Dynamical regimes of small bodies perturbed by an eccentric giant planet

TL;DR

This study explores the complex dynamics of small bodies influenced by an eccentric giant planet across various eccentricities and inclinations, revealing a critical inclination for stability and the dominance of the ZLK mechanism at higher inclinations.

Contribution

It extends previous analyses by examining non-hierarchical configurations and applying semi-analytical models to understand resonance and secular dynamics in these systems.

Findings

Identification of a critical inclination around 30 degrees affecting stability.

Discovery of a stability barrier related to the vanishing of the pericenter proper frequency.

Observation of longitude of the ascending node concentrations in exterior populations.

Abstract

The dynamics of small bodies perturbed by an eccentric planet was done mostly under the assumption of well separated orbits using analytical approximations appropriate for the hierarchical case. In this work we study the dynamics of small bodies in a wide range of eccentricities and inclinations perturbed by a giant planet with e_p=0.4, in the non-hierarchical case. We consider small bodies both interior and exterior to the planet. We apply semi-analytical models for the study of resonances and the properties of the secular disturbing function. We perform a frequency analysis of numerical integration of the exact equations of motion to obtain the proper frequencies and corresponding dynamical secular paths. We study the dependence of proper frequencies with the initial mutual inclination and we find a critical inclination around 30 degrees for which the pericenter proper frequency vanishes giving rise to the increase of small bodies eccentricities followed by unstable dynamics. This happens for both interior and exterior small bodies and constitutes a stability barrier in the inclination. For greater inclinations the ZLK mechanism dominates both populations. By means of numerical integration of thousands of small bodies we reproduce the well known pericenter shepherding, but for the exterior populations we also find concentrations of the longitude of the ascending node in the direction of the planetary line of apsides.