Kalliope has one known moon, Linus, or (22) Kalliope I Linus. It is quite big: 30–40 km in diameter. It orbits about 1065 km from Kalliope. This is about 12 times the radius of Kalliope. Linus was found on August 29, 2001 by Jean-Luc Margot and Michael E. Brown, while another team also independently found the moon 3 days later.