Asteroids in the Inner Solar System I – Existence

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. The integrations incorporate the gravitational effects of Sun and the eight planets (Pluto is neglected). Mercury is the least likely planet, as it is unable to retain tadpole orbits over 100 million year timescales. 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 Trojans in the orbital plane of Venus is undertaken for 25 million years. Some 40% of the survivors are on tadpole orbits. For the Earth, the integrations are pursued for 50 million years. The stable zones in the orbital plane are larger for the Earth than for Venus, but fewer of the survivors (∼ 20%) are tadpoles. Both Venus and the Earth also have regions in which inclined test particles can endure near the Lagrange points. For Venus, only test particles close to the orbital plane (i ∼ < 16 •) are stable. For the Earth, there are two bands of stability, one at low inclinations (i ∼ < 16 •) and one at moderate inclinations (24 • ∼ < i ∼ < 34 •). The inclined test particles that evade close encounters are primarily moving on tadpole orbits. Two Martian Trojans (5261 Eureka and 1998 VF31) have been discovered over the last decade and both have orbits moderately inclined to the ecliptic (20.3 • and 31.3 • respectively). 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 •. However, there is a strong linear resonance with Jupiter which destabilises a narrow band of inclinations at ∼ 29 •. Both 5261 Eureka and 1998 VF31 lie deep within the stable zones, which suggests they may be of primordial origin.