Classifying orbits in the restricted three-body problem

Abstract

The case of the planar circular restricted three-body problem is used as a test field in order to determine the character of the orbits of a small body which moves under the gravitational influence of the two heavy primary bodies. We conduct a thorough numerical analysis on the phase space mixing by classifying initial conditions of orbits and distinguishing between three types of motion: (1) bounded, (2) escape and (3) collisional. The presented outcomes reveal the high complexity of this dynamical system. Furthermore, our numerical analysis shows a remarkable presence of fractal basin boundaries along all the escape regimes. Interpreting the collisional motion as leaking in the phase space, we related our results to both chaotic scattering and the theory of leaking Hamiltonian systems. We also determined the escape and collisional basins and computed the corresponding escape/collisional times. We hope our contribution to be useful for a further understanding of the escape and collisional mechanism of orbits in the restricted three-body problem.