(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. depiction of the
horseshoe orbits of Janus and Epimetheus Epimetheus's orbit is
co-orbital with that of
Janus. Janus's
mean orbital radius from Saturn is, as of 2006 (as shown by the green color in the picture below), only 50 km less than that of Epimetheus, a distance smaller than either moon's mean radius. In accordance with
Kepler's laws of planetary motion, the object which is closer to Saturn completes its
orbit more quickly. The orbit is completed only around 30 seconds more quickly, due to the small difference between the moons' distances from Saturn. Each day, the inner moon progresses 0.25° more around Saturn than the outer moon. As the inner moon catches up to the outer moon, their mutual gravitational attraction increases the inner moon's momentum and decreases that of the outer moon. This added momentum causes the inner moon's distance from Saturn and its
orbital period to increase while those of the outer moon are decreased. The timing and magnitude of the
momentum exchange is such that the moons effectively swap orbits, never approaching closer than about 10,000 km to each other. At each encounter Janus's orbital radius changes by ~20 km and Epimetheus's by ~80 km: Janus's orbit is less affected because it is four times the mass of Epimetheus. The exchange of orbits takes place approximately every four years; the last close approaches occurred in January 2006, 2010, 2014, 2018, and 2022. This type of orbit is sometimes referred to as a
horseshoe orbit, due to the shape of each moon's orbit, as seen from the perspective of the other moon. The two librate about their mutual L4 and L5
Lagrange points. Some asteroids are known to have horseshoe orbits but this is the only known such orbital configuration for moons within the
Solar System. The orbital relationship between Janus and Epimetheus can be understood in terms of the
circular restricted three-body problem, as a case in which the two moons (the third body being Saturn) are similar in size to each other. In the far future, the two moons' orbits will migrate outward due to their gravitational interactions with the A Ring, which will probably cause their co-orbital configuration to collapse into one where Epimetheus librates around Janus' L4 or L5 point, becoming a
trojan of Janus. While Epimetheus is the outer moon relative to Janus, it participates in both a 15:17
mean-motion resonance with
Prometheus and a 19:21 mean-motion resonance with
Pandora. No state of resonance exists while Epimetheus is on the inner orbit or for Janus in general. == Physical characteristics ==