Effects of non-spherical symmetry on binary orbits of asteroids and comets

TL;DR

This paper develops a theoretical model for binary orbits involving a spherical and a non-spherical body, revealing unique orbital behaviors and energy transfer mechanisms, with implications for asteroid and comet dynamics.

Contribution

It introduces a new framework for calculating orbits around non-spherical bodies, specifically prolate ellipsoids, and analyzes energy and angular momentum exchanges in such systems.

Findings

Distinct orbital trajectories around prolate spheroids compared to spherical systems

Verification of energy and angular momentum conservation in non-spherical systems

Conditions for satellite capture and escape around non-spherical bodies

Abstract

We develop a theoretical framework for the calculation of orbits for a system consisting of a spherical object and a non-spherical body, which is then specialized to a prolate ellipsoid. Particular trajectories are presented that illustrate a drastic contrast between the familiar elliptical orbits of spherical binary systems and the trajectories around the prolate spheroid. We also show here, and in a media video representation of the computed orbits, how the spherical satellite instantaneous orbital plane and eccentricity evolve. We also explicitly verify the conservation of the total angular momentum and energy of the system, prolate plus satellite, while the intrinsic rotational angular momentum and energy of the prolate changes with time at the expense of the orbital energy and angular momentum of the sphere. We then consider a particular orbit where an initially bound satellite gains sufficient orbital energy and eventually escapes, with its total energy now positive. The inverse process, where a satellite is captured by a prolate, is also considered, and we determine the probability of this event occurring, as a function of the initial relative velocity and parameter of impact of the system. We end with a discussion of a plausible scenario where an escaping satellite in the Oort cloud could wind up with a new heliocentric Earth`s crossing orbit. In the Appendices we develop the necessary equations for the application of the above formalism to orbits around a general homogeneous ellipsoid.