Highly eccentric exoplanets trapped in mean-motion resonances

Abstract

We herein utilize the general three-body problem (GTBP) as a model, in order to simulate resonant systems consisting of a star and two planets, where at least one of them is highly eccentric. We study them in terms of their long-term stability, via the construction of maps of dynamical stability and the computation of the corresponding families of periodic orbits. We identify the way their survival is connected with the regions of regular motion in phase space, which, in turn, were created by stable resonant periodic orbits in their vicinity. Consequently, a phase protection mechanism is provided and the planets avoid close encounters and collisions even on long timescales. We apply our methodology to the extrasolar system HD 82943.