Abstract
The three-body problem with masses mo, εm1, εm2 is considered in the limiting case ε → 0. By appropriately scaling the coordinates the motion is described by the following two matched approximations: (1) the outer solution consisting of two independent Kepler motions about mo, (2) the inner solution satisfying Hill’s lunar equation. The discussion of Hill’s problem with appropriate boundary conditions at infinity correctly predicts that Saturn’s coorbiting satellites Janus and Epimetheus exchange orbits at the close encounter, whereas the F ring shepherds (1980S26 and 1980S27) do not.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aksnes, K., 1982: The Dynamics of Close Planetary Satellites and Rings. In: V. Szebehely (ed.), Applications of Modern Dynamics to Celestial Mechanics and Astrodynamics, 1–20, Reidel Publ. Co.
Aksnes, K., 1985: Satellite Ring Interactions. In: V. Szebehely (ed.). Stability of the Solar System and its Minor Natural and Artificial Bodies, Reidel Publ. Co.
Brouwer, D., Clemence, G.M., 1961: Methods of Celestial Mechanics. Academic Press.
Colombo, G., 1982: The Motion of Saturn’s Coorbiting Satellites 1980S1 and 1980S2. In: V. Szebehely (ed.), Applications of Modern Dynamics to Celestial Mechanics and Astrodynamics, 21–23, Reidel Publ. Co.
Dermott, S.F., Murray, C.D., 1981: The Dynamics of Tadpole and Horseshoe Orbits, I. Icarus 48, 1–11.
Dermott, S.F., Murray, C.D., 1981: The Dynamics of Tadpole and Horseshoe Orbits, II. Icarus 48, 12–22.
Garfinkel, B., 1978: Theory of the Trojan Asteroids, II. Celest. Mech. 18, 259–275.
Kevorkian, J., Cole, J.D., 1981: Perturbation Methods in Applied Mathematics. Spriger Verlag.
Szebehely, V., 1967: Theory of Orbits. Academic Press.
Waldvogel, J., 1973: Collision Singularities in Gravitational Problems. In: B.P. Tapley and V. Szebehely (eds.), Recent Advances in Dynamical Astronomy, 21–33. Reidel Publ. Co.
Yoder, C.F., Colombo, G., Synnott, S.P., Yoder, K.A., 1983: Theory of Motion of Saturn’s Coorbiting Satellites. Icarus 53, 431–443.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 D. Reidel Publishing Company
About this chapter
Cite this chapter
Spirig, F., Waldvogel, J. (1985). The Three-Body Problem with Two Small Masses: A Singular-Perturbation Approach to the Problem of Saturn’s Coorbiting Satellites. In: Szebehely, V.G. (eds) Stability of the Solar System and Its Minor Natural and Artificial Bodies. NATO ASI Series, vol 154. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5398-7_5
Download citation
DOI: https://doi.org/10.1007/978-94-009-5398-7_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8883-1
Online ISBN: 978-94-009-5398-7
eBook Packages: Springer Book Archive