A numerical criterion evaluating the robustness of planetary architectures; applications to the $\upsilon$ Andromed{\ae} system

TL;DR

This paper introduces a numerical criterion to evaluate the robustness of planetary architectures, applied to the $$ Andromedae system modeled as a three-body problem, aiding in identifying stable orbital configurations consistent with observations.

Contribution

It presents a new numerical criterion for assessing the stability of planetary systems, specifically applied to the $$ Andromedae system modeled as a three-body problem.

Findings

The criterion effectively identifies stable orbital configurations.

Application to $$ Andromedae shows compatible stable solutions.

Provides a practical tool for stability analysis in exoplanetary systems.

Abstract

We revisit the problem of the existence of KAM tori in extrasolar planetary systems. Specifically, we consider the $\upsilon$ Andromed{\ae} system, by modelling it with a three-body problem. This preliminary study allows us to introduce a natural way to evaluate the robustness of the planetary orbits, which can be very easily implemented in numerical explorations. We apply our criterion to the problem of the choice of a suitable orbital configuration which exhibits strong stability properties and is compatible with the observational data that are available for the $\upsilon$ Andromed{\ae} system itself.