2001 QR322
2001 QR322 (also written 2001 QR322) was the first Neptune trojan discovered, in 2001 by the Deep Ecliptic Survey. It orbits ahead of Neptune at its L4 Lagrangian point.
With an absolute magnitude of 7.8 to 8.2, it has a diameter in the range of 60 to 160 km.
Other Neptune trojans have been discovered since. A study by Scott S. Sheppard and Chad Trujillo from the Carnegie Institution suggests that Neptune could possibly have twenty times more trojans than Jupiter.
Dynamical stability
Early studies of the dynamical stability of 2001 QR322, which used a small number of test particles spread over the uncertainties of just a few orbital parameters that were derived from a limited observation arc, suggested that 2001 QR322 is on a remarkably stable orbit, because most test particles remained on trojan orbits for 5 Gyr. Thereafter, the stability of Neptune trojans was simply assumed.
A more recent study, which used a very large number of test particles spread over the 3σ uncertainties in all six orbital parameters derived from a longer observational arc, has indicated that 2001 QR322 is far less dynamically stable than previously thought. The test particles were lost exponentially with a half life of 553 Myr. Further observations can determine whether 2001 QR322's orbit is actually within the dynamically stable or within the unstable part.