Statistics – Computation
Scientific paper
May 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008dda....39.0901s&link_type=abstract
American Astronomical Society, DDA meeting #39, #9.01
Statistics
Computation
Scientific paper
Equilibrium conditions for a mutually attracting general mass distribution and point mass are derived and their stability computed. This ``sphere-restricted'' problem is a simplification of the more difficult problem of finding the relative equilibrium and stability of two arbitrary mass distributions relative to each other. The main difficulty comes about in the loss of symmetry in the mass distributions, which removes certain analytical simplifications and forces the development of more robust equilibrium conditions. However, inclusion of these non-symmetric effects is important if one is to understand the evolution of real proto-binary systems and evaluate estimated asteroid shapes using these theories.
The equilibrium conditions can be reduced to six equations in six unknowns, plus the existence of four integrals of motion consisting of the total angular momentum and energy of the system. There are various methods for further reducing the equilibrium conditions to two independent equations. We have developed a methodology for computation and stability evaluation of relative equilibrium that directly uses energy variations at constant levels of angular momentum (Scheeres, Celestial Mechanics 94: 317--349, 2006). This methodology provides us with a rigorous and implementable approach to these difficult computations, and is a promising direction for robustly finding the relative equilibria between two non-symmetric bodies. The method is applied to estimated non-symmetric asteroid shape models of interest. Explicit conditions for the spectral and energetic stability of the resulting equilibria are also derived and computed.
This research was funded in part by a grant from the NASA Office of Space Science Planetary Geology and Geophysics Program.
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