Modeling resonant trojan motion in planetary systems

TL;DR

This paper models the complex resonant motion of trojan companions in planetary systems, focusing on secular perturbations and chaotic diffusion, using Hamiltonian dynamics to understand their long-term stability.

Contribution

It introduces a Hamiltonian decomposition approach to analyze resonant trojan motion under secular perturbations, highlighting modulational diffusion as a key process.

Findings

Resonant trojan motion can be effectively modeled with a two-degree-of-freedom Hamiltonian.

Secular perturbations induce slow chaotic diffusion at resonances.

Modulational diffusion explains the long-term evolution of trojan orbits.

Abstract

We consider the dynamics of a small trojan companion of a hypothetical giant exoplanet under the secular perturbations of additional planets. By a suitable choice of action-angle variables, the problem is amenable to the study of the slow modulation, induced by secular perturbations, to the dynamics of an otherwise called `basic' Hamiltonian model of two degrees of freedom (planar case). We present this Hamiltonian decomposition, which implies that the slow chaotic diffusion at resonances is best described by the paradigm of modulational diffusion.