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Analytic properties of Hansen coefficients

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Abstract

Hansen’s coefficients in the theory of elliptic motion with eccentricity e are studied as functions of the parameter η = (1 − e 2)1/2. Their analytic behavior in the complex η plane is described and some symmetry relations are derived. In particular, for every Hansen coefficient, multiplication by suitable powers of e and η results in an entire analytic function of η. Consequently, Hansen’s coefficients can be in principle computed by means of rapidly convergent series in powers of η. A representation of Hansen’s coefficients in terms of two entire functions of e 2 follows.

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  1. Memorial University of Newfoundland, St. John’s, NL, Canada, A1C 5S7

    Sergey Yu. Sadov

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  1. Sergey Yu. Sadov
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Correspondence to Sergey Yu. Sadov.

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Sadov, S.Y. Analytic properties of Hansen coefficients. Celest Mech Dyn Astr 100, 287–300 (2008). https://doi.org/10.1007/s10569-008-9123-z

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  • DOI: https://doi.org/10.1007/s10569-008-9123-z

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