The Saturn, Janus and Epimetheus dynamics as a gravitational three–body problem in the plane
A. Bengochea* and E. Piña**
Department of Physics, Universidad Autónoma Metropolitana – Iztapalapa, P.O. Box 55 534, México, D.F., 09340 México, e–mail: abc@xanum.uam.mx* , pge@xanum.uam.mx** .
Recibido el 7 de abril de 2008
Aceptado el 13 de marzo de 2009
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.
Keywords: Three–body problem; Saturn; Janus; Epimetheus.
Resumen
Se usa un sistema de coordenadas dado por los ejes principales de inercia, determinados por un ángulo, y además, dos distancias relacionadas a los momentos principales de inercia y un ángulo auxiliar. Consideramos al problema de tres cuerpos, que interacciona a través de fuerzas gravitacionales en un plano. La dinámica de la terna Saturno–Jano–Epimeteo se ha descrito en estas coordenadas como una perturbación adiabática de las soluciónes clásicas triangular equilátera de Lagrange y la solución colinear de Euler. El movimiento co–orbital semejante al comportamiento de Saturno–Jano–Epimeteo se desarrolla teóricamente basados en evidencia numérica y experimental.
Descriptores: Problema de tres cuerpos; Saturno; Jano; Epimeteo.
PACS:45.50.Pk;95.10.Ce
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