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

2026/08/05 by Aleksander Pasiut
Mathematics · #math.DS #msc:37C29 #msc:37J46 #msc:70F07

paper · pdf

41 pages, 8 figures

arxiv created 2026/08/05 · arxiv updated 2026/08/07

Abstract

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

Citations

• Oscillatory motions, parabolic orbits and collision orbits in the planar circular restricted three-body problem
• Oscillatory collision approach in the Earth-Moon restricted three body problem
• Oscillatory Motions and Parabolic Manifolds at Infinity in the Planar Circular Restricted Three Body Problem
• CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems
• Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems
• Oscillatory motions for the restricted planar circular three body problem
• Oscillatory orbits in the restricted elliptic planar three body problem
• Sur l'allure du mouvement dans le problème des trois corps quand le temps croît indéfiniment