THE THREE TROJAN PROBLEM

Abstract

This paper is devoted to the stability study of three Trojan planets around a central star of 1 M Sun in a distance of 1 AU. In an earlier study, the stability of this coorbital configuration was computed if the mutual angular separation is 47.4° [Salo & Yoder, 1988]. We investigated by using numerical integrations the largeness of the stable region around these stable equilibrium points, depending on the mass parameter and the distances of the three planets. It turned out that even initial deviations in semimajor axis in the order of 5% can lead to very stable orbits. Also differences in the initial angular distance from the equilibrium points up to 70° do not mean that the orbits will be unstable. But the extensions in semimajor axis and angles depend sensitively on the masses involved, which were given the same values for our investigations in a first step. Test computations for different masses of the three planets involved show that they may be quite large without destroying the stability.