Asteroid 588, the first Trojan asteroid to be discovered, by Max Wolf in 1906. It is a member of the group of Trojans at the L4 Lagrangian point 60° ahead of Jupiter. Achilles is a D-type asteroid of diameter 135 km. Its orbit has a semimajor axis of 5.21 au, period 11.88 years, perihelion 4.44 au, aphelion 5.97 au, and inclination 10°.3.