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On solving Kepler's equation

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Abstract

Intrigued by the recent advances in research on solving Kepler's equation, we have attacked the problem too. Our contributions emphasize the unified derivation of all known bounds and several starting values, a proof of the optimality of these bounds, a very thorough numerical exploration of a large variety of starting values and solution techniques in both mean anomaly/eccentricity space and eccentric anomaly/eccentricity space, and finally the best and simplest starting value/solution algorithm: M + e and Wegstein's secant modification of the method of successive substitutions. The very close second is Broucke's bounds coupled with Newton's second-order scheme.

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References

  • Battin, R. H.: 1964, Astronautical Guidance, McGraw-Hill, New York.

    Google Scholar 

  • Brent, R. P.: 1971, The Computer J. 14, 422.

    Google Scholar 

  • Broucke, R.: 1980, J. Astronaut. Sci. 28, 255.

    Google Scholar 

  • Conway, B. A.: 1986, Celest. Mech. 39, 199.

    Google Scholar 

  • Danby, J. M. A. and Burkardt, T. M.: 1983, Cel. Mech. 31, 95.

    Google Scholar 

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

    Google Scholar 

  • Jeeves, T. A.: 1957, Comm. Assoc. Comput. Mach. 1 (8), 9.

    Google Scholar 

  • Kristiansen, G. K.: 1963, B.I.T 3, 205.

    Google Scholar 

  • Ng, E. W.: 1979, Celest. Mech. 20, 243.

    Google Scholar 

  • Saaty, T. L. and Bram, J.: 1964, Nonlinear Mathematics, McGraw-Hill, New York, p. 75.

    Google Scholar 

  • Serafin, R. A.: 1986, Celest. Mech. 38, 111.

    Google Scholar 

  • Smith. G. R.: 1979, Celest. Mech. 19, 163.

    Google Scholar 

  • Taff, L. G. and S. Sayer 1985, Lincoln Laboratory Technical Memorandum 94L-0120.

  • Wegstein, J. H.: 1958, Comm. Assoc. Comput. Mach. 1 (6), 9.

    Google Scholar 

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Authors and Affiliations

  1. Lincoln Laboratory, M.I.T., 02173-0073, Lexington, MA, U.S.A.

    L. G. Taff & T. A. Brennan

Authors
  1. L. G. Taff
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  2. T. A. Brennan
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Additional information

This work was sponsored by the Department of the Air Force under Contract F19628-85-C-0002. The views are those of the authors and do not reflect the official policy or position of the U.S. Government.

Now at Space Telescope Science Institute operated by AURA, Inc. for NASA.

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Taff, L.G., Brennan, T.A. On solving Kepler's equation. Celestial Mech Dyn Astr 46, 163–176 (1989). https://doi.org/10.1007/BF00053046

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  • DOI: https://doi.org/10.1007/BF00053046

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