Model on picometer-level light gravitational delay in the GRACE Follow-On-like missions

doi:10.1088/1674-1056/ad7af9

Abstract Laser interferometry plays a crucial role in laser ranging for high-precision space missions such as GRACE (Gravity Recovery and Climate Experiment) Follow-On-like missions and gravitational wave detectors. For such accuracy of modern space missions, a precise relativistic model of light propagation is required. With the post-Newtonian approximation, we utilize the Synge world function method to study the light propagation in the Earth's gravitational field, deriving the gravitational delays up to order $c^{-4}$. Then, we investigate the influences of gravitational delays in three inter-satellite laser ranging techniques, including one-way ranging, dual one-way ranging, and transponder-based ranging. By combining the parameters of Kepler orbit, the gravitational delays are expanded up to the order of $e^2$ ($e$ is the orbital eccentricity). Finally, considering the GRACE Follow-On-like missions, we estimate the gravitational delays to the level of picometer. The results demonstrate some high-order gravitational and coupling effects, such as $c^{-4}$-order gravitational delays and coupling of Shapiro and beat frequency, which may be non-negligible for higher precision laser ranging in the future.

Keywords: classical general relativity post-Newtonian approximation phase shifting interferometry

Received: 20 June 2024
Revised: 14 August 2024
Accepted manuscript online: 14 September 2024

PACS:	04.20.-q	(Classical general relativity)
	04.25.Nx	(Post-Newtonian approximation; perturbation theory; related Approximations)
	42.87.Bg	(Phase shifting interferometry)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12247150, 12305062, 12175076, and 11925503), the Post-doctoral Science Foundation of China (Grant No. 2022M721257), and the Guangdong Major Project of Basic and Applied Basic Research (Grant No. 2019B030302001).

Corresponding Authors: Cheng-Gang Qin, Cheng-Gang Shao
E-mail: cgqin@hust.edu.cn;yjtan@hust.edu.cn;cgshao@hust.edu.cn

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Jin-Zhuang Dong(董金壮), Wei-Sheng Huang(黄玮圣), Cheng-Gang Qin(秦成刚), Yu-Jie Tan(谈玉杰), and Cheng-Gang Shao(邵成刚) Model on picometer-level light gravitational delay in the GRACE Follow-On-like missions 2024 Chin. Phys. B 33 110401

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Model on picometer-level light gravitational delay in the GRACE Follow-On-like missions

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