ORIGINAL ARTICLE
Satellite Laser Ranging technique as a tool for the determination of the Schwarzschild, de Sitter and Lense-Thirring effects
 
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1
Space Research Centre, Polish Academy of Sciences, Bartycka 18A, 00-716 Warsaw, Poland
 
2
Faculty of Civil Engineering, Environmental and Geodetic Sciences, Koszalin University of Technology, Śniadeckich 2, 75-453 Koszalin, Poland
 
3
Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdansk, Poland
 
 
Submission date: 2023-08-31
 
 
Acceptance date: 2023-12-12
 
 
Publication date: 2023-12-29
 
 
Corresponding author
Mateusz Matyszewski   

Space Research Centre, Polish Academy of Sciences, Bartycka 18A, 00-716 Warsaw, Poland
 
 
Reports on Geodesy and Geoinformatics 2023;116:77-84
 
KEYWORDS
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ABSTRACT
Satellite Laser Ranging (SLR) is a modern technique used in various research areas and applications related to geodesy and geodynamics. It is commonly used for tasks such as establishing the International Terrestrial Reference Frame (ITRF), monitoring Earth Orientation Parameters (EOP), determining the geocenter, measuring fundamental physical constants, calibrating microwave tracking techniques, conducting time transfer experiments, and studying gravitational and general relativistic effects. Laser measurements of the LARES and LAGEOS satellites are used to determine the relativistic effects acting on these satellites. The objective of the present research is to analyze the perturbing forces of relativistic origin (Schwarzschild, de Sitter and Lense-Thirring effects) acting on the LARES, LAGEOS-1 and LAGEOS-2 satellites. By using data from fifteen SLR measurement stations, the precise orbits of these satellites were determined over a span of 840 hours using the GEODYN II orbital software package. The calculation process used a set of procedures, models of forces, and constants that are currently recommended by the International Earth Rotation and Reference Systems Service (IERS) and the International Laser Ranging Service (ILRS). Based on the precise orbits of the LARES, LAGEOS-1, and LAGEOS-2 satellites, calculations were made to determine the values of relativistic accelerations acting on these satellites. These values oscillate with a period equal to half of the orbital period for the de Sitter and Lense-Thirring effects, and a quarter of the orbital period for the Schwarzschild effect.
REFERENCES (49)
1.
Arnold, D., Montenbruck, O., Hackel, S., and Sośnica, K. (2019). Satellite laser ranging to low Earth orbiters: orbit and network validation. Journal of geodesy, 93(11):2315–2334, doi:10.1007/s00190-018-1140-4.
 
2.
Ashby, N. (2004). The Sagnac effect in the Global Positioning System. In Rizzi, G. and Ruggiero, M. L., editors, Relativity in rotating frames: relativistic physics in rotating reference frames, pages 11–28. Springer.
 
3.
Bloßfeld, M., Rudenko, S., Kehm, A., Panafidina, N., Müller, H., Angermann, D., Hugentobler, U., and Seitz, M. (2018). Consistent estimation of geodetic parameters from SLR satellite constellation measurements. Journal of Geodesy, 92:1003–1021, doi:10.1007/s00190-018-1166-7.
 
4.
Bogusz, J., Brzezinski, A., Kosek, W., and Nastula, J. (2015). Earth rotation and geodynamics. Geodesy and Cartography, 64(2), doi:10.1515/geocart-2015-0013.
 
5.
Brzeziński, A., Barlik, M., Andrasik, E., Izdebski, W., Kruczyk, M., Liwosz, T., Olszak, T., Pachuta, A., Pieniak, M., Próchniewicz, D., Rajner, M., Szpunar, R., Tercjak, M., and Walo, J. (2016a). Geodetic and geodynamic studies at Department of Geodesy and Geodetic Astronomy WUT. Reports on Geodesy and Geoinformatics, 100(1):165–200, doi:10.1515/rgg-2016-0013.
 
