Computer simulation of the formation of asteroid belt structure

Abstract

The system of two gravitational centers with variable separation between components one of which (the primary) loses its mass onto another (the secondary) is investigated under condition of total mass and angular momentum conservation. When the primary/secondary mass ratio becomes about that of Jupiter/Sun the small bodies ejected with the gaseous matter through the inner Lagrange point from the Roche lobe of the primary form a ring similar to the asteroid belt of the solar system. The formation of ring structure is calculated by numerical integration of Newtonian equations of N-body problem in orbital plane of the gravitational centers. The results are compared with the planar subsystem of the asteroid belt. The presence of the main gaps in the distribution of their mean motions at 2/1, 3/1, 5/2 and some other commensurabilities with the primary mean motion is found. More fine details of the belt structure are obtained, e.g. the gap asymmetry and a qualitative agreement with the eccentricity distribution. Within the scope of the same model the external part of the ring is investigated all the pairwise interactions being included. The clustering of bodies near 3/2 commensurability isolated from the main belt by the wide gap centered at 5/3 commensurability is obtained. It is supposed that the ring structure and the interplanetary spacing law for the terrestrial planets are due to the same mechanism.