On the "Blue sky catastrophe termination" in the restricted four-body problem

TL;DR

This paper investigates the occurrence of the 'Blue Sky Catastrophe' termination phenomenon in the restricted four-body problem, analyzing stable and unstable manifolds at the collinear equilibrium point L2 through analytical and numerical methods.

Contribution

It extends the understanding of the 'Blue Sky Catastrophe' phenomenon from the three-body to the four-body problem, providing analytical and numerical verification.

Findings

Confirmation of the 'Blue Sky Catastrophe' in the four-body problem

Identification of conditions for the phenomenon at L2

Analysis of stable and unstable manifolds

Abstract

The restricted three-body problem posses the property that some classes of doubly asymptotic orbits are limits members of families of periodic orbits, this phenomena has been known as the "Blue Sky Catastrophe" termination. A similar case occurs in the restricted four body problem for the collinear equilibrium point named L2. We make an analytical and numerical study of the stable and unstable manifolds to verify that the hypothesis under which this phenomena occurs are satisfied.