5126 Achaemenides /ækɪˈmɛnɪdiːz/ is a Jupiter trojan from the Greek camp, approximately 50 kilometers (31 miles) in diameter. It was discovered on 1 February 1989, by American astronomer Carolyn Shoemaker at the Palomar Observatory in California.^[1] The dark Jovian asteroid belongs the 100 largest Jupiter trojans and has a long rotation period of 32.4 hours.^[9] It was named after one of Odysseus's crew members, Achaemenides, from Greek mythology.^[1]

Achaemenides is a dark Jovian asteroid orbiting in the leading Greek camp at Jupiter's L₄ Lagrangian point, 60° ahead of the Gas Giant's orbit in a 1:1 resonance (see Trojans in astronomy).^[4] It is also a non-family asteroid in the Jovian background population.^[5] It orbits the Sun at a distance of 5.1–5.4 AU once every 12 years (4,385 days; semi-major axis of 5.24 AU). Its orbit has an eccentricity of 0.02 and an inclination of 30° with respect to the ecliptic.^[3] The body's observation arc begins with a precovery at Palomar in January 1953, more than 36 years prior to its official discovery observation.^[1]

Achaemenides is an assumed C-type asteroid.^[9]

This minor planet was named from Greek mythology after the Greek warrior Achaemenides, one of few surviving members of Odysseus's crew. Left behind when Odysseus fled the blinded Cyclops, he was later rescued by the Trojan Aeneas.^[1] The official naming citation was published by the Minor Planet Center on 4 June 1993 (M.P.C. 22249).^[10]