An Earth-pointing dynamically symmetric satellite with Lorentz attitude control system is under consideration. The problem of the satellite attitude stabilization in the orbital reference frame in the presence of gravitational disturbing torque is studied. The averaging technique is developed and applied in the problem. A rigorous mathematical justification is proposed, which makes it possible to obtain estimates for control parameters that provide asymptotic stability of the satellite equilibrium position and ensures satellite attitude stabilization despite the underactuation due to the Lorentz control torque. The proof is based on the averaging technique and the Lyapunov direct method. Original constructions of nonstationary Lyapunov functions are proposed. These constructions take into account the structure of perturbations acting on the considered system. The quadrupole approximation of the Earth's magnetic field is used.