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New Formulation of De Sitter’s Theory of Motion for Jupiter I-IV. I. Equations of Motion and the Disturbing Function

Published online by Cambridge University Press:  12 April 2016

K. Aksnes
K. Aksnes*
Affiliation:
Tokyo Astronomical Observatory, University of Tokyo, Mitaka, Tokyo and Center for Astrophysics, 60 Garden St., Cambridge, Mass. 02138

Abstract

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A brief discussion is given of the basic features of de Sitter’s theory. The main advantage of his theory is that it contains no small divisors, thanks to the use of elliptic rather than circular intermediate orbits in the first approximation. A 50-year extension of the satellite observations available to de Sitter makes it desirable to rederive the elements of his intermediate orbits, whose perijoves have a common retrograde motion. Furthermore, the theory suffers from a convergence problem, which can be avoided by reformulating the theory in terms of canonical variables, a task that is begun here. We adopt a formulation in Poincaré’s canonical relative coordinates rather than, as customary, in ordinary relative coordinates or in the Jacobian canonical coordinates. By means of the generalized Newcomb operators devised by Izsak, the disturbing function is expanded in a form that is very convenient for use with the modified Delaunay variables, G, L – G, H – G, l + ω + Ω, l, and ω and their associated Poincaré variables.

Type
Part IV. Satellites of Jupiter and Saturn, and Artificial Satellites
Information
International Astronomical Union Colloquium , Volume 41: Dynamics of Planets and Satellites and Theories of their Motion , 1978 , pp. 189 - 206
Copyright
Copyright © Reidel 1978

References

Aksnes, K., and Franklin, F.A. (1975). Nature 258, 503.Google Scholar
Aksnes, K., and Franklin, F.A. (1976). Astron. J. 81, 464.Google Scholar
Brouwer, D. (1959). Astron. J. 64, 378.Google Scholar
Cayley, A. (1861). Mem. R. Astron. Soc. 21), 191.Google Scholar
Charlier, C. L. (1902). Die Mechanik Des Himmels, Vol. I (Von Veit & Co., Leipzig).Google Scholar
de Sitter, W. (1918). Leiden Annals 12, Part I.Google Scholar
de Sitter, W. (1931). Mon. Not. R. Astron. Soc. 91, 705.Google Scholar
Hori, G. (1966). Publ. Astron. Soc. Japan 18, 287.Google Scholar
Izsak, I. G., and Benima, B. (1963). Smiths. Astrophys. Obs. Spec. Rep. No. 129.Google Scholar
Izsak, I.G., Benima, B., and Mills, S. B. (1965). Smiths. Astrophys. Obs. Spec. Rep. No. 164.Google Scholar
Izsak, I.G., Gerard, J.M., Efimba, R., and Barnett, M.P. (1964). Smiths. Astrophys. Obs. Spec. Rep. No. 140.Google Scholar
Lieske, J. (1975). Cel. Mech. 12, 5.Google Scholar
Marsden, B.G. (1964). Doctoral Thesis, Yale Univ., New Haven, Conn.Google Scholar
Poincaré, H. (1897). Bull. Astron. 14, 53.Google Scholar
Sampson, R.A. (1910). Tables of the Four Great Satellites of Jupiter (Wesley, London).Google Scholar
Yuasa, M., and Hori, G. (1975). In Proceedings of a Symposium on Celestial Mechanics, held in Tokyo, February 12-13, 1975 (Ed. by Hori, and Yuasa, ). To be published in Publ. Astron. Soc. Japan.Google Scholar