Dynamical Stability of Planetary Systems

Abstract: The study of dynamical stability in planetary systems has become possible during the last few decades due to the development of numerical methods for long-term integrations of N-body systems. Since the 90’s the number of exoplanet detections has been increased significantly, making the simulations of other real planetary systems besides the Solar System feasible. One of the exciting new-found worlds is the system Kepler-11. Six planets which are located very close to each other orbit a solar-type star. In this project we first investigate the behavior of Kepler-11 when we change some of the initial conditions of the outermost planet of the system and then we approximate the Red Giant phase of solar-type stars in order to see how the planetary orbits are altered. For the first part we run three series of simulations (groups A,B,C). Each group has a different value for the mean density of planet Kepler-11g (1.0,1.5,2.0 g/cm 3 ). We run simulations for 36 different combinations of mass and eccentricity of planet Kepler-11g for each group. In nine configurations all six planets of the system continue to orbit the star until the end of the simulations. These nine stable configurations of Kepler-11 are used in the second part where we implement a constant mass-loss rate for the star which results in 30% mass loss after 30 million years, trying to approximate that way the mass loss of solar-type stars in Red Giant Branch. We also run nine simulations of a hypothetical system consisting only of the Sun, Earth and Jupiter where we implement the constant mass-loss rate to the Sun. In the Kepler-11 system, the orbits of planets Kepler-11g and Kepler-11e change by ∼45% and ∼54% respectively, after 30 million years, due to the mass loss of the star, while in the hypothetical planetary system the orbits of the two planets change by ∼43%. The study of orbits and how they move outward during the Post-Main Sequence evolution of stars is essential for our understanding of the existence of a Habitable Zone, not just around stars in Main-Sequence phase, but also around stars in late stages of their evolution.