Relativistic Corrections for the Earth Artificial Satellite Theory

In the persesnt work an artificial satellite theory is developed including all the zonal harmonics of the geopotential besides the post-Newtnian effects arising from the Schwarzschild solution and the Earth's oblateness. The Hamiltonian is formed in terms of the Deluanay canonical variables allowing for the coupling between the Newtonian and the post-Newtonian terms. Small quantities are retained up to J2 O . The perturbation approach used is outlined. The solution of the Hamiltonian equations of motion is obtained. Finally a scheme for computing the position and velocity is addressed. KeywordsZonal harmonics, Relativistic corrections, Hamiltonian.