Problems of critical inclination and commensurability in the motion of artificial satellites

We discuss the resonance problems resulting from critical inclination and commensurability in the motion of an artificial satellite. We consider the perturbation due to the Earth's asphericity on the average model and we derive the equilibrium solution and the corresponding region of libration and compare with the actual motion of a satellite. We find that the resonance plays a stabilizing role in the motion and that the luni-solar perturbations have a significant effect on the orbital resonance of 24-h synchronous satellites.