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V. M. Guibout, D. J. Scheeres (U. Michigan, Aerospace Engineering Dept.)
The dynamical environment on the surface of a rotating, solid ellipsoid is studied, with applications to surface motion on an asteroid. The analysis is performed using a combination of classical dynamics and geometrical analysis. Due to the small size of most asteroids, their shapes tend to differ from the spheroidal shapes found for the planets. The tri-axial ellipsoid model provides a non-trivial approximation of the gravitational potential of an asteroid and is amenable to analytical computation. Using this model, we develop the conditions for equilibrium on the surface. In general an ellipsoid will only have 6 unique equilibrium points (each symmetric about the origin), but we also find situations where every point on the surface may be in equilibrium. We also study stability of these equilibria and show that it is intimately related to the well-known families of Jacobi and MacLaurin ellipsoids. Using geometrical analysis we can define global constraints on motion as a function of shape, rotation rate, and density. We find that some asteroids should have accumulation of material at their ends, while others should have accumulation of surface material at their poles, depending on what their shape and rotation rate are in relation to the classical figures of equilibrium.
The current analysis ignores the small scale geometry of a real surface and considers frictionless dynamics. Although we use such an idealized model, this study has implications for the global trends of natural material distribution on asteroids and for the ballistic motions of an artificial vehicle close to the surface of an asteroid.
The author(s) of this abstract have provided an email address for comments about the abstract: guibout@umich.edu
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Bulletin of the American Astronomical Society, 35 #4
© 2003. The American Astronomical Soceity.