A general algorithm for the solution of Kepler's equation for elliptic orbits

Details A general algorithm for the solution of Kepler's equation for elliptic orbits A general algorithm for the solution of Kepler's equation for elliptic orbits

Oct 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979cemec..20..243n&link_type=abstract

Celestial Mechanics, vol. 20, Oct. 1979, p. 243-249.

Computer Science

10

Algorithms, Elliptical Orbits, Kepler Laws, Orbital Mechanics, Anomalies, Eccentricity, Iterative Solution, Newton-Raphson Method, Univac 1108 Computer

Scientific paper

An efficient algorithm is presented for the solution of Kepler's equation f(E)=E-M-e sin E=0, where e is the eccentricity, M the mean anomaly and E the eccentric anomaly. This algorithm is based on simple initial approximations that are cubics in M, and an iterative scheme that is a slight generalization of the Newton-Raphson method. Extensive testing of this algorithm has been performed on the UNIVAC 1108 computer. Solutions for 20,000 pairs of values of e and M show that for single precision, 42.0% of the cases require one iteration, 57.8% two and 0.2% three. For double precision one additional iteration is required.

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