Dynamics around Non-Spherical Symmetric Bodies: I. The case of a spherical body with mass anomaly

TL;DR

This paper investigates the dynamics around non-spherical bodies with a focus on spherical bodies with mass anomalies, revealing stable and chaotic regions, and providing new analytical tools for understanding such systems in celestial mechanics.

Contribution

It introduces the first analytical and numerical methods specifically designed to study the dynamics of bodies with mass anomalies, including the application to Chariklo.

Findings

Existence of chaotic inner and stable outer regions around a mass anomaly body.

Identification of classical 3-body problem structures in the stable outer region.

Chariklo rings likely related to first kind periodic orbits, not 1:3 resonance.

Abstract

The space missions designed to visit small bodies of the Solar System boosted the study of the dynamics around non-spherical bodies. In this vein, we study the dynamics around a class of objects classified by us as Non-Spherical Symmetric Bodies, including contact binaries, triaxial ellipsoids, spherical bodies with a mass anomaly, among others. In the current work, we address the results for a body with a mass anomaly. We apply the pendulum model to obtain the width of the spin-orbit resonances raised by non-asymmetric gravitational terms of the central object. The Poincare surface of section technique is adopted to confront our analytical results and to study the system's dynamics by varying the parameters of the central object. We verify the existence of two distinct regions around an object with a mass anomaly: a chaotic inner region that extends beyond the corotation radius and a stable outer region. In the latter, we identify structures remarkably similar to those of the classical restrict and planar 3-body problem in the Poincare surface of sections, including asymmetric periodic orbits associated with 1:1+p resonances. We apply our results to a Chariklo with a mass anomaly, obtaining that Chariklo rings are probably related to first kind periodic orbits and not with 1:3 spin-orbit resonance, as proposed in the literature. We believe that our work presents the first tools for studying mass anomaly systems.