A centenary survey of orbits of co-orbitals of Jupiter

Jupiterʹs Trojan asteroids fulfill the prediction of Lagrange that orbits can be stable when a small body orbits in specific locations relative to its ‘parent’ planet and the Sun. The first such Trojan asteroid was discovered slightly over 100 years ago, in 1906, and subsequently similar asteroids have been discovered associated with Mars and with Neptune. To date no Trojans have been discovered associated with Earth, but several horseshoe asteroids, co-orbital asteroids moving along a large range of the Earthʹs orbit, have been found. Since the number of detected Jupiter Trojans has increased dramatically in the last few years, we have conducted a numerical survey of their orbital motions, focusing on comparing results about libration properties to theory. We use the enlarged database of information about Trojans from the Minor Planet Center Orbital Database (MPCORB), as well as the Mercury integrator package developed by Chambers [1999. A hybrid symplectic integrator that permits close encounters between massive bodies. Mon. Not. R. Astron. Soc. 304(4), 793–799] to summarize their properties as now known.