Long-Term Stability of Horseshoe Orbits

TL;DR

This study investigates the long-term stability of horseshoe orbits around planets, revealing that such orbits can be stable over Gyr timescales in systems with certain mass ratios, challenging previous assumptions.

Contribution

The paper provides new insights into the stability conditions of horseshoe coorbital orbits, especially regarding the influence of planetary mass ratios and orbital proximity.

Findings

Horseshoe coorbitals are long-lived for systems with primary-to-secondary mass ratios >1200.

Horseshoe orbits are unstable at smaller mass ratios due to close approaches within 5 Hill radii.

Tadpole orbits are more stable than horseshoe orbits near the secondary.

Abstract

Unlike Trojans, horseshoe coorbitals are not generally considered to be long-term stable (Dermott and Murray, 1981; Murray and Dermott, 1999). As the lifetime of Earth's and Venus's horseshoe coorbitals is expected to be about a Gyr, we investigated the possible contribution of late-escaping inner planet coorbitals to the lunar Late Heavy Bombardment. Contrary to analytical estimates, we do not find many horseshoe objects escaping after first 100 Myr. In order to understand this behaviour, we ran a second set of simulations featuring idealized planets on circular orbits with a range of masses. We find that horseshoe coorbitals are generally long lived (and potentially stable) for systems with primary-to-secondary mass ratios larger than about 1200. This is consistent with results of Laughlin and Chambers (2002) for equal-mass pairs or coorbital planets and the instability of Jupiter's horseshoe companions (Stacey and Connors, 2008). Horseshoe orbits at smaller mass ratios are unstable because they must approach within 5 Hill radii of the secondary. In contrast, tadpole orbits are more robust and can remain stable even when approaching within 4 Hill radii of the secondary.