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Stability of the Solar System

Published online by Cambridge University Press:  14 August 2015

Victor Szebehely
Victor Szebehely*
Affiliation:
The University of Texas at Austin

Abstract

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This paper reviews the present status of research on the problem of stability of satellite and planetary systems in general. In addition new results concerning the stability of the solar system are described. Hill's method is generalized and related to bifurcation (or catastrophe) theory. The general and the restricted problems of three bodies are used as dynamical models. A quantitative measure of stability is introduced by establishing the differences between the actual behavior of the dynamical system as given today and its critical state. The marginal stability of the lunar orbit is discussed as well as the behavior of the Sun-Jupiter-Saturn system. Numerical values representing the measure of stability of several components of the solar system are given, indicating in the majority of cases bounded behavior.

Type
Part I: Stability, N- and 3-Body Problems, Variable Mass
Information
Symposium - International Astronomical Union , Volume 81: Dynamics of the Solar System , 1979 , pp. 7 - 15
Copyright
Copyright © Reidel 1979 

References

Arnol'd, V.I., (1963), Usp. Math. Nauk., 18, 5, 6, 13, 91.Google Scholar
Birn, J., (1973), Astronaut. Astrophys., 24, 283.Google Scholar
Bozis, G., (1976), Astrophys. Sci., 43, 355.CrossRefGoogle Scholar
Bruns, H., (1887), Acta Math., 11, 25.CrossRefGoogle Scholar
Cohen, C.J., Hubbard, E.C. and Oesterwinter, C., (1968), Astron. J., 72, 973.CrossRefGoogle Scholar
Golubev, V.G., (1968), Doklady Akad. Nauk, USSR, 180, 308.Google Scholar
Hadjidemetriou, J., (1976), Proc. NATO Adv. Study Inst., Reidel Publ.Google Scholar
Hagihara, Y., (1952), Proc. Japan Acad., 28, 182.Google Scholar
Hagihara, Y., (1957), “Stability in Celestial Mechanics,” Kasai Publ., Tokyo.Google Scholar
Hagihara, Y., (1970-1976), “Celestial Mechanics,” Vol. 1-5, MIT Press and Japan Soc. Promotion of Science, Tokyo.Google Scholar
Hénon, M., (1970), Astron. and Astrophys., 9, 24.Google Scholar
Hénon, M. and Heiles, C., (1964), Astron. J., 69, 73.CrossRefGoogle Scholar
Hill, G.W., (1878), Am. J. Math., 1, 5, 129, 245.CrossRefGoogle Scholar
Jefferys, W.H. and Szebehely, V., (1978), “Dynamics and Stability of the Solar System,” Cosmic Physics, in print.Google Scholar
Kolmogorov, A.N., (1954), Doklady Akad. Nauk, 98, 4.Google Scholar
Kuiper, G.P., (1953), Proc. Natl. Acad. Sci., U.S., 39, 1154, 1159.Google Scholar
Kuiper, G.P., (1973), Celest. Mech., 9, 359.Google Scholar
Marchal, C., (1975), ONERA Rept., No. 77.Google Scholar
Marchal, C. and Saari, D., (1975), Celest. Mech., 12, 115.CrossRefGoogle Scholar
Message, J., (1978), Proc. IAU Symp. 41, Reidel Publ.Google Scholar
Moser, J., (1973), “Stable and Random Motions,” Princeton Univ. Press, Princeton, N.J. Google Scholar
Nacozy, P., (1976), Astron. J., 81, 787.Google Scholar
Poincaré, H., (1892-1899), “Les Méthodes Nouvelles,” Gauthier-Villars, Paris.Google Scholar
Smale, S., (1970), Invent. Math., 11, 45.CrossRefGoogle Scholar
Sundman, K.F., (1912), Acta Math., 36, 105.CrossRefGoogle Scholar
Szebehely, V., (1967), “Theory of Orbits,” Acad. Press, N.Y. Google Scholar
Szebehely, V., (1971), Celest. Mech., 4, 116.CrossRefGoogle Scholar
Szebehely, V., (1974), Celest. Mech., 9, 359.CrossRefGoogle Scholar
Szebehely, V., (1977), Celest. Mech., 15, 107.CrossRefGoogle Scholar
Szebehely, V., (1978), Celest. Mech., 17, in print.Google Scholar
Szebehely, V. and McKenzie, R., (1977), Astron. J., 82, 79.CrossRefGoogle Scholar
Szebehely, V. and McKenzie, R., (1978), Celest. Mech., 17, in print.Google Scholar
Szebehely, V. and Zare, K., (1977), Astron. and Astrophys., 58, 145.Google Scholar
Zare, K., (1977), Celest. Mech., 16, 35.CrossRefGoogle Scholar