Revealing the dynamical properties of Jupiter-size exoplanets on elliptic orbits

Our study delves into the orbital dynamics of an exoplanetary system, comprising a solar-mass host star, a transiting Jupiter-sized body, and an Earth-sized exoplanet. This exploration is grounded in the general three-body problem framework. We undertake a comprehensive and systematic numerical analysis of the available phase space, employing a rigorous orbit classification methodology to determine the final states and/or dynamical properties of the Earth-sized exoplanet. Our classification scheme adeptly distinguishes between three fundamental orbital outcomes: escape trajectories, collisional events, and bounded motion for the Earth-sized exoplanet. Furthermore, when the motion exhibits regularity in the Liouville sense, we categorize the initial conditions, contingent upon the characteristics of their respective trajectories. These regular orbits not only possess intriguing dynamical attributes but also provide valuable insights into phase space regions where the motion of the Earth-sized exoplanet may maintain long-term dynamical stability. Specifically, we highlight exotic high-eccentricity orbital architectures rendering a regular quasi-periodic time-evolution. Of particular significance is our discovery of special cases where the Earth-sized exoplanet follows trajectories that render it an exomoon in relation to the transiting Jupiter-sized exoplanet. This investigation extends our understanding of the complex dynamics within exoplanetary systems, shedding light on the dynamics, and the potential pathways for exomoon formation possibly via accretion on the host planet.