Energy Loss in Collisions of Icy Spheres: Loss Mechanism and Size-Mass Dependence

Abstract

The coefficient of restitution of collisions of icy spheres at low impact velocities has been measured by A. P. Hatzes, F. G. Bridges, and D. N. C. Lin (1988, Mon. Not. R. Astron. Soc. 231, 1091-1115) and by F. G. Bridges, A. Hatzes, and D. N. C. Lin (1984, Nature 309, 333-335). However, the measurements were made only for spheres against massive ice bricks and must be extended or extrapolated if they are to describe collisions of ring particles of arbitrary size and mass. Physical models based upon a perfectly elastic low velocity region, i.e., plastic deformation or brittle fracture, do not accurately describe either the velocity dependence or the size dependence of the data. This failure suggests that the cancellation of size dependence and mass dependence predicted by plastic deformation/brittle fracture models may not occur for icy rings. This means that in ring systems, where sizes vary by orders of magnitude, that the coefficient of restitution for most collisions may be quite different from the measured values. I propose an alternative model, based upon energy loss through viscous dissipation, which matches both the velocity and size dependence of the data quite well. The model should predict the coefficient of restitution for collisions of particles having arbitrary size and mass once the mass dependence is determined by further experiments.