Primordial migration of co-orbital satellites as a mechanism for the horseshoe orbit of Janus-Epimetheus

We analyze the orbital motion of two natural satellites initially in co-orbital configuration with a third (guiding) satellite embedded into a circumplanetary gas disc and undergoing tidal interactions with the central planet. By solving the exact equations of motion, including the dissipative effects and the mutual gravitational perturbations, we investigate the configuration of the system soon after the guiding satellite is disrupted when crossing the Roche limit with the central planet during its orbital decay. The application is done for the system composed of Saturn and the two small co-orbital satellites Janus and Epimetheus. We perform a large number of numerical simulations, varying the mass of the hypothetical guiding satellite, Saturn's tidal quality factor and the initial configuration and the masses of the small satellites. Analyzing the orbital configurations of Janus and Epimetheus soon after the disruption of the guiding satellite, we obtain that the mutual horseshoe co-orbital orbits appear as a natural outcome of the numerical simulations.