Geometry of Weak Stability Boundaries

TL;DR

This paper generalizes the concept of weak stability boundaries in celestial mechanics, proving their relation to stable manifolds in the three-body problem, which aids in designing low-energy space trajectories.

Contribution

It provides an analytical proof linking weak stability boundaries to stable manifolds in the planar circular restricted three-body problem, under specific conditions.

Findings

Weak stability boundary coincides with a branch of the global stable manifold.

Analytical proof established under certain mass ratio and energy conditions.

Enhances understanding of low-energy transfer trajectories in celestial mechanics.

Abstract

The notion of a weak stability boundary has been successfully used to design low energy trajectories from the Earth to the Moon. The structure of this boundary has been investigated in a number of studies, where partial results have been obtained. We propose a generalization of the weak stability boundary. We prove analytically that, in the context of the planar circular restricted three-body problem, under certain conditions on the mass ratio of the primaries and on the energy, the weak stability boundary about the heavier primary coincides with a branch of the global stable manifold of the Lyapunov orbit about one of the Lagrange points.