The Angular Momenta of Solar System Bodies: Implications for Asteroid Strengths
Abstract
The angular momentum H is plotted versus mass M for the planets and for all asteroids with known rotation rates and shapes, primarily taken from D. C. McAdoo and J. A. Burns [ Icarus18, 285293 (1973)]. An asteroid's angular momentum is derived from its rotation rate as determined by the period of its lightcurve, its shape as indicated by the lightcurve amplitude, and where possible its size as given by polarimetry or radiometry. The asteroid is assumed to be rotating about its axis of maximum moment of inertia. As previously found by F. F. Fish [ Icarus7, 251256 (1967]) and W. K. Hartmann and S. M. Larson [ Icarus7, 257260 (1967)], H is approximately proportional to M ^{5/3}, which shows that the asteroids and most planets spin with nearly the same rate. The very smallest asteroids on the plot deviate from the above reaction, usually containing excess angular momentum. This suggests that collisions have transferred substantial angular momentum to the smallest asteroids, perhaps causing their internal stress states to be substantially modified by centrifugal effects. The forces produced by gravitation are then compared to centrifugal effects for a rotating, triaxial ellipsoid of density 3 g cm ^{3}. For all asteroids with known properties the gravitational attraction is shown to be larger than the centrifugal acceleration of a particle on the surface: thus the observed asteroid regoliths are gravitationally bound. Poisson's equation for the gravitational potential is investigated and it is shown by mathematical and physical arguments that any arbitrarily shaped ellipsoid with the attractive surface force boundary condition found above will have only attractive internal forces. Thus the internal stress states in asteroids are always compressive so that asteroids could be internally fractured without losing their integrity.
 Publication:

Icarus
 Pub Date:
 August 1975
 DOI:
 10.1016/00191035(75)900354
 Bibcode:
 1975Icar...25..545B
 Keywords:

 Angular Momentum;
 Asteroids;
 Gravitational Effects;
 Rotating Bodies;
 Solar System;
 Celestial Bodies;
 Centrifugal Force;
 Planetary Mass;
 Residual Stress;
 Spin Dynamics