Pattern Formation by Inelastic Collisions, Especially in Planetary Systems

Abstract

The Titius–Bode law governs the planet distribution in our Solar system. In this paper a possible explanation is proposed based on inelastic collision effects among planetessimals during the evolution of the Solar system. The main purpose of this paper is, however, to introduce a strategy to study phenomena driven by rare but drastic events such as colllisions in the planetary problem. Many complex systems evolve through rare but violent events, so that an efficient strategy to simulate such systems is desirable. An event-driven strategy is proposed in this article, and is used to produce many runs of 108 year evolution history of planetary systems. I have found that the Titius–Bode law holds approximately, if the gravitational effect (scattering) and the collisions are taken into account. The result illustrates the importance of inelastic collisions, which are often neglected in the standard classical mechanics courses. Therefore, for completeness, other simpler particle systems under the effect of inelastc collisions, such as one-dimensional systems, are also included.