Investigación

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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References

1. K. Aksnes in Stability of the Solar System and its Minor Natural and Artificial Bodies, V. Szebehely ed. ( Reidel Publ. Co. 1985) p. 3        [ Links ]

2. P.D. Nicholson, D.P. Hamilton, K. Mathews, and C.F. Yoder Icarus 100 (1992) 464.        [ Links ]

3. R.S. Harrington and P.K. Seidelman, Icarus 47 (1981) 97.        [ Links ]

4. G. Colombo in Applications of Modern Dynamics to Celestial Mechanics and Astrodynamics (Reidel, Netherlands, 1982) 21.        [ Links ]

5. J.N. Spitale, R.A. Jacobson, C.C. Porco, and W.M. Owen, The Astronomical Journal 132 (2006) 692.        [ Links ]

6. S.F. Dermott and C.D. Murray, Icarus 48 (1981) 1, 12.        [ Links ]

7. C.D. Murray and S.F. Dermott, Solar System Dynamics (Cambridge University Press, Cambridge, 1999).        [ Links ]

8. C.F. Yoder, G. Colombo, S.P. Synott, and K.A. Yoder, Icarus 53 (1983) 431.        [ Links ]

9. C.F. Yoder, S.P. Synnott, and H. Salo, The Astronomic al Journal 98 (1989) 1875.        [ Links ]

10. J. Libre and M. Ollé, Astronomy & Astrophysics 378 (2001) 1087.        [ Links ]

11. F. Spirig and J. Waldvogel in Stability of the Solar System and its Minor and Artificial Bodies, V. Szebehely ed. (D. Reidel Publ. Co. Netherlands, 1985) p. 53.        [ Links ]

12. J. Waldvogel and F. Spirig in Long–Term Dynamical Behaviour of Natural and Artificial N–Body Systems, A.E. Roy ed. (Kluwer Academic Publishers, 1988) p. 223.        [ Links ]

13. A.E. Roy, Orbital Motion (Institute of Physics Publishing, Bristol 2005).        [ Links ]

14. J.–M. Petit and M. Henon, Icarus 66 (1986) 536.        [ Links ]

15. M. Henon and J.–M. Petit, Celestial Mechanics and Dynamical Astronomy 38 (1986) 67.        [ Links ]

16. J.M. Cors and G.R. Hall, SIAM J. Appl. Dyn. Sys. 2 (2003) 219.        [ Links ]

17. E. Piña, Celest. Mech. 74 (1999) 163.        [ Links ]

18. E. Piña and L. Jiménez–Lara, Celest. Mech. 82 (2002) 1.        [ Links ]

19. L. Jimenez–Lara and E. Piña, J. of Math. Phys. 44 (2003) 4078.        [ Links ]

20. J.V. Jose and E.J. Saletan, Classical Mechanics, A Contemporary Approach (Cambridge University Press, Cambridge, 1998).        [ Links ]

21. A. Bengochea, Horseshoe Orbits in the Saturn–Janus–Epimetheus Dynamics (in Spanish) Ph.D. Thesis (Universidad Autónoma Metropolitana, México, 2009).        [ Links ]

22. L. Landau and E. Lifshitz, Mechanics (Pergamon Press, Reading, 1960).        [ Links ]

23. R. Becker, Theory of Heat (Springer Verlag, Berlin, 1967) p. 132.        [ Links ]