Simulation experiments for testing gravitational redshift using three optical frequency signals between satellite and ground station

Gravitational redshift, one of the fundamental predictions of general relativity, describes the relationship between the oscillation frequency of clocks and the gravitational field. Testing the gravitational redshift effect with higher precision not only provides an important verification of general relativity but may also reveal new physical phenomena. In this study, an uplink and two downlink signals are established between a geostationary satellite (S) and a ground station (E). By combining three signals with different frequencies, the first-order Doppler effects, as well as influences from the ionosphere and troposphere, can be effectively suppressed, allowing high-precision extraction of the gravitational redshift signal. This research presents simulated experimental results. The geostationary satellite, a BeiDou-3 satellite, is linked to the ground station located at the Luojia Time and Frequency Laboratory in Wuhan. Both the satellite and the ground are equipped with optical atomic clocks, each with a stability of 2×10⁻¹⁸ at 1 day. The uplink signal frequency is 1 THz, while the two downlink signals’ frequencies are 1.1 THz and 0.8 THz, respectively. The simulation results indicate that after 10 days of continuous observation, the accuracy in determining the geopotential difference between the average positions of the ground station and the satellite is better than 10 cm. This enables testing of the gravitational redshift effect at a precision level of 2×10⁻⁸. This study provides valuable insights and references for future high-precision gravitational redshift tests utilizing geostationary or even arbitrary satellites, with potential applications in gravity potential measurements. This study is supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 42388102, 42030105, and 42274011).