Stability chart of the triangular points in the elliptic restricted problem of three bodies

TL;DR

This paper analyzes the stability of Trojan-like objects in the elliptic restricted three-body problem using Hill's equations and the energy-rate method, revealing key stability mechanisms and resonant behaviors.

Contribution

It introduces a numerical stability map based on resonant frequencies and identifies a stability mechanism explaining long-term test particle survival.

Findings

Stability regions depend on resonant frequencies and system parameters.

A stability mechanism extends the lifetime of particles in unstable zones.

Long period libration significantly influences the stability structure.

Abstract

The possible observations of Trojan-like extrasolar planets stimulate the deeper understanding of the stability behaviour of the co-orbital resonant motion. By using Hill's equations and the energy-rate method an analysis of the stability map of the elliptic restricted three-body problem is performed. Regions of the $\mu-e$ parameter plane are described numerically and related to the resonant frequencies of librational motion. Stability and instability can therefore be obtained by analysing the two independent frequency modes depending on system parameters. The key role of the long period libration in determining the structure of the stability is demonstrated and also a stability mechanism is found that is responsible for extended life time of the test particle in the unstable domain of the stability map.