Abstract
Taiji-1 is the first technology demonstration satellite of the Taiji program of China’s space-borne gravitational wave antenna. After the demonstration of the key individual technologies, Taiji-1 continues collecting the data of the precision orbit determinations, satellite attitudes, and non-conservative forces exerted on the S/C. Therefore, during its free-fall, Taiji-1 can be viewed as operating in the high-low satellite-to-satellite tracking mode of a gravity recovery mission. In this work, we have selected and analyzed the one month data from Taiji-1’s observations, and developed the techniques to resolve the long term interruptions and disturbances in the data due to the scheduled technology demonstration experiments. The first global gravity model TJGM-r1911, that independently derived from China’s own satellite mission, is successfully built from Taiji-1’s observations. Compared with gravity models from CHAMP and other satellite gravity missions, the accuracy discrepancies exist, which is mainly caused by the data discontinuity problem. As the extended free-falling phase been approved, Taiji-1 could serve as a gravity recovery mission for China since 2022 and it will provide us the independent measurement of both the static and the monthly time-variable global gravity field.
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References
Abbott, B.P., Abbott, R., Abbott, T.D., Abernathy, M.R., Acernese, F., Ackley, K., et al.: Observation of gravitational waves from a binary black hole merger. Phys Rev Lett. 116(6), 061102 (2016a). https://doi.org/10.1103/PhysRevLett.116.061102
Abbott, B.P., Abbott, R., Abbott, T.D., Abernathy, M.R., Acernese, F., Ackley, K., et al.: Observing gravitational-wave transient GW150914 with minimal assumptions. Physical Review D. 93(12), 122004 (2016b). https://doi.org/10.1103/PhysRevD.93.122004
Abbott, B.P., Abbott, R., Abbott, T.D., Abernathy, M.R., Acernese, F., Ackley, K., et al.: Properties of the Binary Black Hole Merger GW150914. Physical Review Letters. 116(24), 241102 (2016c). https://doi.org/10.1103/PhysRevLett.116.241102
Anderson, G., Anderson, J., Anderson, M., Aveni, G., Bame, D., Barela, P., et al.: Experimental results from the ST7 mission on LISA Pathfinder. Physical Review D. 98(10), 102005 (2018). https://doi.org/10.1103/PhysRevD.98.102005
Armano, M.: LISA_Pathfinder. arXiv. 1903.08924 (2019). https://doi.org/10.1142/9789811207402_0013
Armano, M., Audley, H., Auger, G., Baird, J.T., Bassan, M., Binetruy, P., et al.: Sub-Femto- g free fall for space-based gravitational wave observatories: LISA Pathfinder Results. Phys Rev Lett. 116(23), 231101 (2016). https://doi.org/10.1103/PhysRevLett.116.231101
Armano, M., Audley, H., Baird, J., Binetruy, P., Born, M., Bortoluzzi, D., et al.: Beyond the required LISA free-fall performance: new LISA pathfinder results down to 20 \(\mu\) Hz. Phys Rev Lett. 120(6), (2018). https://doi.org/10.1103/PhysRevLett.120.061101
Armano, M., Audley, H., Baird, J., Binetruy, P., Born, M., Bortoluzzi, D., et al.: LISA Pathfinder platform stability and drag-free performance. Physical Review D. 99(8), 082001 (2019). https://doi.org/10.1103/PhysRevD.99.082001
Badura, T., Sakulin, C., Gruber, C., Klostius, R.: Derivation of the CHAMP-only global gravity field model TUG-CHAMP04 applying the energy integral approach. Stud. Geophys. Geod. 50(1), 59–74 (2006). https://doi.org/10.1007/s11200-006-0002-3
Bender, P.L.: Additional astrophysical objectives for LISA follow-on missions. Classical and Quantum Gravity. 21(5), S1203–S1208 (2004). https://doi.org/10.1088/0264-9381/21/5/120
