Resonant planetary dynamics: Periodic orbits and long-term stability

TL;DR

This paper reviews the modeling of resonant periodic orbits in the planar and spatial three-body problem to understand long-term stability in multi-planet exo-solar systems, highlighting stable regimes and chaos indicators.

Contribution

It introduces a comprehensive analysis of symmetric periodic trajectories and their stability in resonant planetary systems, extending previous models to both planar and spatial cases.

Findings

Stable periodic orbits exist with regular evolution regimes.

Unstable orbits are linked to chaos and potential planetary destabilization.

The model helps identify conditions for long-term stability in resonant systems.

Abstract

Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet system shows complicated dynamics with mostly chaotic trajectories. We can determine possible stable configurations by computing resonant periodic trajectories of the general planar three body problem, which can be used for modeling a two-planet system. In this work, we review our model for both the planar and the spatial case. We present families of symmetric periodic trajectories in various resonances and study their linear horizontal and vertical stability. We show that around stable periodic orbits there exist regimes in phase space where regular evolution takes place. Unstable periodic orbits are associated with the existence of chaos and planetary destabilization.