Stability analysis of planetary systems via second-order R\'enyi entropy

TL;DR

This paper introduces a novel stability analysis method for planetary systems using second-order Renyi entropy derived from radial velocity data, offering a computationally efficient alternative to traditional N-body simulations.

Contribution

It presents a new entropy-based approach for planetary stability analysis that leverages phase space reconstruction and recurrence properties, reducing computational effort.

Findings

Entropy-based analysis aligns well with chaos detection methods.

Requires only tens of thousands of orbital periods for stability assessment.

Effective with observational radial velocity data.

Abstract

The long-term dynamical evolution is a crucial point in recent planetary research. Although the amount of observational data is continuously growing and the precision allows us to obtain accurate planetary orbits, the canonical stability analysis still requires N-body simulations and phase space trajectory investigations. We propose a method for stability analysis of planetary motion based on the generalized R\'enyi entropy obtained from a scalar measurement. The radial velocity data of the central body in the gravitational three-body problem is used as the basis of a phase space reconstruction procedure. Then, Poincar\'e's recurrence theorem contributes to finding a natural partitioning in the reconstructed phase space to obtain the R\'enyi entropy. It turns out that the entropy-based stability analysis is in good agreement with other chaos detection methods, and it requires only a few tens of thousands of orbital period integration time.