Cyranoski, D.: Chinese gravitational-wave hunt hits crunch time. Nature. 531(7593), 150–151 (2016). https://doi.org/10.1038/531150a
Danzmann, K.: LISA revealing a hidden universe. European Space Agency. (2011)
Dobslaw, H., Bergmann-Wolf, I., Dill, R., Poropat, L., Thomas, M., Dahle, C., et al.: A new high-resolution model of non-tidal atmosphere and ocean mass variability for de-aliasing of satellite gravity observations: AOD1B RL06. Geophys. J. Int. 211(1), 263–269 (2017). https://doi.org/10.1093/gji/ggx302
Foldvary, L., Svehla, D., Gerlach, C., Wermuth, M., Gruber, T., Rummel, R., et al.: Gravity Model TUM-2Sp Based on the energy balance approach and kinematic CHAMP Orbits. In: Reigber, C., Lühr, H., Schwintzer, P., Wickert, J., (eds.) Earth Observation with CHAMP, pp. 13–18. Berlin/Heidelberg: Springer-Verlag (2005). Available from: http://link.springer.com/10.1007/3-540-26800-6_2
Folkner, W.M., Williams, J.G., Boggs, D.H.: The planetary and lunar ephemeris DE 421. vol. 42–178, pp. 1–34. (2009)
Gerlach, C., Foldvary, L., Svehla, D., Gruber, T., Wermuth, M., Sneeuw, N., et al.: A CHAMP-gravity field model from kinematic orbits using the energy integral. Geophys. Res. Lett. 30(20), 2003GL018025 (2003). https://doi.org/10.1029/2003GL018025
Gerlach, C., Sneeuw, N., Visser, P., Svehla, D.: CHAMP gravity field recovery using the energy balance approach. Adv. Geosci. 1, 73–80 (2003). https://doi.org/10.5194/adgeo-1-73-2003
Gong, X., Xu, S., Bai, S., Cao, Z., Chen, G., Chen, Y., et al.: A scientific case study of an advanced LISA mission. Classical and Quantum Gravity. 28(9), 094012 (2011). https://doi.org/10.1088/0264-9381/28/9/094012
Gong, X., Lau, Y.K., Xu, S., Amaro-Seoane, P., Bai, S., Bian, X., et al.: Descope of the ALIA mission. J Phys Conf Ser. 610, 012011 (2015). https://doi.org/10.1088/1742-6596/610/1/012011
Gong, X.-F., Xu, S.-N., Yuan, Y.-F., Bai, S., Bian, X., Cao, Z.-J., et al.: Laser interferometric gravitational wave detection in space and structure formation in the early universe. Chin. Astron. Astrophys. 39(4), 411–446 (2015). https://doi.org/10.1016/j.chinastron.2015.10.001
Han, S.C., Jekeli, C., Shum, C.K.: Efficient gravity field recovery using in situ disturbing potential observables from CHAMP: gravity field recovery from champ. Geophys Res Lett. 29(16), 36–1–36–4 (2002). https://doi.org/10.1029/2002GL015180
Hotine, M., Morrison, F.: First integrals of the equations of satellite motion. Bull. Géod. 91(1), 41–45 (1969). https://doi.org/10.1007/BF02524844
Hu, W.R., Wu, Y.L.: The Taiji program in space for gravitational wave physics and the nature of gravity. Natl Sci Rev 4(5), 685–686 (2017). https://doi.org/10.1093/nsr/nwx116
Jacobi, J.C.G.: Uber ein neues Integral für den Fall der drei Körper, wenn die Bahn des störenden Planeten kreisförmig angenommen und die Masse des gestörten vernachlässigt wird. Monthly Reports of the Berlin Academy of Science. July, (1836)
Jaggi, A., Bock, H., Prange, L., Meyer, U., Beutler, G.: GPS-only gravity field recovery with GOCE, CHAMP, and GRACE. Adv. Space Res. 47(6), 1020–1028 (2011). https://doi.org/10.1016/j.asr.2010.11.008
Jekeli, C.: The determination of gravitational potential differences from satellite-to-satellite tracking. Celest. Mech. Dyn. Astron. 75, 85–101 (1999)
Li, Y., Liu, H., Zhao, Y., Sha, W., Wang, Z., Luo, Z., et al.: Demonstration of an ultraprecise optical bench for the Taiji space gravitational wave detection pathfinder mission. Appl. Sci. 9(10), (2019). https://doi.org/10.3390/app9102087
