Resonance Caused by the Gravitational waves On an Earth Satellite

The present work deals with the motion of an Earth satellite taking into account the oblateness of the Earth and of a passing Gravitational wave. The oblateness of the Earth is truncated beyond the second zonal harmonic, J2, which plays the role of the small parameter of the problem. The conditions for resonance are determined and the resonance resulting from the commensurabilities between the wave frequency and the mean motions of the satellite, the nodal regression, and the apsidal rotation are analyzed.