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

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 .

Advancing Ultra-High Precision in Satellite–Ground Time–Frequency Comparison: Ground-Based Experiment and Simulation Verification for the China Space Station

“…The architecture of the simulation and verification platform is illustrated in Figure 4. Within the framework of the simulation and verification platform, parameters are strictly set according to the actual conditions of the CSS [20]. In this simulation, we have comprehensively considered the Earth's model and the forces acting on the spacecraft and modeled various error factors, including geometric distance, motion time delay (distance error and clock error), atmospheric time delay, and relativistic time delay, among others [13].…”

“…Remote Sens. 2023, 13, x FOR PEER REVIEW 8 of 13 Within the framework of the simulation and verification platform, parameters are strictly set according to the actual conditions of the CSS [20]. In this simulation, we have comprehensively considered the Earth's model and the forces acting on the spacecraft and modeled various error factors, including geometric distance, motion time delay (distance ous two-way transmission delay errors in the satellite-ground comparison.…”

Higher order ionospheric effects in testing gravitational redshift by space frequency signal transfer

“…Due to the increasing requirements for high precision of time and frequency measurements, such as tests of GRS (Shen et al 2017;Sun et al 2021), fundamental quantum physics (Delva et al 2017), gravity potential, orthometric height determination (Cai et al 2020) and redefinition of the second by optical clocks (Riehle 2015), high-precision atomic clocks have developed very quickly, especially in the case of optical atomic clocks (OACs). The stability of atomic clocks had been greatly improved to 7 × 10 −19 (Oelker et al 2019;McGrew et al 2018) and the technique of OACs down-conversion for microwave frequencies has since reached an instability of 10 −18 (Nakamura et al 2020).…”

“…Recently, by focusing on frequency links between the space-ground station, a tri-frequency combination approach was used to test GRS. The simulation results show that based on ACES onboard the ISS, an accuracy level of at least 2 × 10 −6 could be achieved (Sun et al 2021). However, since it is limited by the measurement accuracy of the atomic clocks, until now the frequency transfer model only considered the first-order ionospheric frequency shift (Shen et al 2017;Sun et al 2021).…”

Analysis of orbit error effect on ultra-high space-ground two-way time comparison

“…On the basis, the use of microgravity environment to run onboard high-precision atomic clocks to achieve ultra-high microwave time comparison accuracy (better than 100 ps) is a research hotspot in the future. Therefore, many countries over the world have carried out relevant research and verification, including the ESA's Atomic Clock Ensemble in Space (ACES) project, China's China Space Station Time-Frequency Experiment Payload (CSSTFEP) project, etc [9][10].…”