# Eccentricities and the Stability of Closely-Spaced Five-Planet Systems

## TL;DR

This study investigates the long-term stability of five-planet systems with closely spaced, Earth-mass planets on initially eccentric orbits, revealing how eccentricity and resonances influence system lifetimes.

## Contribution

It extends previous stability analyses to include initially eccentric orbits, showing the exponential relationship between orbital separation and system lifetime persists.

## Key findings

- Higher initial eccentricity shortens system lifetime.
- Mean motion resonances can destabilize systems but less so than in circular cases.
- Aligned periapse angles with high eccentricity can prolong stability.

## Abstract

Observations of exoplanets have revealed that systems with planets on closely-spaced orbits are common, which motivates the question "How closely can planets orbit to one another and still be dynamically-stable for very long times?". To address this question, we investigate the stability of idealized planetary systems consisting of five planets, each equal in mass to the Earth, orbiting a one solar mass star. All planets orbit in the same plane and in the same direction, and the planets are uniformly spaced in units of mutual Hill Sphere radii. Most of the systems that we integrate begin with one or more planets on eccentric orbits, with eccentricities $e$ as large as $e= 0.05$ being considered. For a given initial orbital separation, larger initial eccentricity of a single planet generally leads to shorter system lifetime, with little systematic dependence of which planet is initially on an eccentric orbit. The approximate trend of instability times increasing exponentially with initial orbital separation of the planets found previously for planets with initially circular orbits is also present for systems with initially eccentric orbits. Mean motion resonances also tend to destabilize these systems, although the reductions in system lifetimes are not as large as for initially circular orbits. Systems with all planets having initial $e= 0.05$ and aligned periapse angles typically survive far longer than systems with the same spacing in initial semi-major axis and one planet with $e= 0.05$, but they have slightly shorter lifetimes than those with planets initially on circular orbits.