Existence of asteroids in the inner solar system

Ensembles of in-plane and inclined orbits in the vicinity of the Lagrange points of the terrestrial planets are integrated for up to 100 million years. Mercurian Trojans probably do not exist, although there is evidence for long-lived, corotating horseshoe orbits with small inclinations. Both Venus and the Earth are much more promising, as they possess rich families of stable tadpole and horseshoe orbits. Our survey of in-plane test particles near the Martian Lagrange points shows no survivors after 60 million years. Low inclination test particles do not persist, as their inclinations are quickly increased until the effects of a secular resonance with Jupiter cause de-stabilisation. Numerical integrations of inclined test particles for timespans of 25 million years show stable zones for inclinations between 14 and 40 degrees. Both Martian 'Ihojans 5261 Eureka and 1998 VF31 lie deep within the stable zones, which suggests they may be of primordial origin.