Orbit classification in the Copenhagen problem with oblate primaries

Abstract

This article aims to numerically investigate the orbital dynamics of the planar circular‐restricted three‐body problem, where the two primary bodies have equal masses and an oblate spheroid shape. By numerically integrating several large sets of initial conditions of both retrograde and prograde orbits, we classify them into three main categories: (a) bounded (regular or chaotic), (b) escaping, and (c) collision orbits. We reveal the motion of the test particle by presenting color‐coded diagrams, where the initial conditions are mapped to the orbit type and studied as a function of the total orbital energy (or equivalently of the Jacobi constant) as well as of the oblateness coefficient. Our numerical results are compared with related previous ones, corresponding to the classical version of the planar‐restricted three‐body problem. The presented outcomes have practical physical applications as they can be used for modeling the motion of a massless test particle in the gravitational field of a binary system of two oblate exoplanets.

Numerical Investigation for Periodic Orbits in the Hill Three-Body Problem

“…Furthermore, several modifications of the restricted problem have been proposed in the past so as to make it more realistic to certain systems of Celestial Mechanics. Such modifications include the radiation and oblateness effects of the primaries [14][15][16][17] or the incorporation of some relativistic terms [18,19], while various works involve also a larger number for the primary bodies [20,21].…”