An improved approach for testing gravitational redshift via spacecraft based three frequency links combination

We propose a new approach for testing the gravitational redshift based on frequency signals transmission between a spacecraft and a ground station. By a combination of one uplink signal and two downlink signals, the gravitational redshift can be tested at about 6.5×10^-6 level for a GNSS satellite (the signals’ frequencies are about 1.2~1.6 GHz), and about 2.2×10^-6 level for the International Space Station (the signals’ frequencies are up to 14.7 GHz), under the assumption that the clock accuracy is about 10^-17 level. For better desinged cases the accuracy of gravitational redshift test can be improved to several parts in 10^-8 level (the signals’ frequencies are about 8~12 GHz). Compared to the scheme of Gravity Probe-A (GP-A) experiment conducted in1976, the new approach does not require any onboard signal transponders, and the frequency values of the three links can be quite arbitrarily given. As the hardware requirement is reduced, a number of spacecrafts could be chosen as candidates for a gravitational redshift experiment. This approach could also be used in gravitational potential determination, which has prospective applications in geodesy. This study is supported by 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).