A Solution of Kepler’s Equation

Abstract

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.