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The solution of Kepler's equation, I

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Abstract

Methods of iteration are discussed in relation to Kepler's equation, and various initial ‘guesses’ are considered, with possible strategies for choosing them. Several of these are compared; the method of iteration used in the comparisons has local convergence of the fourth order.

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References

  • Burniston, E. E. and Siewart, C. E.: 1972, ‘An Exact Analytical Solution of Kepler's Equation’,Celest. Mech. 6, 294.

    Google Scholar 

  • Isaacson, E. and Keller, H. B.: 1966,Analysis of Numerical Methods, Wiley, New York, p. 102.

    Google Scholar 

  • Moulton, F. R.: 1914,An Introduction to Celestial Mechanics, MacMillan, New York.

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  • Ng, E. W.: 1979, ‘A General Algorithm for the Solution of Kepler's Equation for Elliptic Orbits’,Celest. Mech. 20, 243.

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  • Smith, G. R.: 1979, ‘A Simple Efficient Starting Value for the Iterative Solution of Kepler's Equation’,Cel. Mech. 19, 163.

    Google Scholar 

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Danby, J.M.A., Burkardt, T.M. The solution of Kepler's equation, I. Celestial Mechanics 31, 95–107 (1983). https://doi.org/10.1007/BF01686811

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  • DOI: https://doi.org/10.1007/BF01686811

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