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This paper is devoted to the study of secondary resonances and the stabilityof the Lagrangian point L4 in the spatial restricted three-body problem formoderate mass ratios (mu), meaning that mu is smaller than 0.0045. However, weconcentrated our investigations on small mass ratios for mu smaller than 0.001,which represent the mass ratios for stable configurations of tadpole orbits inthe Solar system. The stability is investigated by numerical methods, computingstability maps in different parameter planes. We started investigating the massof the secondary; from Earth-mass bodies up to Jupiter-mass bodies. In additionwe changed the orbital elements (eccentricity and inclination) of the secondaryand Trojan body. For this parameter space we found high order secondaryresonances, which are present for various inclinations. To determine secondaryresonances we used Rabe's equation and the frequency analysis. In addition weinvestigated the stability in and around these secondary resonances.

Stability and secondary resonances in the spatial restricted three-body problem for small mass ratios