Stability and self-organization of planetary systems

Abstract

We show that stability of planetary systems is intimately connected with their internal order. An arbitrary initial distribution of planets is susceptible to catastrophic events in which planets either collide or are ejected from the planetary system. These instabilities are a fundamental consequence of chaotic dynamics and of Arnold diffusion characteristic of many body gravitational interactions. To ensure stability over astronomical time scale of a {\it realistic} planetary system -- in which planets have masses comparable to those of planets in the solar system -- the motion must be quasi-periodic. A dynamical mechanism is proposed which naturally evolves a planetary system to a quasi-periodic state from an arbitrary initial condition. A planetary self-organization predicted by the theory is similar to the one found in our solar system. %