Secondary resonances of co-orbital motions

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.

arXiv comment9 pages, 7 figures, accepted for publication in MNRAS

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• New Hamiltonian expansions adapted to the Trojan problem
• Stability and secondary resonances in the spatial restricted three-body problem for small mass ratios
• The structure of the co-orbital stable regions as a function of the mass ratio
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• Chaos Control with Ion Propulsion
• Stability of librational motion in the spatial circular restricted three-body problem for high inclinations and mass ratios
• Modeling resonant trojan motion in planetary systems
• Searching for Exotrojans in Pulsar Systems