Systems of colliding bodies in a gravitational field: I  Numerical simulations of the standard model.
Abstract
The paper gives numerical results of a systematic analysis of the dynamic evolution of a system consisting of particles interacting through inelastic collisions and moving in the gravitational field of a massive central body. The model was kept simple by neglecting selfattraction of the particles, by assuming the particle orbits to be Keplerian and that the particles are all spheres with same mass and radius. Initially, there is a very fast flattening until the system reaches a quasiequilibrium state in which, because of differential rotation, collissions still occur. The disk spreads slowly and energy and angular momentum are constantly transferred outwards. In spreading, the disk loses energy which is 'soaked up' by the inelastic collisions. Applied to Saturn's ring, where Cassini's division is neglected, the model yields an inequality relating the age of the ring and the size of the particles, according to which, if the ring is as old as the solar system, the maximum size of the particles is 2.5 m.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 February 1977
 Bibcode:
 1977A&A....54..895B
 Keywords:

 Astronomical Models;
 Computerized Simulation;
 Gravitational Fields;
 Particle Collisions;
 Saturn Rings;
 Astrophysics;
 Galactic Evolution;
 Inelastic Collisions;
 Astrophysics