On the lunar node resonance of the orbital plane evolution of the Earth's satellite orbits

This paper aims to investigate the effects of lunar node resonance on the circular medium Earth orbits (MEO). The dynamical model is established in classical Hamiltonian systems with the application of Lie transform to remove the non-resonant terms. Resonant condition, stability and phase structures are studied. The lunar node resonance occurs when the secular changing rates of the orbital node (with respect to the equator) and the lunar node (with respect to the ecliptic) form a simple integer ratio. The resonant conditions are satisfied for both inclined and equatorial orbits. The orbital plane would have long period (with typical timescales of several centuries) fluctuation due to the resonance.