Numerical simulations of collisions and gravitational encounters in systems of non-identical particles

Numerical simulations of 200 mutually colliding non-identical particles indicate that the equipartition of random kinetic energy is possible only in systems having a narrow distribution of particle masses. Otherwise the random energy is concentrated on heavy particles. The form of the velocity distribution versus particle mass depends also on the elastic properties of the particles, and on the relative importance of the particle size. If the coefficient of restitution is a weakly decreasing function of impact velocity, a large difference in the equilibrium velocities of largest and smallest particles is possible. On the other hand, if the elasticity drops to a low level even in the small velocity regime, the dispersion of velocities is maintained by finite size and differential rotation, and the velocities of smallest particles are, at most, slightly larger than those of the largest ones. The results of simulations are consistent with the predictions of the collisional theory of non-identical particles (Hämeen-Anttila, 1984). The application to Saturn's rings indicates that the geometric thickness of cm-sized particles is of the order of 50 m in the rarefied regions of the rings. Without the gravitational encounters a thickness of about 30 m is derived. These estimations are made by using the latest measurements (Bridges et al., 1984) for the restitution coefficient of icy particles.