Post-Newtonian Covariant Measurement Formulations in Space Geodesy

Most spatial current high precision geodetic techniques, like those used in the Global Positioning System, have led to widely consider the assumption of a slightly curved space-time in the vicinity of the Earth (according to the general theory of relativity) as the essential basis to build geometric models for measurements formulations that allow correct interpretations of the results, at least up to the level of accuracy required at the present and near-future time. In this contribution, Synge's world function for the local geometric models associated to a global model of that space-time is used to give a flexible and structured set of covariant two-way local formulations for the four basic kind of measurements involved in Space Geodesy. Both local and global models are made compatible by using local and global Fermi coordinates, respectively. The measurements formulations are one-to-one general (weak) relativistic versions of the local classical formulations currently implemented in altimetry, satellite laser ranging and satellite-to-satellite tracking on the one hand, and on the other, of the classical version of the ballistic problem.