Oscillatory collision approach in the Earth-Moon restricted three body problem

2024/01/22 by Maciej J. Capiński, Capiński, Maciej J., Aleksander Pasiut +1
Engineering · Physics and Astronomy · #37C29 #37J46 #70F07 #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.2401.12386

openalex publication_date 2024/01/22 · openalex created_date 2024/01/25 · openalex updated_date 2026/07/28

Abstract

We consider the Earth-Moon planar circular restricted three body problem and present a proof of the existence orbits, which approach arbitrarily close to one of the primary masses, and at the same time after each approach they move away from the mass to a prescribed distance. In other words the orbits oscillate between being arbitrarily close to collision and away from it. We achieve our goal with the use of topological tools combined with rigorous interval computations. We use the Levi-Civita regularization and validate that the dynamics in the regularized coordinates leads to a good topological alignment between various sets. We then perform shadowing arguments that this leads to the required dynamics in the original coordinates of the system.

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