The contact geometry of the restricted 3-body problem

TL;DR

This paper demonstrates that the planar circular restricted three body problem exhibits restricted contact type behavior across a range of energies, enabling the application of Contact Topology to analyze its dynamics.

Contribution

It establishes the contact type property of the restricted three body problem for energies around the first critical value, linking it to Contact Topology methods.

Findings

The system is of restricted contact type below the first critical energy.

It remains of restricted contact type slightly above the critical energy.

This connection allows new topological tools to study the system's dynamics.

Abstract

We show that the planar circular restricted three body problem is of restricted contact type for all energies below the first critical value (action of the first Lagrange point) and for energies slightly above it. This opens up the possibility of using the technology of Contact Topology to understand this particular dynamical system.