General-relativistic celestial mechanics. IV. Theory of satellite motion

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Abstract
The basic equations needed for developing a complete relativistic theory of artificial Earth satellites are explicitly written down. These equations are given both in a local, geocentric frame and in the global, barycentric one. They are derived within our recently introduced general-relativistic celestial mechanics framework. Our approach is more satisfactory than previous ones, especially with regard to its consistency, completeness, and flexibility. In particular, the problem of representing the relativistic gravitational effects associated with the quadrupole and higher multipole moments of the moving Earth, which caused difficulties in several other approaches, is easily dealt with in our approach thanks to the use of previously developed tools: the definition of relativistic multipole moments and transformation theory between reference frames. With this last paper in a series we hope to indicate the way of using our formalism in specific problems in applied celestial mechanics and astrometry.