6.
Brzeziński, A., Jóźwik, M., Kaczorowski, M., Kalarus, M., Kasza, D., Kosek, W., Nastula, J., Szczerbowski, Z., Wińska, M., Wronowski, R., Zdunek, R., and Zieliński, J. B. (2016b). Geodynamic research at the Department of Planetary Geodesy, SRC PAS. Reports on Geodesy and Geoinformatics, 100(1):131–147, doi:10.1515/rgg-2016-0011.
 
7.
Ciufolini, I., Matzner, R., Gurzadyan, V., and Penrose, R. (2017). A new laser-ranged satellite for General Relativity and space geodesy: III. De Sitter effect and the LARES 2 space experiment. The European Physical Journal C, 77:1–6, doi:10.1140/epjc/s10052-017-5339-y.
 
8.
Ciufolini, I., Paolozzi, A., Pavlis, E., Ries, J., Gurzadyan, V., Koenig, R., Matzner, R., Penrose, R., and Sindoni, G. (2012). Testing General Relativity and gravitational physics using the LARES satellite. The European Physical Journal Plus, 127:1–7, doi:10.1140/epjp/i2012-12133-8.
 
9.
Ciufolini, I., Paolozzi, A., Pavlis, E. C., Koenig, R., Ries, J., Gurzadyan, V., Matzner, R., Penrose, R., Sindoni, G., Paris, C., Khachatryan, H., and Mirzoyan, S. (2016). A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model: Measurement of Earth’s dragging of inertial frames. The European Physical Journal C, 76:1–7, doi:10.1140/epjc/s10052-016-3961-8.
 
10.
Ciufolini, I., Paolozzi, A., Pavlis, E. C., Sindoni, G., Ries, J., Matzner, R., Koenig, R., Paris, C., Gurzadyan, V., and Penrose, R. (2019). An improved test of the general relativistic effect of frame-dragging using the LARES and LAGEOS satellites. The European Physical Journal C, 79(10):872, doi:10.1140/epjc/s10052-019-7386-z.
 
11.
Ciufolini, I., Paris, C., Pavlis, E. C., Ries, J., Matzner, R., Paolozzi, A., Ortore, E., Bianco, G., Kuzmicz-Cieslak, M., Gurzadyan, V., et al. (2023). First results of the LARES 2 space experiment to test the general theory of relativity. The European Physical Journal Plus, 138(11):1054, doi:10.1140/epjp/s13360-023-04696-6.
 
12.
Ciufolini, I. and Pavlis, E. C. (2004). A confirmation of the general relativistic prediction of the Lense-Thirring effect. Nature, 431(7011):958–960, doi:10.1038/nature03007.
 
13.
Combrinck, L. (2010). Satellite Laser Ranging. In Xu, G., editor, Sciences of Geodesy – I, pages 301–338. Springer, doi:10.1007/978-3-642-11741-1_9.
 
14.
De Sitter, W. (1917). Einstein’s theory of gravitation and its astronomical consequences. Third paper. Monthly Notices of the Royal Astronomical Society, 78:3–28, doi:10.1093/mnras/78.1.3.
 
15.
Dickey, J. O., Bender, P., Faller, J., Newhall, X., Ricklefs, R., Ries, J., Shelus, P., Veillet, C., Whipple, A., Wiant, J., Williams, J. G., and Yoder, C. F. (1994). Lunar Laser Ranging: A continuing legacy of the Apollo Program. Science, 265(5171):482–490, doi:10.1126/science.265.5171.482.
 
16.
Everitt, C., Muhlfelder, B., DeBra, D., Parkinson, B., Turneaure, J., Silbergleit, A., Acworth, E., Adams, M., Adler, R., Bencze, W., et al. (2015). The Gravity Probe B test of general relativity. Classical and Quantum Gravity, 32(22):224001, doi:10.1088/0264-9381/32/22/224001.
 
