A parametric study of stability and resonances around L 4 in the elliptic restricted three-body problem

The size of the stable region around the Lagrangian point L ₄ in the elliptic restricted three-body problem is determined by numerical integration as a function of the mass parameter and eccentricity of the primaries. The size distribution of the stable regions in the mass parameter-eccentricity plane shows minima at certain places that are identified with resonances between the librational frequencies of motions around L ₄. These are computed from an approximate analytical equation of Rabe relating the frequency, mass parameter and eccentricity. Solutions of this equation are determined numerically and the global behaviour of the frequencies depending on the mass parameter and eccentricity is shown and discussed. The minimum sizes of the stable regions around L ₄ change along the resonances and the relative strength of the resonances is analysed. Applications to possible Trojan exoplanets are indicated. Escape from L ₄ is also investigated.