Determination of the time-variable geopotential by means of orbiting clocks

Abstract

Monitoring the time-variable geopotential identifies the mass redistribution across the Earth and reveals, e.g., climate change and availability of water resources. The features of interest are characterized by spatial and temporal scales accessible only through space missions. Among the most important gravity missions are GRACE (2002–2017), its successor GRACE-FO (since 2018), and GOCE (2009–2013), which all sense the Earth’s gravity field via the geopotential derivatives. We investigate the geopotential estimation through frequency comparisons between orbiting clocks by means of the Doppler-canceling technique, describing the clocks’ behavior in the Earth’s gravitational field via Einstein’s general relativity. The novelty of this approach lies in measuring gravity by sensing the geopotential itself. The proof of principle for the measurement is achieved through an innovative mission scenario: for the first time, the observations are collected by a probing clock in LEO. We show gravity solutions obtained by simulating an estimation problem via our proposed architecture. The results suggest that we can conceivably retrieve the geopotential coefficients with accuracy comparable to the GRACE measurement concept by employing clocks with stabilities of order \({10}^{-18}\). Presently, terrestrial clocks can routinely attain fractional frequency stabilities of \({10}^{-18}\), whereas spaceborne clocks are still at the \({10}^{-15}\) level. While our findings are promising, further analysis is needed to obtain more realistic indications on the feasibility of an actual mission, whose realization will be possible when clock technology reaches the required performance. The goal is for the technique investigated in this study to become a future staple for gravity field estimation.