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Based on gravity frequency shift effect predicted by general relativity theory, this study discusses an approach for determining the gravity potential (geopotential) difference between arbitrary two points P and Q by remote comparison of two precise optical clocks via optical fiber frequency transfer. After synchronization, by measuring the signal’s frequency shift based upon the comparison of bidirectional frequency signals from P and Q oscillators connected with two optical atomic clocks via remote optical fiber frequency transfer technique, the geopotential difference between the two points could be determined, and its accuracy depends on the stabilities of the optical clocks and the frequency transfer comparison technique. Due to the fact that the present stability of optical clocks achieves 1.6×10−18 and the present frequency transfer comparison via optical fiber provides stabilities as high as 10−19 level, this approach is prospective to determine geopotential difference with an equivalent accuracy of 1.5 cm. In addition, since points P and Q are quite arbitrary, this approach may provide an alternative way to determine the geopotential over a continent, and prospective potential to unify a regional height datum system.

According to Einstein’s general relativity theory, a precise (atomic) clock runs faster at a position with higher gravitational potential than a clock at a position with lower potential. Here, we provide a direct clock comparison using a fixed hydrogen clock and a portable hydrogen clock for geopotential determination based on the two-way satellite time and frequency transfer (TWSTFT) technique. After synchronizing the two hydrogen clocks at positions at the same height, the clocks were compared for a height difference of 22 m over a period of 14 days using the TWSTFT technique. Interpretation of the observed time elapse implies a height difference of 175 m +/- 59 m, which matches the frequency stability of our instruments. This study and relevant experiments provide a way of determining the geopotential using ultra-high precise clocks based on the TWSTFT technique in the near future.

The general relativity theory provides a potential way to directly determine the gravitational potential (GP) difference by comparing the running rate or vibration frequencies of two optical-atomic clocks located at two stations. Recently we proposed an approach referred to as satellite frequency signal transmission based on the Doppler canceling technique or tri-frequency combination technique to determine the GP difference between a satellite and a ground site via exchanging microwave signals. Here, as an extension of our previous study, we aim to formulate determination of GP at ground stations and establish simulation experiments in different cases, including determining the GP at a ground station via one or more satellites and determining the GP difference between two ground stations via one or more satellites. Concerning each case we made simulating experiments, and results show that the precision of the GP at a ground station and that of the GP difference between two stations, determined via one satellite, are, respectively, about 0.383 and 0.454 m $$^{2}$$ /s $$^{2}$$ , assuming the clocks with inaccuracy of about $$1\times 10^{-18}$$ (s/s) level are available. If more satellites equipped with ultra-high-precise clocks are available, the precision of the determined GP (difference) at ground stations can be further improved.