Our Solar System is teeming with small bodies trapped in resonances with planets. Prime examples of these resonant small bodies are the thousands of Trojan companions of Jupiter. Trojan asteroids are locked in a 1:1 resonance with Jupiter -- orbiting the sun with the same 12 year period as the giant planet. A more exotic class of 1:1 resonance is the quasi-satellites. PSI's Dr. Steve Kortenkamp has been investigating the behaviour of quasi-satellites as shown in these animations of the orbital behaviour of a quasi-satellite (yellow) and a planet (red). Currently only a single quasi-satellite is known -- near-Earth object 2003 YN107 is a quasi-satellite of Earth.

For more details on these animations and a description of how quasi-satellites might be captured as true satellites, follow this link.