Stability of Circular Orbits in the Three-Body Problem. Dynamical characterisation of planetary systems

João Nuno Monteiro Júlio Taquelim da Cruz

Key information

Authors:

João Nuno Monteiro Júlio Taquelim da Cruz (João Nuno Monteiro Júlio Taquelim da Cruz)

Supervisors:

Rui Manuel Agostinho Dilão (Rui Manuel Agostinho Dilão)

Published in

June 21, 2021

Abstract

In this work we study stability conditions for the general three-body problem within the scope of planetary systems, i.e., with two planets orbiting a central star. It is shown through numerical simulations that stability of such systems depends on the ratio between the mass of the planets and the star, as well as on the ratio between the initial distances of the planets to the star. By simulating several configurations and obtaining for each initial distance the value of the mass parameters under which they are stable with a Padé approximant technique, a stability diagram was constructed. A stability and an instability zone are observed, which meet on a non-trivial transition strip. The stability zone was characterised, and we found that it has three different regions depending on the initial parameters - a quasi-Keplerian one, another with orbit precession due to the appearance of libration frequencies, and a region where planets have halo-like orbits. Moreover, we found that these stable systems are quasi-periodic in the vicinity of circular orbits and that there is no chaos.