Approximate Equilibrium Shapes for Spinning, Gravitating Rubble AsteroidsJoseph A. Burns, Ishan Sharma and James T. Jenkins Many asteroids are thought to be particle aggregates held together principally by self-gravity. Here we study those equilibrium shapes of spinning asteroids that are permitted for rubble piles. As in the case of spinning fluid masses, not all shapes may be compatible with a granular rheology. We take the asteroid to always be an ellipsoid with an interior modeled as a rigid-plastic, cohesion-less material. Using an approximate volume-averaged procedure, based on the classical method of moments, we investigate the dynamical process by which such objects may achieve equilibrium. First, to instill confidence in our approach, we have collapsed our dynamical approach to its statical limit to re-derive regions in spin-shape parameter space that allow equilibrium solutions to exist. Not surprisingly, our results duplicate static results reported by Holsapple (Icarus 154 , 432; 172 , 272) since the two sets of final equations match, although the formalisms to reach these expressions differ. We note that the approach applied here was obtained independently by I.S. in his Ph.D. dissertation (Cornell University, 2004); it provides a general, though approximate, framework that is amenable to systematic improvements and flexible enough to incorporate the dynamical effects of a changing shape, different rheologies and complex rotational histories. To demonstrate the power of our technique, we investigate the non-equilibrium dynamics of rigid-plastic, spinning, prolate asteroids to watch the simultaneous histories of shape and spin rate for rubble piles. We have succeeded in recovering most results of Richardson et al. (Icarus 173 , 349), who obtained equilibrium shapes by studying numerically the passage into equilibrium of aggregates containing discrete, interacting, frictionless, spherical particles. Our mainly analytical approach aids in understanding and quantifying the previous numerical simulations.
AAS/Division for Planetary Sciences Meeting Abstracts #39
- Pub Date:
- October 2007