Motion in the gravitational field of an oblate spheroid

We present the theory of motion in the gravitational field of an attracting object, considering its equatorial bulge. There is a secular precession of the orbit that occurs in the direction opposite to the orbital revolution. The precession rate increases as the gravitating body’s flattening increases and the orbit’s characteristic size decreases. Using the perturbation approach, we derive the equations for finding the precession period and the apocentric distance. We also construct the generalized version of the Laplace-Runge-Lenz vector for this type of motion.