Secular evolution of co-orbital motion of two exoplanets: semi-analytical investigation

We consider a system consisting of a star and two planets in co-orbital motion. The masses of the planets are much smaller than the mass of the star. The problem is planar, the motion of all three bodies taking place in a fixed plane. Since the co-orbital motion corresponds to the 1:1 mean motion resonance, it can be studied by methods developed to investigate resonance effects. In this work, we employ one of the semi-analytical methods intended for studying resonance effects—an adiabatic approximation proposed by J. Wisdom. Evolutionary equations are constructed, which describe secular effects in the dynamics of the system. Using them, various scenarios for the behaviour of the system over long time intervals are analysed in detail. For clarity, diagrams are provided illustrating possible variants of secular evolution.