GENERAL-RELATIVISTIC CELESTIAL MECHANICS .4. THEORY OF SATELLITE MOTION

The basic equations needed for developing a complete relativistic theo ry of artificial Earth satellites are explicitly written down. These e quations are given both in a local, geocentric frame and in the global , barycentric one. They are derived within our recently introduced gen eral-relativistic celestial mechanics framework. Our approach is more satisfactory than previous ones, especially with regard to its consist ency, completeness, and flexibility. In particular, the problem of rep resenting the relativistic gravitational effects associated with the q uadrupole and higher multipole moments of the moving Earth, which caus ed difficulties in several other approaches, is easily dealt with in o ur approach thanks to the use of previously developed tools: the defin ition of relativistic multipole moments and transformation theory betw een reference frames. With this last paper in a series we hope to indi cate the way of using our formalism in specific problems in applied ce lestial mechanics and astrometry.