Trojan asteroids are bodies occupying the Lagrange Points of a larger body's orbit (dynamically stable points at which the gravity of the orbiting and orbited bodies cancel one-another out); typically the L₄ and L₅ points, 6o° ahead and behind the larger body respectively. The best known group of these bodies is the Jupiter Trojans (of which over 5000 are known). But in the past few years a number of Trojans have been found sharing the orbit of Neptune, mostly in the L₄ proceeding Lagrange Point, since the L₅ trailing Lagrange point is currently in alignment with the Galactic Centre, making it hard to for Earth-based telescopes to pick out small asteroids against the thick backdrop of stars.
Diagram showing the Lagrange Points of Neptune, and its proceeding Trojans (the trailing Neptune Trojans are very recent discoveries, and are not shown). Scott Sheppard.
It is thought that Neptune may have more Trojan asteroids than Jupiter, and that both bodies may have more Trojan asteroids than are present in the Main Asteroid Belt. Interestingly the International Astronomical Union currently defines a planet as a body in orbit around the sun (or another star) that is spherical due to its own gravity, and which has largely cleared its orbit of other bodies. Bodies that orbit the Sun and are spherical, but which have not cleared their orbits of other material should be referred to as 'Dwarf Planets'. If Jupiter and Neptune do in fact share their orbits with more asteroids than are present in the Main Asteroid Belt, then both should be referred to as Dwarf Planets - or the definitions will need to be changed again.
Diagram of the Solar System showing the Jupiter Trojans and the Proceeding Neptune Trojans (the trailing Neptune Trojans are very recent discoveries, and are not shown). The Encyclopedia of Science.
In a paper published on the online arXiv database at Cornell University Library on 26 February 2012, and accepted for publication in the peer-reviewed conference proceedings of the 11th annual Australian Space Science Conference, Jonathan Horner of the Department of Astrophysics at the School of Physics at the University of New South Wales, and Patryk Lykawka of the Astronomy Group at the Faculty of Social and Natural Sciences at Kinki University describe a model of the stability of two Neptune Trojans, the proceeding Trojan 2001 QR₃₂₂ and the trailing Trojan 2008 LC₁₈.
Horner and Lykawka calculated that the orbit of 2001 QR₃₂₂ has a half life of 593 million years; that is to say in 593 million years half the number of bodies with orbits similar to that of 2001 QR₃₂₂ would be shifted into other orbits, probably falling into the inner Solar System or joining the Centaur Asteroids, bodies with elliptical, planet-crossing orbits between Jupiter and Neptune. This suggests that 2001 QR₃₂₂ is a captured body, rather than one in an ancient orbit (i.e. in an orbit it has occupied for more than four billion years). However Horner and Lykawka point out that if there had originally been a large enough population of ancient proceeding Neptune Trojans in similar orbits to 2001 QR₃₂₂, then we would expect there to be surviving bodies of this population (since half would be lost every 593 million years).
2008 LC₁₈ proved to be less easy to model, since it is a more recent discovery with fewer observations, so Horner and Lykawka chose to reserve judgement of the long term stability of its orbit.