Secondary resonances of co-orbital motions

TL;DR

This paper investigates the stability regions around L4 in the elliptic restricted three-body problem, revealing how secondary resonances influence the size of these regions and implications for Trojan planets.

Contribution

It identifies minimum zones in the stability region size distribution linked to secondary resonances, enhancing understanding of co-orbital motion stability.

Findings

Minimum zones in stability regions are connected to secondary resonances.

Stability region size varies with mass parameter and eccentricity.

Results inform predictions of Trojan planet existence.

Abstract

The size distribution of the stability region around the Lagrangian point L4 is investigated in the elliptic restricted three-body problem as the function of the mass parameter and the orbital eccentricity of the primaries. It is shown that there are minimum zones in the size distribution of the stability regions, and these zones are connected with secondary resonances between the frequencies of librational motions around L4. The results can be applied to hypothetical Trojan planets for predicting values of the mass parameter and the eccentricity for which such objects can be expected or their existence is less probable.