General Relativistic Chronometry from Ground and in Space

Geodesy's primary objective lies in the determination of Earth's gravity field through ground and space-based measurements. General relativity and, thus, relativistic geodesy, introduce a novel perspective, leveraging high-precision clock comparisons to potentially unveil a new tool for globally determining Earth's gravito-electric potential based on the gravitational redshift.

In the pursuit of clock-based gravimetry, which involves chronometry in stationary spacetimes, precise expressions for the relativistic redshift and timing among observers in different configurations are presented. These observers, equipped with standard clocks, move on arbitrary worldlines. The analysis reveals how redshift measurements, employing clocks on the ground and/or in space, can be harnessed to deduce the (mass) multipole moments of the underlying spacetime geometry. Importantly, our findings align with the Newtonian potential determination via conventional methods such as the energy approach.

The framework of chronometric geodesy is introduced and demonstrated across various exact vacuum spacetimes for clarity. The study extends to gravity degrees of freedom, encompassing gravito-magnetic contributions, with investigations into potential experiments for their determination. Looking ahead, upcoming gravity field recovery missions might incorporate clock comparisons as an additional resource for advanced data fusion.