  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.
