New insights into the stability of L4 in the spatial restricted three-body problem

This paper is devoted to the study of the stability of the Lagrangian point L4 in the spatial restricted three-body problem. In our Solar system, the range of eccentricities of stable Trojan asteroids are wide and are often far greater than that of their host planet. Therefore, we investigated the stability by varying the eccentricity of the secondary planet (ep) and the third Trojan (eTro) body. The stability is investigated by numerical methods, computing stability maps for different inclinations of the Trojan. With the help of the libration amplitude σ we could show that not all stable asteroids are moving in Trojan motion (=tadpole orbits). We could show that the percentage of stable tadpole orbits is similar for large inclinations of the Trojan body (20° ≤ iTro ≤ 60°) for all initial conditions.