Theory of the orbital motion of an artificial Earth satellite

Considering dominant perturbative influences and coupling effects among them, a unified theory of the orbital motion of an artificial Earth satellite is developed. The theory includes very realistic and complex perturbation models and provides analytically a relatively accurate visualization of the effects of the various perturbations. As the dominating perturbative influences the Earth's gravitational perturbations, the luni-solar perturbations, the solar radiation pressure perturbation, the atmospheric drag perturbation, and small perturbing forces provided by the thrusts of propulsion systems are taken into account. As the reference system an intermediate, quasi-inertial reference frame is adopted. Using the general perturbation method, the complete set of Lagrange's equations for variations of the orbital elements is applied. The equations are expressed by means of the usual form and the Gaussian form. Further, the equations are modified to include the effects of motion of the reference system. Disturbing functions, perturbing accelerations, and angular elements referred to the adopted system are expressed analytically. On referring to the expressions of disturbing functions, perturbing accelerations, and angular elements referred to the adopted system, the time rates of change of the orbital elements are derived by use of the equations of motion.