588 Achilles

588 Achilles was the first of the Trojan asteroids to be found, in 1906 by Max Wolf. Its discovery, at Jupiter's fourth Lagrangian point (L4), preceding the planet in its orbit, confirmed Joseph-Louis Lagrange's theory that two-body systems have points where a third object of negligible mass can reside in stable equilibrium. Within a couple of years of its discovery, two more Trojans were found: 617 Patroclus , near the trailing Lagrangian point, and 624 Hektor, near the leading Lagrangian point. It was later decided to continue naming such asteroids after participants in the Trojan War as recounted in Homerian legend.

diameter 116 km
spectral class C
semimajor axis 5.175 AU
perihelion 4.40 AU
aphelion 5.95 AU
inclination 10.3°
period 11.77 years