Li, Y., Luo, Z., Liu, H., Gao, R., Jin, G.: Laser interferometer for space gravitational waves detection and earth gravity mapping. Microgravity Sci Technol. 30, 817–829 (2018). https://doi.org/10.1007/s12217-018-9624-7
Li, Y., Wang, C., Wang, L., Liu, H., Jin, G.: A laser interferometer prototype with pico-meter measurement precision for Taiji space gravitational wave detection mission in China. Microgravity Sci Technol. 32, 331–338 (2020). https://doi.org/10.1007/s12217-019-09769-9
Liu, H., Dong, Y., Gao, R., Luo, Z., Jin, G.: Principle demonstration of the phase locking based on the electro-optic modulator for Taiji space gravitational wave detection pathfinder mission. Opt. Eng. 57(5), 1–5 (2018). https://doi.org/10.1117/1.OE.57.5.054113
Liu, H., Li, Y., Jin, G.: Numerical simulations of arm-locking for Taiji space gravitational waves detection. Microgravity Sci Technol. 33, 41 (2021). https://doi.org/10.1007/s12217-021-09875-7
Liu, H., Luo, Z., Jin, G.: The development of phasemeter for Taiji space gravitational wave detection. Microgravity Sci Technol. 30, 775–781 (2018). https://doi.org/10.1007/s12217-018-9625-6
Luo, Z., Guo, Z., Jin, G., Wu, Y., Hu, W.: A brief analysis to Taiji: science and technology. Results in Physics. 16, 102918 (2020). https://doi.org/10.1016/j.rinp.2019.102918
Luo, Z., Wang, Y., Wu, Y., Hu, W., Jin, G.: The Taiji program: a concise overview. Progress of Theoretical and Experimental Physics. ptaa083 (2020) . https://doi.org/10.1093/ptep/ptaa083
Mayer-Gurr, T., Ilk, K.H., Eicker, A., Feuchtinger, M.: ITG-CHAMP01: a CHAMP gravity field model from short kinematic arcs over a one-year observation period. J. Geod. 78(7–8), 462–480 (2005). https://doi.org/10.1007/s00190-004-0413-2
Min, J., Lei, J.G., Li, Y.P., Xi, D.X., Tao, W.Z., Li, C.H., et al.: Performance tests and simulations for Taiji-1 inertial sensor. International Journal of Modern Physics A. 36(11n12), 2140011 (2021). https://doi.org/10.1142/S0217751X2140011X
Moore, P., Turner, J.F., Qiang, Z.: Champ orbit determination and gravity field recovery. Adv. Space Res. 31(8), 1897–1903 (2003). https://doi.org/10.1016/S0273-1177(03)00164-9
Naeimi, M., Flury, J. (eds.).: Global gravity field modeling from satellite-to-satellite tracking data. Lecture Notes in Earth System Sciences. Cham: Springer International Publishing (2017). Available from: http://link.springer.com/10.1007/978-3-319-49941-3
O’Keefe, J.A.: An application of Jacobi’s integral to the motion of an earth satellite. Astron. J. 62, 265 (1957). https://doi.org/10.1086/107530
Pavlis, N.K., Holmes, S.A., Kenyon, S.C., Factor, J.K.: The development and evaluation of the Earth Gravitational Model 2008 (EGM2008): THE EGM2008 EARTH GRAVITATIONAL MODEL. J. Geophys. Res. Solid Earth. 117(B4), n/a–n/a (2012). https://doi.org/10.1029/2011JB008916
Peng, X., Jin, H., Xu, P., Wang, Z., Luo, Z., Ma, X., et al.: System modeling in data processing of Taiji-1 mission. International Journal of Modern Physics A. 36(11n12), 2140026 (2021). https://doi.org/10.1142/S0217751X21400261
Petit, G., Luzum, B., IERS Conventions.: International earth rotation and reference systems service; 2011. No. 36. (2010). Available from: https://apps.dtic.mil/sti/citations/ADA535671
Picone, J.M., Hedin, A.E., Drob, D.P., Aikin, A.C.: NRLMSISE-00 empirical model of the atmosphere: statistical comparisons and scientific issues: TECHNIQUES. J Geophys Res Space Physics. 107(A12), SIA 15–1–SIA 15–16 (2002). https://doi.org/10.1029/2002JA009430
