Rapidly converging series approximation to Kepler's equation

Details Rapidly converging series approximation to Kepler's equation Rapidly converging series approximation to Kepler's equation

Aug 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984adans..54.1039p&link_type=abstract

IN: Astrodynamics 1983; Proceedings of the Conference, Lake Placid, NY, August 22-25, 1983. Part 2 (A84-30526 13-13). San Diego,

Astronomy and Astrophysics

Astronomy

Eccentricity, Elliptical Orbits, Kepler Laws, Orbit Calculation, Power Series, Series Expansion, Algorithms, Boundary Value Problems, Chebyshev Approximation, Convergence, Newton-Raphson Method

Scientific paper

A power series solution in eccentricity e and normalized mean anomaly f has been developed for elliptic orbits. Expansion through the fourth order yields approximate errors about an order of magnitude smaller than the corresponding Lagrange series. For large e, a particular algorithm is shown to be superior to published initializers for Newton iteration solutions. The normalized variable f varies between zero and one on each of two separately defined intervals: 0 to x = (pi/2-e) and x to pi. The expansion coefficients are polynomials based on a one-time evaluation of sine and cosine terms in f.

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