The post-Newtonian effects in the critical inclination problem in artificial satellite theory

The critical inclination problem in artificial satellite theory and the post-Newtonian (PN) effects on it are discussed. The Hamiltonian is constructed and is expressed in terms of the Delaunay variables containing the zonal harmonics up to J4 and the PN contribution up to order J2/cl2. The Hamiltonian is ordered out such that the PN terms are of order J2. Two successive canonical transformations based on Lie series and transform are carried out to remove short and long period terms from the Hamiltonian, respectively. Terms are retained up to the third order in the secular perturbations and to the second order in the periodic perturbations, where J2 is considered of first order.