Classification of orbits in three-dimensional exoplanetary systems

¹ Department of Physics, School of Science, Aristotle University of Thessaloniki, 541 24 Thessaloniki, Greece
e-mail: evzotos@physics.auth.gr
² Department of Astronomy, Eötvös University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
³ Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, PO Box 80203, Jeddah 21589, Saudi Arabia

Received: 15 October 2020
Accepted: 11 December 2020

Abstract

The three-dimensional version of the circular restricted problem of three bodies is utilized to describe a system comprising a host star and an exoplanet. The third body, playing the role of a test particle, can be a comet or an asteroid, or even a small exomoon. Combining the grid classification method with two-dimensional color-coded basin maps, we determine the nature of the motion of the test particle by distinguishing between collision, escaping, and bounded motion. In the case of ordered bounded motion, we also obtain the orientation (retrograde or prograde) as well as the geometry (circulating around one or both of the two main bodies) of the trajectories of the third body, which starts from either the pericenter or apocenter. Following this approach, we are able to systematically explore the dependence of the motion type of the test particle on the initial values of the semimajor axis, eccentricity, and inclination of its orbit.