Crash test for the restricted three-body problem

Abstract

The restricted three-body problem serves to investigate the chaotic behavior of a small body under the gravitational influence of two heavy primary bodies. We analyze numerically the phase space mixing of bounded motion, escape, and crash in this simple model of (chaotic) celestial mechanics. The presented extensive numerical analysis reveals a high degree of complexity. We extend the recently presented findings for the Copenhagen case of equal main masses to the general case of different primary body masses. Collisions of the small body onto the primaries are comparatively frequent, and their probability displays a scale-free dependence on the size of the primaries as shown for the Copenhagen case. Interpreting the crash as leaking in phase space the results are related to both chaotic scattering and the theory of leaking Hamiltonian systems.