Time-Variable Gravity Recovery from Clock Frequency Comparisons in Formation-Flying Missions
Abstract
Recent advances in optical clock technology offer the possibility of directly sensing differences in the Earth’s gravitational potential through frequency comparisons between satellites. This study investigates the performance of different satellite formation-flying architectures for recovering the time-variable gravity field using optical clock measurements.Four formation geometries are considered: a GRACE-like along-track configuration and three multidirectional formations, namely Cartwheel, Pendulum, and Helix. We performed a simulation analysis over 2016-2018 and synthesized the observable, geopotential difference, based on Hydrology, Icesheet and Solid Earth components of the v3 of the ESA Earth System Model. The observations were then contaminated with AOD1B error (from AOe07) and various clock noise levels from 10-17 to 10-20. We estimated monthly spherical harmonic solutions to degree 60, and evaluated the results in the spectral and spatial domain, as well as through examining timeseries of terrestrial water storage changes and icesheet mass change. The results show that formation geometry strongly influences the quality and spatial characteristics of time-variable gravity solutions. Our results show that a clock noise level of 10-19-10-20 is required to reliably recover time-variable gravity fields. Compared with the GRACE-like formation, multidirectional formations such as the Pendulum provide substantially improved solutions, both in terms of error magnitude and isotropy, making the errors easier to mitigate with a simple Gaussian filter. The performance of formation-flying missions depends strongly on clock noise, highlighting an important interplay between measurement precision and formation geometry. As clock performance improves, the influence of constellation geometry becomes increasingly important, with the Pendulum and Helix configurations showing particularly promising time-variable gravity recovery capabilities, especially at smaller spatial scales.