A Simulation of the Co-Orbital Relationship between Epimethius and Janus, Two Satellites of Saturn

We have simulated the uniquely interacting orbits of these fifth and sixth moons of Saturn. With a mean radial separation less than the diameter of either body, and nearly equal orbital velocities, the two satellites circle around Saturn relatively unaffected by each other until the inner satellite begins to ``catch up'' to the outer one. When this occurs, the inner satellite is boosted into a higher orbit, while the outer satellite is dropped into a lower orbit. For simplicity, a two--dimensional closed system was considered, with calculated interactions between Saturn and each satellite as well interactions between the two satellites. Various FORTRAN program--generated graphs demonstrate the interactive behavior. The two moons are visually recorded exchanging orbits in a time that agrees with mathematical calculations, providing support to the claim that the satellites do indeed maintain a co--orbital relationship.