Comparison of starting values for iterative solutions to a universal Kepler's equation

Details Comparison of starting values for iterative solutions to a universal Kepler's equation Comparison of starting values for iterative solutions to a universal Kepler's equation

Mar 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982jansc..30...75b&link_type=abstract

Journal of the Astronautical Sciences, vol. 30, Jan.-Mar. 1982, p. 75-84.

Computer Science

Numerical Analysis

5

Conics, Elliptical Orbits, Iterative Solution, Kepler Laws, Orbital Position Estimation, Algorithms, Computer Programs, Convergence, Newton Theory, Numerical Analysis

Scientific paper

General starting values for the iterative numerical solution of a universal Kepler's equation for position in a conic orbit at a specified time are investigated. Three starting values based on recent refinements of previously obtained bounds on the solution are derived and tested numerically. Of these, a simple starting value based on a cubic approximation to Kepler's equation provides the most rapid convergence using both first and second order Newton algorithms. The performance of the starting values are compared with similar studies which used the restricted case of elliptical orbits with the initial epoch at periapse.

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