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An exact analytical solution of Kepler's equation

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Abstract

Complex-variable analysis is used to develop an exact solution to Kepler's equation, for both elliptic and hyperbolic orbits. The method is based on basic properties of canonical solutions to appropriately posed Riemann problems, and the final results are expressed in terms of elementary quadratures.

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References

  • Ahlfors, L. V.: 1953,Complex Analysis, McGraw Hill, New York.

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  • Burniston, E. E. and Siewert, C. E.: 1972,Proc. Camb. Phil. Soc. (in press).

  • Muskhelishvili, N. I.: 1953,Singular Integral Equations, Noordhoff, Groningen, The Netherlands.

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  • Siewert, C. E. and Burniston, E. E.: 1972,Astrophys. J. 173, 405.

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Authors and Affiliations

  1. Dept. of Nuclear Engineering, North Carolina State University, Raleigh, N.C., USA

    C. E. Siewert

  2. Dept. of Mathematics, North Carolina State University, Raleigh, N.C., USA

    E. E. Burniston

Authors
  1. C. E. Siewert
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  2. E. E. Burniston
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Siewert, C.E., Burniston, E.E. An exact analytical solution of Kepler's equation. Celestial Mechanics 6, 294–304 (1972). https://doi.org/10.1007/BF01231473

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  • DOI: https://doi.org/10.1007/BF01231473

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