1540s, "follower or attendant of a superior person," from Middle French satellite (14c.), from Latin satellitem (nominative satelles) "an attendant" upon a distinguished person; "a body-guard, a courtier; an assistant," in Cicero often in a bad sense, "an accomplice, accessory" in a crime, etc. A word of unknown origin. Perhaps from Etruscan satnal (Klein), or a compound of roots *satro- "full, enough" + *leit- "to go" (Tucker); compare English follow, which is constructed of similar roots. De Vaan has nothing on it.
Meaning "planet that revolves about a larger one" first attested 1660s, in reference to the moons of Jupiter, from Latin satellites, which was used in this sense 1610s by German astronomer Johannes Kepler (1571-1630). Galileo, who had discovered them, called them Sidera Medicæa in honor of the Medici family. Meaning "man-made machinery orbiting the Earth" first recorded 1936 as theory, 1957 as fact. Meaning "country dependent and subservient to another" is recorded from 1800.