Regular and chaotic orbits in the dynamics of exoplanets

TL;DR

This paper investigates the stability of exoplanetary systems, especially those in mean-motion resonance, by analyzing periodic orbits within a three-body problem model to identify regions of long-term stability.

Contribution

It introduces a methodology using families of periodic orbits in the three-body problem to determine stable regions for resonant exoplanet systems, aiding in understanding their long-term stability.

Findings

Stable resonant systems are centered at stable periodic orbits.

Application to specific exoplanet systems confirms the methodology.

Resonant regions can be identified for long-term planetary stability.

Abstract

Many of exoplanetary systems consist of more than one planet and the study of planetary orbits with respect to their long-term stability is very interesting. Furthermore, many exoplanets seem to be locked in a mean-motion resonance (MMR), which offers a phase protection mechanism, so that, even highly eccentric planets can avoid close encounters. However, the present estimation of their initial conditions, which may change significantly after obtaining additional observational data in the future, locate most of the systems in chaotic regions and consequently, they are destabilized. Hence, dynamical analysis is imperative for the derivation of proper planetary orbital elements. We utilize the model of spatial general three body problem, in order to simulate such resonant systems through the computation of families periodic orbits. In this way, we can figure out regions in phase space, where the planets in resonances should be ideally hosted in favour of long-term stability and therefore, survival. In this review, we summarize our methodology and showcase the fact that stable resonant planetary systems evolve being exactly centered at stable periodic orbits. We apply this process to co-orbital motion and systems HD 82943, HD 73526, HD 128311, HD 60532, HD 45364 and HD 108874.