On Relativistic Equations of Motion of an Earth Satellite

For numerical integration of the geocentric equations of motion of Earth satellites in the general relativity framework one may choose now between rather simple equations involving in their relativistic dynamical part only the Earth-induced terms and very complicated equations taking into account the relativistic third-body action. However, it is possible quite easily to take into account the relativistic indirect third-body perturbations and to neglect much lesser direct third-body perturbations. Such approach is based on the use of the Newtonian third-body perturbations in geocentric variables with expressing them in the relativistic manner in terms of the barycentric arguments. Together with it, to extend the known results for the spheroid model of the Earth, the Earth-induced terms are treated in great detail by including the non-spin part of the Earth vector-potential and the Earth triaxial non-sphericity.