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

¹ Time and Frequency Observation Center, School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, PR China
e-mail: wbshen@sgg.whu.edu.cn
² State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, 129 Luoyu Road, Wuhan 430079, PR China
³ School of Resource, Environmental Science and Engineering, Hubei University of Science and Technology, 88 Xianning Avenue, Xianning 437100, Hubei Province, PR China
⁴ Geomatics Engineering Department, Faculty of Engineering at Shoubra, 108 Shoubra street, Benha University, Cairo 11629, Egypt
⁵ Civil Engineering Department, Faculty of Engineering, Misr Aswan Agricultural Road, EL MAHATTA, Minia University, Minia 61111, Egypt

Received: 2 November 2021
Accepted: 31 July 2023

Abstract

Context. When a microwave passes through the ionosphere, it produces ionospheric refraction and path bending, leading to changes in frequency and reducing the accuracy of frequency transmission. Currently, the Atomic Clock Ensemble in Space (ACES, 2023) and China Space Station (CSS, 2022) carry atomic clocks with a long-term stability of 10⁻¹⁶ and 10⁻¹⁸. The accuracy of the frequency comparison and gravitational redshift (GRS) test matches the corresponding order of magnitude.

Aims. Based on ground-space frequency links and considering the frequency shift caused by the higher order terms of the ionosphere, the gravitational redshift (GRS) test could be achieved at a higher level of accuracy.

Methods. We formulated a higher order ionospheric frequency shift model and analyzed the ionosphere effects on the one-way frequency transfer, as well as the dual- and tri-frequency combination methods, for frequency transfer between a space station (ACES or CSS) and a ground-based station.

Results. The analysis shows that for one-way frequency transfer, the second-order ionospheric frequency shift is about 10⁻¹⁵, 10⁻¹⁷, and 10⁻¹⁸ for the S-, Ku-, and Ka-bands, respectively. The second- and third-order ionospheric frequency shifts were eliminated using the dual-frequency combination method for CSS frequency transfer. When using the tri-frequency combination method for frequency transfer, the second ionospheric frequency shifts are about 10⁻¹⁶ ~ 10⁻¹⁷ for ACES and 10⁻¹⁹ for CSS, while the third-order frequency shifts are smaller than 10⁻¹⁹ for two missions.

Conclusions. Concerning the current atomic clock’s accuracy and microwave link frequencies for ACES and CSS missions, the second-order ionospheric frequency shift needs to be considered and eliminated, but the third-order term does not need to be considered. To get the accuracy of the GRS test to reach 10⁻⁶ ~ 10⁻⁸, we can use the dual- or tri-frequency combination method. Our study also shows that even for the mm accuracy level requirement, the third-order ionospheric frequency shift can be neglected.