A numerical solution of the Kepler problem

Details A numerical solution of the Kepler problem A numerical solution of the Kepler problem

Feb 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981acaau...8..225m&link_type=abstract

Acta Astronautica, vol. 8, Feb. 1981, p. 225-228. In French.

Astronomy and Astrophysics

Astronomy

Celestial Mechanics, Equations Of Motion, Kepler Laws, Newton-Raphson Method, Eccentricity, Gravitational Fields, Interpolation, Iterative Solution

Scientific paper

An efficient numerical method is presented for the solution of the Kepler problem of the motion of a body in a closed orbit in a central gravitational field. The method employs the Newton-Raphson interpolation algorithm to obtain successive approximations of the orbital angle starting from the classical initial approximation for cases of orbital eccentricity less than one half the square root of 2, and from a closer, more complex approximation for large eccentricities. A result accurate to six decimal places can thus be obtained in not more than four iterations, even in the case of eccentricities close to unity.

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