Global stability of L4 and L5 Trojans

Richard Schwarz

01.10.2002 - 09.11.2005

Abstract

The first part of this work was to investigate the dynamical stability of Jupiter Trojans. Therefore long-term integrations - up to 100 Myrs - were done. The goal of this investigation is twofold: first it was tried to find out how the largeness of the stable areas around the Lagrangian points of Jupiter changes with the inclination and the eccentricity of the asteroids. This was done for different dynamical models: the elliptic restricted problem (Sun + Jupiter + massless Trojan), a model including also Saturn and one model consisting the outer planets Jupiter, Saturn, Neptun, Uranus and the massless Trojan. Second it was tried to check why there is a different number of real Trojans around L4 and L5 (~1000:600); a slight difference in their dynamics was found. In the second part the possibility that terrestrial planets on stable orbits could exist in a 1:1 mean-motion-resonance with Jovian like planets of extrasolar planetary systems was examined. Out of approximately 120 known extrasolar planetary systems, only 15 systems were found with a giant planet in the habitable zone. To study the orbital behaviour respectively the size of the stable zone in the different systems we used extensive numerical computations. The results showed that Trojan planets - in most of the extrasolar planetary systems - can be stable in the 1:1 mean-motion-resonance.