In celestial mechanics, a horseshoe orbit is a type of co-orbital motion of a small orbiting body relative to a larger orbiting body. The osculating (instantaneous) orbital period of the smaller body remains very near that of the larger body, and if its orbit is a little more eccentric than that of the larger body, during every period it appears to trace an ellipse around a point on the larger object's orbit.
However, the loop is not closed but drifts forward or backward so that the point it circles will appear to move smoothly along the larger body's orbit over a long period of time. When the object approaches the larger body closely at either end of its trajectory, its apparent direction changes. Over an entire cycle the center traces the outline of a horseshoe, with the larger body between the 'horns'.
Figure 1. Plan showing possible orbits along gravitational contours. In this image, the Earth (and the whole image with it) is rotating counterclockwise around the Sun.
Figure 2. Thin horseshoe orbit
Janus is an inner satellite of Saturn. It is also known as Saturn X. It is named after the mythological Janus.
Janus as imaged by Cassini on 7 April 2010: highest-resolution full-disk image to date
Epimetheus (lower left) and Janus (right) seen on 20 March 2006, two months after swapping orbits. The two moons appear close only because of foreshortening; in reality, Janus is about 40,000 km farther from Cassini than Epimetheus.
Janus as viewed by Voyager 2 (1981-08-25).
Janus and Prometheus lie above and below Saturn's rings (2006-04-29).