Abstract
In this research article, a new idea concerning the application of concept of the continued fractions to the expansion of the geopotential is treated. The perturbed motion of the satellite in the oblate gravitational field of the Earth using a potential of a continued fractions procedure is studied. To compare with the usual perturbation theory, the continued fraction series is truncated beyond the third term. The first oblateness term of the potential is retained. The equations of motion are constructed using the Lagrange planetary equations. The integrals and averages required for solving the problem is outlined as well as the different cases are highlighted. The perturbations in all orbital elements due to considered model of continued fractions are evaluated. The new findings of the manuscript contrast with classical oblate potential field, the semi-major axis, eccentricity, and inclination, nonzero averaged terms in perturbations are obtained. Extra nonzero averaged perturbing terms in the argument of perigee and ascending node are revealed in addition to the classical perturbations.