The contact geometry of the spatial circular restricted 3-body problem

TL;DR

This paper demonstrates that certain energy levels in the spatial circular restricted three-body problem have a contact geometric structure, implying specific dynamical properties and ruling out blue sky catastrophes in that range.

Contribution

It establishes the contact type of energy hypersurfaces in the spatial circular restricted three-body problem below and slightly above the first critical value, linking contact geometry with dynamical behavior.

Findings

Energy hypersurfaces are of contact type below the first critical value.

Energy hypersurfaces are of contact type slightly above the first critical value.

No blue sky catastrophe occurs in this energy range.

Abstract

We show that a hypersurface of the regularized, spatial circular restricted three-body problem is of contact type whenever the energy level is below the first critical value (the energy level of the first Lagrange point) or if the energy level is slightly above it. A dynamical consequence is that there is no blue sky catastrophe in this energy range.