Asteroids in the inner Solar system - I. Existence

Abstract

Ensembles of in‐plane and inclined orbits in the vicinity of the Lagrange points of the terrestrial planets are integrated for up to 100 Myr. The integrations incorporate the gravitational effects of the Sun and the eight planets (Pluto is neglected). Mercury is the least promising planet, as it is unable to retain tadpole orbits over 100‐Myr time‐scales. 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 Myr. Some 40 per cent of the survivors are on tadpole orbits. For the Earth, the integrations are pursued for 50 Myr. The stable zones in the orbital plane are larger for the Earth than for Venus, but fewer of the survivors (∼20 per cent) 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 are stable. For the Earth, there are two bands of stability, one at low inclinations and one at moderate inclinations 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 (203 and 313 respectively). Our survey of in‐plane test particles near the Martian Lagrange points shows no survivors after 60 Myr. Low‐inclination test particles do not persist, as their inclinations are quickly increased until the effects of a secular resonance with Jupiter cause destabilization. Numerical integrations of inclined test particles for time‐spans of 25 Myr show stable zones for inclinations between 14° and 40°. However, there is a strong linear resonance with Jupiter that destabilizes a narrow band of inclinations at ∼29°. Both 5261 Eureka and 1998 VF31 lie deep within the stable zones, which suggests that they may be of primordial origin.

The Hungaria region as a possible source of Trojans and satellites in the inner Solar system

“…Especially for the Earth case, the close encounters decrease the inclination in such a way that the Hungarias enter the window of stability for the Earth co-orbital objects as shown in Tabachnik & Evans (2000).…”

“…3 let us see multiple close approaches to Mars and after that also to the Earth. In the time-span between about 55 Myr and 65 Myr of integration, many close encounters are found, thus the inclination change dramatically and that leads to the Earth asteroids capture: the orbital elements of the captured asteroid lies in the stability window for that planet as shown by Tabachnik & Evans (2000).…”

Space-Based Thermal Infrared Studies of Asteroids

“…• away from Earth in mean anomaly (Tabachnik & Evans 2000), they spend most of their time in regions of the sky that are difficult or impossible for ground-based telescopes to observe. Infrared measurements from NEOWISE have provided preliminary estimates of diameters and albedos .…”

The orbit of 2010 TK7: possible regions of stability for other Earth Trojan asteroids

“…In Mikkola & Innanen (1992) and Zhang & Innanen (1995) the authors found that Venus, Earth, and Mars can host co-orbital asteroids up to 10 Myr. According to the investigation of Tabachnik & Evans (2000), Earth's Trojans are on stable orbits when their inclinations are relatively low (i < 16…”