Geopotential Determination Using an Optical Link and a Cold-Atom Cesium Clock Aboard the ACES Mission

Relativistic geodesy exploits the gravitational redshift predicted by General Relativity (GR) to determine differences in the Earth’s gravitational potential (geopotential) through high-precision clock comparisons. Recent advances in optical atomic clocks and optical time-transfer techniques have achieved fractional frequency uncertainties at or below 10-18 , corresponding to a geopotential variation sensitivity of approximately 0.1m2s-2. This level of precision is sufficient to enable high-resolution chronometric leveling. Compared with conventional microwave time-transfer methods, optical links provide superior resilience to atmospheric perturbations, higher modulation bandwidths, and unambiguous time-transfer observables, making them particularly well suited for relativistic geodesy applications. Motivated by the European Laser Timing (ELT) experiment and the high-precision cesium cold-atom clock aboard the Atomic Clock Ensemble in Space (ACES) mission, characterized by a fractional frequency stability and accuracy of approximately 10-16, we propose and analyze a triple optical time-transfer model for determining the Earth’s geopotential. The model is formulated within a consistent relativistic framework based on post-Newtonian theory, which adequately supports atomic clock comparisons at the accuracy level of 10-18.In the absence of actual ELT/ACES optical data and considering the limitations of current ground-based laser ranging stations, where heterogeneous time and frequency standards exhibit insufficient long-term stability for relativistic geodesy, a high-fidelity numerical simulation framework is developed. This framework incorporates representative ELT/ACES mission parameters, including a ground-based optical clock with a fractional frequency instability of 10⁻¹⁸. Simulation results show that approximately 70% of ELT/ACES mission passes yield geopotential bias estimates within (-0.180±0.846) m2s-2 relative to the reference value, corresponding to centimeter-level height sensitivity. These results demonstrate that optical time and frequency transfer links, when combined with state-of-the-art optical clocks, can support free-space measurement networks capable of global chronometric leveling. Such networks hold significant potential for the realization of a unified height reference system and for advancing high-precision geodetic applications. This study is supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 42388102, 42030105, and 42274011) and the Space Station Project (2020-228). National Gravitation Laboratory, Huazhong University of Science and Technology, Wuhan 430074, P.R. China.