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