Test of gravitational redshift by combining tri-frequency links between spacecraft and ground station

We propose an approach for testing the gravitational redshift based on frequency signals transmitted between a spacecraft and a ground station. The main idea is to integrate one uplink signal from the ground to the spacecraft and two downlink signals from the spacecraft to the ground. Based on the integration and specific correction models, the gravitational shift of the signals between the spacecraft and the ground station can be detected at a high precision level. The gravitational redshift effect can be tested at about E-6 to E-8 levels in different cases for less than one month if the stability of onboard the atomic clock reaches E-17/day. Compared to the scheme of the Gravity Probe-A (GP-A) experiment conducted in 1976, in the new approach, any onboard signal transponder is not required, and the frequency values of the three links can be relatively arbitrary. Since the hardware requirement is decreased, any spacecraft can be a candidate for gravitational redshift experiment if it can emit two different frequency signals and receive a frequency signal from the ground. This study is supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 42030105, 41721003, 41631072, 41874023, 41804012), Space Station Project (2020)228, and Natural Science Foundation of Hubei Province (Grant No. 2019CFB611).