where To is the orbital period of the binary system, Th is the orbital period of the binary system about the sun, and m is the mass distribution parameter for the binary system. The upper limit of the inequality is the familiar result from the restricted 3-body problem and limits the stability of bodies with similar masses. The lower limit of the inequality arises from the solar perturbation, and preferentially limits the stability of small mass fraction systems. Thus, resulting from this inequality (which specifically applies only to systems with zero obliquity) we expect most asteroid binaries that fall into this class to have complete instability in all their synchronous motions. Conversely, if the asteroid system has a relative inclination of 180 degrees, the lower limit disappears, reducing to the more familiar unperturbed case.
This research is supported in part by NASA's Office of Space Science Planetary Geology and Geophysics Program.
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Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.