Gravitational field recovery via inter-satellite redshift measurements

Satellite gravimetry is a common tool to monitor global changes in the Earth system, generally utilising accelerometers aboard satellites to measure acting forces along the orbits. In contrast, high-precision atomic clocks are used in first experiments in terrestrial gravimetry to measure physical heights. In relativistic gravity, a comparison of two clocks is sensitive to their relative positions and velocity, making clocks ideal tools to investigate Earth’s gravity field. However, one important obstacle for Earth-satellite chronometry is the low measurement accuracy of satellite velocities, which enter into the redshift via the Doppler effect.
We present an alternative approach based on the framework of general relativity without velocity measurements from ground stations, instead measuring redshift between satellite pairs equipped with clocks via laser ranging. This method promises higher accuracy for gravity field recovery by improving control of the Doppler effect. We investigate this problem in analytically given spacetimes as well as in the general first post-Newtonian approximation of Earth’s gravity field, and discuss the prospects for gravity field recovery.