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A New Approach for the Construction of Long-Periodic Perturbations

Published online by Cambridge University Press:  12 April 2016

Rudolf Dvorak
Rudolf Dvorak*
Affiliation:
Astronomisches Institut, Universität Graz Universitätsplatz 5, A-8010 Graz, Austria

Abstract

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The aim of this work is to study perturbations of planets of a period of some thousands of years. The use of an analytical method allows us to separate all different influences, e.g. near resonances and is combined with the very precise method of the numerical integration. The truncation to low orders can be avoided which is made by analytical methods in using developments with respect to the small parameters inclinations and eccentricities. For this purpose a special form of the Lagrange Equations is used where the terms containing the inverse distancefrom the planet to the perturbing one are separated as it is the most difficult to compute. To develop this a specific formulation has been found where the short periodic terms can precisely be determined. Although the development seems to be of a certain complexity the small numbers of quantities used can be tabulated once and for all in a specific problem. It should be possible to integrate the new form of the Lagrange Equations within a reasonable computer-time to determine the long periodic perturbations.

Type
Part I. Planetary Theory and Analytical Methods
Information
International Astronomical Union Colloquium , Volume 41: Dynamics of Planets and Satellites and Theories of their Motion , 1978 , pp. 57 - 64
Copyright
Copyright © Reidel 1978

References

Abu-El-Ata, N., Chapront, J.: 1974, Astron. Astrophys. 8, 57.Google Scholar
Anolik, M.V., Krassinsky, B.A., Pius, L.J.: 1969, Trudy Inst. Theor. Astron. Leningrad L4, 3–14.Google Scholar
Brouwer, D., Van Woerkom, A.J.J.: 1950, Astron. Pap. 13, Part 2.Google Scholar
Bretagnon, P.: 1974, Astron. Astrophys. 30, 141.Google Scholar
Brumberg, V.: 1967, Bull. Inst. Theor. Astron. T 11, 125.Google Scholar
Chapront, J., Bretagnon, P., Mehl, M.: 1975, Celes. Mech. 11, 379.Google Scholar
Chapront, J., Dvorak, R.: 1977, Mitt. Astron. Ges. 40, 214.Google Scholar
Cohen, C.J., Hubbard, E.C., Oesterwinter, C.: 1973, Astron. Pap. 22, Part 1.Google Scholar
Hill, G.W.: 1889, Astron. J. 9, 89–91.Google Scholar
Kozai, Y.: 1962, Astron. J. 67, 591.Google Scholar