Mathematics – Probability
Scientific paper
Sep 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009dps....41.5507c&link_type=abstract
American Astronomical Society, DPS meeting #41, #55.07
Mathematics
Probability
Scientific paper
Earth and Venus do have any long-lived co-orbital objects, with known companions like Cruithne being temporary. Trojans of Mars may be primordial or at least very long-lived. Previous studies of terrestrial planet co-orbital stability found that low-inclination co-orbitals of Earth and Venus can last beyond 100 Myr (Tabachnik and Evans 2000). Earth's horseshoe co-orbitals are more stable than the Trojans, while the situation is reverse for Venus. Scholl et al.(2005) found that some of the Venus Trojans have lifetimes up to 1 Gyr, with the population decaying in a non-exponential manner. Analytical estimate for the stability of both Venus and Earth horseshoe co-orbitals is on the order of 1 Gyr (Dermott and Murray 1981).
The Gyr-scale stability of such co-orbitals makes them relevant to the question of the source of the lunar cataclysm. Cuk et al.(2009) show that the size-distribution of lunar craters belonging to the Imbrian system is not consistent with main asteroid belt impactors. An alternative source of the cataclysm could be tidal disruption of a relatively large (D>500km) planetesimal surviving somewhere in the inner solar system. Earth and Venus co-orbital regions might release such an object on the right timescale of 0.5-1 Gyr. In particular, a freshly escaped horseshoe co-orbital of Earth would have a high probability of a low-velocity Earth encounter which could lead to tidal disruption. The resulting fragments would have high probability of impacting Earth and the Moon.
No stable co-orbitals of terrestrial planets have been produced in formation simulation, but as they are dynamically coupled to the parent planet, so-far unmodeled damping of planetary eccentricities could circularize orbits of transient co-orbitals' and separate them from those of neighboring planets. I will present large-scale, long-term integrations of Earth and Venus co-orbitals, and also smaller-scale integrations exploring their secular behavior during planetary formation.
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