The Saturn, Janus and Epimetheus dynamics as a gravitational three-body problem in the plane

Abstract

Using a coordinate system given by the principal axis of inertia, as determined by an angle, and also two distances related to the principal moments of inertia and an auxiliary angle as coordinates, we consider the Three Body Problem, interacting through gravitational forces in a plane. The dynamics of the triple Saturn-Janus-Epimetheus has been considered in these coordinates as an adiabatic perturbation of the classical equilateral triangle Lagrange solution and of the collinear Euler solution. The co-orbital motion remembering the Saturn-Janus-Epimetheus behavior is then developed theoretically based on numerical and experimental evidence.