Energy Balance Relations for Validation of Gravity Field Models and Orbit Determinations Applied to the CHAMP Mission

An extended Jacobi integral describes the energy balance of the motion of a satellite referred to a terrestrial reference frame along its orbit. In addition to its classical form inertia forces and non-conservative force function contributions are included. If force function models and observed satellite orbits are consistent the energy balance sums up to a constant. Deviations from it can be caused either by orbit errors or by insufficiencies in the force function models. Therefore, the energy integral offers itself as a validation tool for consistency checks of force functions and orbit determination results. A basic question is the separation of the various sources of inconsistency. In this paper the theoretical foundation of the validation procedure is presented. It is shown that the validation method can be used to detect deficiencies in the orbit modeling and in the gravity field recovery results. Examples are presented how to separate the various causes of inconsistency. Applications to the results of the CHAMP mission demonstrate the procedure.