Theory and application of extremely precise frequency standards on low Earth orbit to the determination of geopotential time-variability

Earth’s gravity plays a major role in molding our world. Monitoring the geopotential and its time variability reveals the mass redistribution occurring across our planet, thus informing us on matters like climate change and availability of water resources. The gravity features we are most interested in are characterized by spatial and temporal scales that can only be accessed via a mission in space. Among the most important gravity missions are GRACE/GRACE-FO and GOCE, which sense gravity through the derivatives of the Earth’s gravity field. We propose to apply chronometric geodesy, whose task is to measure gravity with clocks, in space through frequency comparison between orbiting clocks by means of the Doppler-canceling technique. The novelty of this approach consists in estimating Earth’s gravity via measurements of the geopotential itself, rather than its derivatives. The behavior of clocks in a gravitational field is governed by Einstein’s general relativity, which provides the best available description of gravitation. On the other hand, the frequency stability of clocks is now reaching 10¹⁹, becoming precise enough for geodesy applications. After describing the proposed gravity mission architecture, we provide a mathematical derivation of the Doppler-canceled frequency shift measurement. Then, we outline the estimation method and its numerical implementation, followed by a presentation of results. Our findings indicate the measurement can retrieve the geopotential coefficients with an accuracy potentially better than currently available gravity models employing clocks with a frequency stability of 10¹⁹. This result represents a proof of concept for the measurement, with gravity field solutions obtained from a mission simulation being shown here for the first time. However, once we introduce the orbit error, the kinematical approach utilized to solve the estimation problem presents severe limitations. The remedy is to adopt a dynamical approach, which would let us directly address the orbit error and other issues, e.g., frequency drift in clocks. In the conclusions, we discuss how to improve on our analysis and the necessary steps to follow in preparation for a future gravity mission, whose realization will be possible only when clock technology reaches the required performance (high frequency stability in a short integration time)