Oscillatory motion to collision and infinity in the Earth-Moon restricted three body problem

Abstract

We present a computer assisted proof of the existence of the oscillatory motion to collision and to infinity in the Earth-Moon planar circular restricted three body problem. In particular, we show that all types of motion (hyperbolic, parabolic, oscillatory to infinity, oscillatory to collision and terminating in collision) can be combined. We also prove the existence of arbitrarily large ejection/collision orbits. The results are achieved with the use of the Levi-Civita regularization, the McGehee regularization, topological tools and rigorous numerical computations.