General Relativistic Chronometry with Clocks on Ground and in Space

TL;DR

This paper develops a relativistic framework for using high-precision clocks on ground and in space to determine Earth's gravitational field, enabling new methods for gravity field recovery through clock-based measurements.

Contribution

It derives exact expressions for relativistic redshift and timing in stationary spacetimes, enabling clock-based gravimetry and extending traditional geodesy methods.

Findings

Redshift measurements can determine Earth's multipole moments.

Results align with Newtonian potential determination methods.

Framework applicable to future gravity field recovery missions.

Abstract

One of geodesy's main tasks is to determine the gravity field of the Earth. High precision clocks have the potential to provide a new tool in a global determination of the Earth's gravitational potential based on the gravitational redshift. Towards this clock-based gravimetry or chronometry in stationary spacetimes, exact expressions for the relativistic redshift and the timing between observers in various configurations are derived. These observers are assumed to be equipped with standard clocks and move along arbitrary worldlines. It is shown that redshift measurements, involving clocks on ground and/or in space, can be used to determine the (mass) multipole moments of the underlying spacetime. Results shown here are in agreement with the Newtonian potential determination from, e.g., the so-called energy approach. The framework of chronometric geodesy is exemplified in different exact vacuum spacetimes for illustration and future gravity field recovery missions may use clock comparisons as an additional data channel for advanced data fusion.