Simple integrals for solving of Kelper's equation

Details Simple integrals for solving of Kelper's equation Simple integrals for solving of Kelper's equation

Aug 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986ap%26ss.125...77n&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 125, no. 1, Aug. 1986, p. 77-83.

Astronomy and Astrophysics

Astrophysics

3

Integrals, Kepler Laws, Two Body Problem, Elliptical Orbits, Hyperbolic Trajectories, Laguerre Functions, Numerical Integration

Scientific paper

A simplified variation of Siewert and Burniston's (1972) inversion of Kepler's equation of the two-body problem is proposed which leads to an exact representation of position as a function of time. The integrands consist only of rational expressions of the integration variable and its exponential, and they are superior to those used previously. Highly accurate values are obtained using a numerical integration by Laguerre's method, and the calculations have been verified with the computer algebra system, REDUCE.

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