A new simple method for the analytical solution of Kepler's equation

Details A new simple method for the analytical solution of Kepler's equation A new simple method for the analytical solution of Kepler's equation

Apr 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..35..305i&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 35, April 1985, p. 305-316.

Statistics

Computation

1

Computational Astrophysics, Elliptical Orbits, Kepler Laws, Numerical Integration, Orbital Mechanics, Two Body Problem, Nonlinear Equations, Roots Of Equations, Transcendental Functions

Scientific paper

A new simple method for the closed-form solution of non-linear algebraic and transcendental equations through integral formulae is proposed. This method is applied to the solution of the famous Kepler equation in the two-body problem for elliptic orbits. The resulting formulae are quite elementary and, beyond their analytical interest, they can also provide quite accurate numerical results by using Gauss-type quadrature rules.

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