The Limits of Stable Shapes of "Rubble Pile” Asteroids

Details The Limits of Stable Shapes of "Rubble Pile” Asteroids The Limits of Stable Shapes of "Rubble Pile” Asteroids

Sep 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008dps....40.5501h&link_type=abstract

American Astronomical Society, DPS meeting #40, #55.01; Bulletin of the American Astronomical Society, Vol. 40, p.498

Astronomy and Astrophysics

Astronomy

Scientific paper

Over decades, there have been numerous attempts to model the shapes of spinning asteroids in terms of "fluid equilibrium” figures, and even infer densities therefrom. This game has only intensified with the evidence that most small, and possibly quite large, asteroids are composed of rubble rather than being solid rocks. But even rubble is not fluid; the compressive cohesion of loose rubble can sustain substantially non-equilibrium shapes. Holsapple (Icarus 187, 500-509, 2007) has investigated the limits of fast spin rates for rubble piles using realistic "angle of friction” limits for rubble. Here we do the same for essentially non-spinning bodies to define the limits of shapes that can be sustained by loose rubble with only compressive strength modeled by the angle of friction (repose). We find, for an angle of friction of 40 deg., that an extremely elongate prolate ellipsoid, a/b/c = 5/1/1, will "landslide” to a shortened figure approximately three times as long as its new short dimension. The longest non-rotating prolate ellipsoid which is stable without landsliding has axis ratios a/b/c = 2.8/1/1. For an oblate spheroid, even more extreme axis ratios can be supported, up to a/b/c = 5/5/1 remains stable without landsliding. Rotation (about the short axis) only increases the limits of stable figures to even more extreme shapes. We conclude from this that modeling shapes of small bodies as fluid equilibrium figures, and in particular inferring bulk densities corresponding to minimum deviation from fluid equilibrium, is a useless exercise for small sub-critically spinning bodies. This conclusion holds for bodies up to at least 100, and probably several hundred, km diameter, but even for very large bodies such as 2003 EL61, substantial disequilibrium shape can be sustained, so inferring a density from the measured shape and spin rate is subject to large uncertainty (Holsapple 2007).

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