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Chin. Phys. B, 2024, Vol. 33(11): 110401    DOI: 10.1088/1674-1056/ad7af9
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Model on picometer-level light gravitational delay in the GRACE Follow-On-like missions

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)§
MOE Key Laboratory of Fundamental Physical Quantities Measurement & Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
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, Yu-Jie Tan, Cheng-Gang Shao     E-mail:  cgqin@hust.edu.cn;yjtan@hust.edu.cn;cgshao@hust.edu.cn

Cite this article: 

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

[1] Abich K, Abramovici A, Amparan B, et al. 2019 Phys. Rev. Lett. 123 031101
[2] Amaro-Seoane P, Audley H, Babak S, Baker J, et al. 2017 arXiv: 1702.00786
[3] Wu J, Li J and Jiang Q Q 2023 Chin. Phys. B 32 090401
[4] Poncin-Lafitte C Le, Linet B and Teyssandier P 2004 Classical and Quantum Gravity 21 4463
[5] Thorne K S, Misner C W and Wheeler J A 2000 Gravitation (Freeman San Francisco) p. 265
[6] Bertotti B, Iess L and Tortora P 2003 Nature 425 374
[7] Turyshev S G, Shao M, Girerd A and Lane B 2009 Int. J. Mod. Phys. D 18 1025
[8] Tso R and Bailey Q G 2010 Phys. Rev. D 84 085025
[9] Kostelecký V A and Tasson J D 2011 Phys. Rev. D 83 016013
[10] Qin C G, Ke J, Li Q, Chen Y F, Luo J, Tan Y J and Shao C G 2023 Classical and Quantum Gravity 40 205005
[11] eLISA Consortium, et al. 2013 ESA: Paris, Freance 2013 1
[12] Turyshev S G, Sazhin M V and Toth V T 2014 Phys. Rev. D 89 105029
[13] Turyshev S G, Toth V T and Sazhin M V 2013 Phys. Rev. D 87 024020
[14] Klioner S and Kopeikin S 1992 Astron. J. 104 897
[15] Linet B and Teyssandier P 2013 Classical and Quantum Gravity 30 175008
[16] Kopeikin S and Mashhoon B 2002 Phys. Rev. D 65 064025
[17] He G and Lin W 2016 Phys. Rev. D 94 063011
[18] Jiang C and Lin W 2018 Phys. Rev. D 97 024045
[19] Ghosh S and Bhattacharyya A 2022 J. Cosmol. Astropart. Phys. 2022 006
[20] Teyssandier P 1978 Phys. Rev. D 18 1037
[21] Zschocke S 2015 Phys. Rev. D 92 063015
[22] Zschocke S 2016 Phys. Rev. D 93 103010
[23] Zschocke S 2016 Phys. Rev. D 94 124007
[24] Teyssandier P and Le Poncin-Lafitte C 2008 Classical and Quantum Gravity 25 145020
[25] Le Poncin-Lafitte C and Teyssandier P 2008 Phys. Rev. D 77 044029
[26] Hees A, Bertone S and Le Poncin-Lafitte C 2014 Phys. Rev. D 89 064045
[27] Teyssandier P 2022 arXiv:2212.06671
[28] Linet B and Teyssandier P 2016 Phys. Rev. D 93 044028
[29] Qin C G and Shao C G 2017 Phys. Rev. D 96 024003
[30] Deng X M and Xie Y 2012 Phys. Rev. D 86 044007
[31] Qin C G, Tan Y J, Chen Y F and Shao C G 2019 Phys. Rev. D 100 064063
[32] Hees A, Bertone S and Le Poncin-Lafitte C 2014 Phys. Rev. D 90 084020
[33] Jiang C, Yang B and Lin W 2023 arXiv:2306.10129
[34] Soffel M, Klioner S A, Petit G, et al. 2003 Astronom. J. 126 2687
[35] Linet B and Teyssandier P 2002 Phys. Rev. D 66 024045
[36] Müller V 2017 Hannover: Gottfried Wilhelm Leibniz Universität Hannover
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