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Recurrence formulae for the Hansen's developments

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Abstract

In this paper we derive some recurrence formulae which can be used to calculate the Fourier expansions of the functions (r/a)n cosmv and (r/a)n sinmv in terms of the eccentric anomalyE or the mean anomalyM. We also establish a recurrence process for computing the series expansions for alln andm when the expansions of two basic series are known. These basic series were given in explicit form in the classical literature. The recurrence formulae are linear in the functions involved and thus make very simple the computation of the series.

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References

  • Barton, D.: 1967, ‘On Literal Developments of the Lunar Theory with the Aid of a Computer’,Astron. J. 71, No. 10, 1281–1287.

    Google Scholar 

  • Broucke, R.: 1970, ‘Computerized Series Expansions of the Two-Body Problem, Application to Lunar Theory’,Celestial Mechanics (in press).

  • Brouwer, D. and Clemence, G. M.: 1961,Methods of Celestial Mechanics, Academic Press, New York.

    Google Scholar 

  • Brown, E. W. and Shook, C. A.: 1933,Planetary Theory, The University Press, Cambridge.

    Google Scholar 

  • Cayley, A.: 1861, ‘Tables of the Developments of Functions in the Theory of Elliptic Motion’,Mem. Roy. Astron. Soc. 29, 191–306.

    Google Scholar 

  • Deprit, A. and Rom, A. R. M.: 1967, ‘Computerized Expansions in Elliptic Motion’,Bull. Astron. 2 Fasc. 3, 425–447.

    Google Scholar 

  • Hansen, P. A.: 1838,Fundamenta Nova Investigationis Orbitae verae quam Luna perlustrat, Gotha.

  • Jarnagin, M. P.: 1965,Astron. Papers Amer. Ephem. and Nautical Almanac,18, U.S. Printing Office, Washington.

    Google Scholar 

  • LeSchack, A. R. and Sconzo, P.: 1968, ‘FORMAC Language and its Application to Celestial Mechanics’,Astron. J. 73, No. 3, 217–220.

    Google Scholar 

  • Moulton, F. R.: 1920,Periodic Orbits, Carnegie Institution of Washington, Washington, D.C., pp. 55–60.

    Google Scholar 

  • Schubert, Th.: 1822,Astronomie théorique, St Petersburg.

  • Tisserand, F.: 1894,Traité de mécanique céleste, Vol. I, Gauthier-Villars, Paris, pp. 228–248.

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Aerospace Engineering, The University of Michigan, Ann Arbor, Mich., USA

    N. X. Vinh

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  1. N. X. Vinh
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Vinh, N.X. Recurrence formulae for the Hansen's developments. Celestial Mechanics 2, 64–76 (1970). https://doi.org/10.1007/BF01230451

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  • DOI: https://doi.org/10.1007/BF01230451

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