Future Satellite Gravity Field Missions: Feasibility Study of Post-Newtonian Method

Abstract

Modern satellite gravity field recovery missions use accelerometric, intersatellite tracking or gradiometric observables for deducing gravity field related data. In this study an alternative observable type for gravity field recovery, the relativistic frequency shift, is investigated. As Einstein stated in his general theory of relativity, gravity can be considered as attribute of space-time. In this view mass alters the geometric shape of the metric tensor. Moreover mass, respectively gravity, has effects on electromagnetic wave propagation [Einstein (Annalen der Physik 35:898–908 1911)]. Although these relativistic effects are quite small and difficult to measure, with upcoming atomic clocks which have sufficient accuracy and short-term stability it will be possible to derive meaningful gravity related information. Since relativistic effects are used this method is called Post-Newtonian method. The main target of this paper is to demonstrate the validity of the derived relativistic equations.

The scientific quality of the relativistic frequency shift observed by means of highly accurate atomic clocks is investigated. In our basic scenario a low earth orbit (LEO) sends an electromagnetic wave to a receiver. The reference station determines the frequency shift of the signal, which is connected to the time dilatation between the atomic clock of the satellite and an identical atomic clock nearby the receiver. A simplified, mathematical model for numerical simulations of this configuration is presented. The effect of different error sources are investigated by numerical closed-loop simulations. Thus, the performance requirements of atomic clocks, position and velocity determination and limiting factors for deducing earth’s gravity field can be derived.