Classification of Trajectories in a Two-planet Exosystem Using the Generalized Three-body Problem

We deploy the theory of the generalized three-body problem to describe an exosystem composed of a host star, a transiting Jupiter-sized exoplanet, and an Earth-sized exoplanet. By performing a thorough and systematic orbit classification we map a large section of the phase space and determine the final states of the Earth-sized exoplanet. In particular, we manage to classify the initial conditions of the perturber into several categories such as bounded regular or chaotic motion, collision, and escaping motion. Bounded regular motion corresponds to regions of the phase space in which the orbit of the Earth-sized planet would be stable. In our computations, we use realistic values of the involved parameters and initial conditions corresponding to real observable exosystems. Our analysis provides important information on how the mass of the host star as well as the mass of the Jupiter size affects the orbital dynamics of the Earth-sized exoplanet.