Dynamical Evolution of Planetary Systems and the Significance of Bode’s Law

Abstract

We examine the question of whether an arbitrary configuration of planets in orbit about the sun could evolve by point gravitational interaction to become a very regular system such as the actual solar system. The evolution of a number of sample planetary systems with varying original distributions has been examined to determine the degree of “arbitrariness”allowed to the initial conditions which will yet yield the regularities presently observed in the solar system. Previous researchers have identified “quasi-stable” periods in the evolution of such systems but we show that frequently, when the integrations are continued to greater lengths, violent interactions again occur. This study suggests that only a geometric (or Bode-type) initial distribution of planetary semimajor axes is likely to yield the present (geometric) spacing of the planets of the solar system.