Oscillatory Motions and Parabolic Manifolds at Infinity in the Planar Circular Restricted Three Body Problem

TL;DR

This paper proves the existence of oscillatory and other complex motions in the Sun-Jupiter restricted three-body problem, using computer-assisted methods to analyze trajectories that cross Jupiter's orbit without close encounters.

Contribution

It introduces a computer-assisted proof of oscillatory motions and final motions in the planar circular restricted three-body problem with realistic parameters.

Findings

Existence of oscillatory motions in the Sun-Jupiter system.

Trajectories cross Jupiter's orbit without close encounters.

Method relies on correctly aligned windows and computer assistance.

Abstract

Consider the Restricted Planar Circular 3 Body Problem with both realistic mass ratio and Jacobi constant for the Sun-Jupiter pair. We prove the existence of all possible combinations of past and future final motions. In particular, we obtain the existence of oscillatory motions. All the constructed trajectories cross the orbit of Jupiter but avoid close encounters with it. The proof relies on the method of correctly aligned windows and is computer assisted.