# Temporary Capture of Asteroids by an Eccentric Planet

## TL;DR

This study analyzes the likelihood of asteroids being temporarily captured by planets, revealing that capture probability decreases with planetary eccentricity and is influenced by the planet's orbital parameters.

## Contribution

It provides an analytical and numerical assessment of how planetary eccentricity affects asteroid capture probability, including a critical eccentricity threshold.

## Key findings

- Capture probability is about 0.1% for circular orbits.
- Capture probability decreases as planetary eccentricity exceeds a critical value.
- Mars's current eccentricity suggests past asteroid captures are possible.

## Abstract

We have investigated the probability of temporary capture of asteroids in eccentric orbits by a planet in a circular or an eccentric orbit through analytical and numerical calculations. We found that in the limit of the circular orbit, the capture probability is $\sim 0.1\%$ of encounters to the planet's Hill sphere, independent of planetary mass and semimajor axis. In general, the temporary capture becomes more difficult as the planet's eccentricity ($e_{\rm p}$) increases. We found that the capture probability is almost independent of $e_{\rm p}$ until a critical value ($e_{\rm p}^{\rm c}$) that is given by $\simeq$ 5 times the Hill radius scaled by the planet's semimajor axis. For $e_{\rm p} > e_{\rm p}^{\rm c}$, the probability decreases approximately in proportion to $e_{\rm p}^{-1}$. The current orbital eccentricity of Mars is several times larger than $e_{\rm p}^{\rm c}$. However, since the range of secular change in Martian eccentricity overlaps $e_{\rm p}^{\rm c}$, the capture of minor bodies by the past Mars is not ruled out.