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On the Stability of Resonant Asteroid Orbits

Published online by Cambridge University Press:  12 April 2016

J.D. Hadjidemetriou  and
S. Ichtiaroglou
J.D. Hadjidemetriou
Affiliation:
University of Thessaloniki, Thessaloniki, Greece
S. Ichtiaroglou
Affiliation:
University of Thessaloniki, Thessaloniki, Greece

Abstract

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The stability of the asteroid orbits has been studied by the method of surface of section. Families of simple symmetric periodic orbits of the asteroid and their stability have been computed and this served as a guide for the selection of the energy levels for the surface of section. In this way all possible cases for the structure of phase space have been obtained. It was found that the region in phase space around the resonant orbits at the resonances 1/3, 3/5, 5/7,.... is unstable, but small stability regions of doubly symmetric periodic orbits near the above resonances are also present. At the resonances 1/2, 2/3, 3/4, .... it was found that there exist two separate regions in phase space at about the same resonance 1/2, 2/3, 3/4,...., respectively, one being stable and the other unstable. At certain energy levels only the stable region appears. The above results are consistent with the observed distribution of the asteroids.

Type
Part III - Asteroids
Information
International Astronomical Union Colloquium , Volume 74: Dynamical Trapping and Evolution in the Solar System , 1983 , pp. 141 - 152
Copyright
Copyright © Reidel 1983

References

Arenstorf, R.F., 1963, Amer. J. Math. 83, 27.Google Scholar
Arnold, V.I. and Avez, A., 1968, “Ergodic Problems in Classical Mechanics”, Benjamin, Google Scholar
Birkhoff, G.D., 1927, “Dynamical Systems”, Amer, Math. Soc. New York.Google Scholar
Broucke, R.A., 1968, NASA-JPL Technical Report, 32–1168.Google Scholar
Colombo, G., Franklin, F.A., 1982, in Szebehely, V. (ed.) “Applications of Modern Dynamics to Celestial Mechanics and Astrodynamics”, p.339, D. Reidel Publ. Co.Google Scholar
Colombo, G., Franklin, F.A. and Munford, C.M., 1968, Astron. J. 73, 111.CrossRefGoogle Scholar
Dermott, S.F. and Murray, C.D., 1981, Nature 290, 664.CrossRefGoogle Scholar
Froeschlé, C. and Scholl, H., 1979, in Szebehely, V. (ed.), “Instabilities in Dynamical Systems”, p.115, Reidel Publ. Co. Google Scholar
Guillaume, P.: 1969, Astron. Astrophys. 155.Google Scholar
Hadjidemetriou, J.D., 1982a in Szebehely, V. (ed.), “Applications of Modern Dynamics to Celestial Mechanics and Astrodynamics”, p.25, Rei-del Pubi. Co. CrossRefGoogle Scholar
Hadjidemetriou, J.D., 1982b, Celes. Mech. 27, 305.Google Scholar
Hagihara, Y., 1972, “Celestial Mechanics”, Vol.2, part 1, MIT Press.Google Scholar
Lecar, M. and Franklin, F.A., 1973, Icarus 20, 422.Google Scholar
Schmidt, D., 1972a, in Weiss, L. (ed.) “Ordinary Differential equations”, p.553, A.P.Google Scholar
Schmidt, D., 1972b, SIAM J. Appl. Math. 22, No 1.Google Scholar
Scholl, H. and Froeschlé, C.: 1974, Astron. Astrophys. 33, 455.Google Scholar
Scholl, H. and Froeschlé, C.: 1975, Astron. Astrophys. 42, 457.Google Scholar
Sinclair, A.T., 1969, Monthly Not. Roy. Astron. Soc. 142, 289.Google Scholar
Sinclair, A.T., 1970, Monthly Not. Roy. Astron. Soc. 148, 325.Google Scholar
Szebehely, V., 1967, “Theory of Orbits”, Academic Press.Google Scholar
Szebehely, V., Vicente, R. and Lundberg, J.B.: 1983, this volume, p.123.Google Scholar