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A Solution of Kepler’s Equation

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John N. Tokis

^{*}
The
present study deals with a traditional physical problem: the solution of the
Kepler’s equation for all conics (ellipse,
hyperbola or parabola). Solution of the universal Kepler’s equation in closed
form is obtained with the help of the two-dimensional Laplace technique, expressing the universal functions as a function
of the universal anomaly and the time. Combining these new expressions of the universal functions and their
identities, we establish one
biquadratic equation for universal anomaly (

*χ*) for all conics; solving this new equation, we have a new exact solution of the present problem for the universal anomaly as a function of the time. The verifying of the universal Kepler’s equation and the traditional forms of Kepler’s equation from this new solution are discussed. The plots of the elliptic, hyperbolic or parabolic Keplerian orbits are also given, using this new solution.KEYWORDS

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Tokis, J. (2014) A Solution of Kepler’s Equation.

*International Journal of Astronomy and Astrophysics*,**4**, 683-698. doi: 10.4236/ijaa.2014.44062.

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