Test of gravitational red-shift based on tri-frequency combination of microwave frequency links

Abstract

Abstract Over the decades, testing gravitational red-shift (GRS) based on microwave links has made great process, including the GPA experiment, the planned Atomic Clock Ensemble in Space mission, and the China Space Station (CSS). Until now, the formulations of microwave links are almost all based on the time comparison. However, there are advantages of using frequency comparison instead of time comparison to test GRS. Here we develop a tri-frequency combination method based on the measurements of the frequency shifts of three independent microwave links between a space station and a ground station. Aiming at the frequency links’ accuracy of $$3\times 10^{-16}$$ 3 × 10 - 16 , we should consider various effects, including the Doppler effect, second-order Doppler effect, atmospheric frequency shift, tidal effects, refraction caused by the atmosphere, and Shapiro effect, with accuracy levels of tens of centimeters. The CSS will complete construction in 2022, and the formulation proposed in this study will enable us to test GRS at an accuracy level of at least $$2\times 10^{-6}$$ 2 × 10 - 6 , which is one order higher than the present accuracy level of $$7\times 10^{-5}$$ 7 × 10 - 5 .