Dynamics of Trojan planets in extrasolar systems

Today there are about 170 extrasolar planets in 145 extrasolar systems confirmed. We have only observational evidence for gas giants (=GG) up to several Jupiter masses. Most of these discovered planets are near to the central star. That`s the reason why we have to ask, which configurations are possible that a terrestrial planet may exist in the habitable zone of an extrasolar planetary system? This project investigates the dyanmical stability of terrestrial planets in the 1:1 mean motion resonance (called Trojan planets) with Jovian-like planets in extrasolar systems. Most of the discovered extrasolar planets are so called single planetary systems, meaning that only one planet orbits the central star. Only 18 extrasolar systems have two or more planets (so called multi planetary systems) and 13 systems have a stellar companion (double stars). The goal of this project is to study the chaoticity of the Trojan planets in single and multi planetary systems. Therefore numerical longtime integrations are necessary which will be undertaken by several integrators (Lie Integration Method, Hybrid Symplectic-Bulirsch-Stoer Integrator and with a Runge Kutta Method). The dynamical models for the investigation of single planetary systems are the elliptic restricted three body problem (star, gas giant and massless Trojan planet) and the elliptic three body problem. Additionally the n-body problem and the elliptic n-body problem are necessary to study Trojans in multi planetary systems. The methods of analysis are the Maximum Eccentricity Method, the Maximum Lyapunov Exponent and the Fast Lyapunov Indicator. The final goal is to publish a catalogue with the dynamical processes of all planetary systems where possible Trojan Planets may exist. The knowledge of this project could be important for the exploration of extrasolar systems and also useful for the understanding of dynamical processes in our solar system.