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High Order Resonances in the Evolution of the Lunar Orbit

Published online by Cambridge University Press:  12 April 2016

J. Kovalevsky*
Affiliation:
CERGA, Grasse, France

Abstract

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This paper deals with the long term evolution of the motion of the Moon or any other natural satellite under the combined influence of gravitational forces (lunar theory) and the tidal effects. We study the equations that are left when all the periodic non-resonant terms are eliminated. They describe the evolution of the-mean elements of the Moon. Only the equations involving the variation of the semi-major axis are considered here. Simplified equations, preserving the Hamiltonian form of the lunar theory are first considered and solved. It is shown that librations exist only for those terms which have a coefficient in the lunar theory larger than a quantity A which is function of the magnitude of the tidal effects. The solution of the general case can be derived from a Hamiltonian solution by a method of variation of constants. The crossing of a libration region causes a retardation in the increase of the semi-major axis. These results are confirmed by numerical integration and orders of magnitude of this retardation are given.

Type
Part I - Satellites and Planets
Copyright
Copyright © Reidel 1983

References

Brouwer, D. and Hori, G., 1961, Astron. J., 66, p.193.CrossRefGoogle Scholar
Burns, T.J., 1979, Celestial Mechanics, 19, p. 297.Google Scholar
Calame, O. and Mulholland, J.D., 1978, Science, 199, p. 977.CrossRefGoogle Scholar
Cazenave, A. and Daillet, S., 1981, J. Geophys. R., 86, p. 1659.CrossRefGoogle Scholar
Ferrari, A.J., Sinclair, W.S., Sjogren, W.L., Williams, J.G. and Yoder, CF., 1981, J. Geophys. R., 85, p. 3939.Google Scholar
Henrard, J., 1982, Celestial Mechanics, 27, p. 3.Google Scholar
Johnson, G.A.L. and Nudds, J.R., 1974, in “Growth, Rythms and the History of the Earth’s Rotation”, Rosenberg, G.D. and Runcorn, S.K. ed., John Wiley and sons, London, p. 27.Google Scholar
Kovalevsky, J., 1967, “Introduction to Celestial Mechanics”, D. Reidel Publ. Co, p. 116.Google Scholar
Lambeck, K., 1978, in “Tidal Friction and the Earth’s Rotation”, Brosche, P. and Sündermann, J. ed., Springer-Verlag, Berlin, p. 145.Google Scholar
MacDonald, G.J.F., 1966, in “The Earth-Moon System”, Marsden, B.G. and Cameron, A.G.W. ed., Plenum Press, New-York, p. 165.Google Scholar
Melchior, P., 1973, “Physique et dynamique planétaires”, Vander, Louvain, vol. 4, p. 4.Google Scholar
Mignard, F., 1979, The Moon and the Planets, 20, p. 301.CrossRefGoogle Scholar
Mignard, F., 1980, The Moon and the Planets, 23, p. 185.Google Scholar