  In the context of general perturbation theories, the main problem of the
artificial satellite analyses the motion of an orbiter around an Earth-like
planet, only perturbed by its equatorial bulge or J2 effect. By means of a Lie
transform and the Krylov-Bogoliubov-Mitropolsky method, a first-order theory in
closed form of the eccentricity is produced. During the evaluation of the
theory it is necessary to solve a generalization of the classical Kepler's
equation. In this work, the application of a numerical technique and three
initial guesses to the Generalized Kepler's equation are discussed.
