Satellite geodesy on curved space–time manifolds. Earth-fixed charts

Abstract.

The reformulation of geodetic measurement processes within the framework of general relativity is discussed. The metric tensor plays an important role in general relativity and has to be represented with respect to a set of appropriate charts. Almost every quantity of interest in geodetic or geophysical applications refers to a geocentric, Earth-fixed coordinate system (chart), therefore they are of great importance in geodesy and geophysics. The space–time metric with respect to an Earth-fixed chart is derived at first post-Newtonian order. The field equations determining the terrestrial gravitational field are derived and its explicit representation is outlined. The impact of the results on the modelling of geodetic measurement processes including space–time positioning scenarios as well as the high-precision gravitational field estimation is outlined.