Scattered Disk Dynamics: The Mapping Approach

TL;DR

This paper introduces a symplectic map model for the dynamics of bodies on nearly parabolic orbits influenced by a planet, providing insights into chaos, resonances, and the evolution of scattered disk objects.

Contribution

The paper develops a novel symplectic mapping approach to analyze the complex dynamics of highly eccentric bodies perturbed by a planet, matching numerical results and exploring chaotic behavior.

Findings

Map agrees well with numerical integrations

Chaos onset depends on perturber mass and pericenter distance

Resonance sticking influences orbital evolution

Abstract

We derive, and discuss the properties of, a symplectic map for the dynamics of bodies on nearly parabolic orbits. The orbits are perturbed by a planet on a circular, coplanar orbit interior to the pericenter of the parabolic orbit. The map shows excellent agreement with direct numerical integrations and elucidates how the dynamics depends on perturber mass and pericenter distance. We also use the map to explore the onset of chaos, statistical descriptions of chaotic transport, and sticking in mean-motion resonances. We discuss implications of our mapping model for the dynamical evolution of the solar system's scattered disk and other highly eccentric trans-Neptunian objects.