Reigber, C. (ed.).: Earth observation with CHAMP: results from three years in orbit. Berlin; New York: Springer (2005). Meeting Name: CHAMP Science Meeting
Ruan, W.H., Guo, Z.K., Cai, R.G., Zhang, Y.Z.: Taiji program: gravitational-wave sources. International Journal of Modern Physics A. 35(17), 2050075 (2020). https://doi.org/10.1142/S0217751X2050075X
Ruan, W.H., Liu, C., Guo, Z.K., Wu, Y.L., Cai, R.G.: The LISA-Taiji network. Nature Astronomy. 4(2), 108–109 (2020). https://doi.org/10.1038/s41550-019-1008-4
Ruan, W.H., Liu, C., Guo, Z.K., Wu, Y.L., Cai, R.G.: The LISA-Taiji network: precision localization of coalescing massive black hole binaries. Research. 2021, 1–7 (2021). https://doi.org/10.34133/2021/6014164
The LIGO Scientific Collaboration, Aasi, J., Abbott, B.P., Abbott, R., Abbott, T., Abernathy, M.R., et al. Advanced LIGO. Classical and Quantum Gravity. 32(7), 074001 (2015). https://doi.org/10.1088/0264-9381/32/7/074001
The Taiji Scientific Collaboration.: China’s first step towards probing the expanding universe and the nature of gravity using a space borne gravitational wave antenna. Commun. Phys. 4(1), 34 (2021). https://doi.org/10.1038/s42005-021-00529-z
The Taiji Scientific Collaboration, Wu, Y.L., Luo, Z.R., Wang, J.Y., Bai, M., Bian, W., et al.: Taiji program in space for gravitational universe with the first run key technologies test in Taiji-1. International Journal of Modern Physics A. 36(11n12), 2102002 (2021). https://doi.org/10.1142/S0217751X21020024
Visser, P.N.A.M., Sneeuw, N., Gerlach, C.: Energy integral method for gravity field determination from satellite orbit coordinates. J. Geod. 77(3–4), 207–216 (2003). https://doi.org/10.1007/s00190-003-0315-8
Wang, G., Ni, W.T., Han, W.B., Xu, P., Luo, Z.: Alternative LISA-TAIJI networks. Physical Review D. 104(2), 024012 (2021). https://doi.org/10.1103/PhysRevD.104.024012
Wang, R., Ruan, W.H., Yang, Q., Guo, Z.K., Cai, R.G., Hu, B.: Hubble parameter estimation via dark sirens with the LISA-TAIJI network. Natl Sci Rev. nwab054 (2021). https://doi.org/10.1093/nsr/nwab054
Weigelt, M., Dam, T., Jaggi, A., Prange, L., Tourian, M.J., Keller, W., et al.: Time-variable gravity signal in Greenland revealed by high-low satellite-to-satellite tracking. J. Geophys. Res. Solid Earth 118(7), 3848–3859 (2013). https://doi.org/10.1002/jgrb.50283
Wielicki, B.A., Barkstrom, B.R., Baum, B.A., Charlock, T.P., Green, R.N., Kratz, D.P., et al.: Clouds and the Earth’s Radiant Energy System (CERES): algorithm overview. IEEE Trans. Geosci. Remote Sens. 36(4), 1127–1141 (1998)
Wielicki, B.A., Wong, T., Loeb, N., Minnis, P., Priestley, K., Kandel, R.: Changes in Earth’s albedo measured by satellite. Science. 308(5723), 825–825 (2005)
Wolff, M.: Direct measurements of the Earth’s gravitational potential using a satellite pair. J. Geophys. Res. 74(22), 5295–5300 (1969). https://doi.org/10.1029/JB074i022p05295
Funding
This work is supported by the National Key Research and Development Program of China No. 2020YFC2200601 and No. 2020YFC2200104, the Strategic Priority Research Program of the Chinese Academy of Sciences Grant No. XDA15020700, and the Youth Fund Project of National Natural Science Foundation of China No. 11905017.
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Wu, L., Xu, P., Zhao, S. et al. Global Gravity Field Model from Taiji-1 Observations. Microgravity Sci. Technol. 34, 77 (2022). https://doi.org/10.1007/s12217-022-09998-5
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DOI: https://doi.org/10.1007/s12217-022-09998-5