17.
Gourine, B. (2012). Use of Starlette and LAGEOS-1&-2 laser measurements for determination and analysis of stations coordinates and EOP time series. Comptes Rendus Geoscience, 344(6-7):319–333, doi:10.1016/j.crte.2012.05.002.
 
18.
Guo, J., Wang, Y., Shen, Y., Liu, X., Sun, Y., and Kong, Q. (2018). Estimation of SLR station coordinates by means of SLR measurements to kinematic orbit of LEO satellites. Earth, Planets and Space, 70(1):201, doi:10.1186/s40623-018-0973-7.
 
19.
Huang, C., Ries, J., Tapley, B., and Watkins, M. (1990). Relativistic effects for near-earth satellite orbit determination. Celestial Mechanics and Dynamical Astronomy, 48:167–185, doi:10.1007/BF00049512.
 
20.
Hugentobler, U. (2008). Orbit perturbations due to relativistic corrections. Unpublished notes available at https://impacts.obspm.fr/conte....
 
21.
ILRS - LAGEOS (2023). International Laser Ranging Service, LAGEOS-1,-2. Official Website of ILRS. Last accessed January 2023.
 
22.
ILRS - LARES (2023). International Laser Ranging Service, LARES – LAser RElativity Satellite. Official Website of ILRS. Last accessed January 2023.
 
23.
Jagoda, M., Rutkowska, M., and Kraszewska, K. (2016). The evaluation of time variability of tidal parameters h and l using SLR technique. Acta Geodynamica et Geomaterialia, 14(2):153–158, doi:10.13168/AGG.2016.0036.
 
24.
JPL Horizons (2023). Jet Propulsion Laboratory Horizons System. Official Website of JPL. Last accessed January 2023.
 
25.
Lejba, P. and Schillak, S. (2011). Determination of station positions and velocities from laser ranging observations to Ajisai, Starlette and Stella satellites. Advances in Space Research, 47(4):654–662, doi:10.1016/j.asr.2010.10.013.
 
26.
Lense, J. and Thirring, H. (1918). Über den einfluss der eigenrotation der zentralkörper auf die bewegung der planeten und monde nach der einsteinschen gravitationstheorie. Physikalische Zeitschrift, 19:156.
 
27.
Lucchesi, D. M. (2003). LAGEOS II perigee shift and Schwarzschild gravitoelectric field. Physics Letters A, 318(3):234–240, doi:10.1016/j.physleta.2003.07.015.
 
28.
Lucchesi, D. M., Anselmo, L., Bassan, M., Magnafico, C., Pardini, C., Peron, R., Pucacco, G., and Visco, M. (2019). General relativity measurements in the field of earth with Laser-Ranged satellites: state of the art and perspectives. Universe, 5(6):141, doi:10.3390/universe5060141.
 
29.
Lucchesi, D. M. and Peron, R. (2010). Accurate measurement in the field of the earth of the general-relativistic precession of the LAGEOS II pericenter and new constraints on nonnewtonian gravity. Physical Review Letters, 105(23):231103, doi:10.1103/PhysRevLett.105.231103.
 
30.
Lucchesi, D. M. and Peron, R. (2014). LAGEOS II pericenter general relativistic precession (1993–2005): Error budget and constraints in gravitational physics. Physical Review D, 89(8):082002, doi:10.1103/PhysRevD.89.082002.
 
31.
McCarthy, J., Rowton, S., Moore, D., Pavlis, D., Luthcke, S., and Tsaoussi, T. (2015). GEODYN systems description, volume 1. Technical report.
 
32.
Pardini, C., Anselmo, L., Lucchesi, D., and Peron, R. (2017). On the secular decay of the LARES semi-major axis. Acta Astronautica, 140:469–477, doi:10.1016/j.actaastro.2017.09.012.
 
33.
Pearlman, M., Arnold, D., Davis, M., Barlier, F., Biancale, R., Vasiliev, V., Ciufolini, I., Paolozzi, A., Pavlis, E. C., Sośnica, K., and Blossfeld, M. (2019a). Laser geodetic satellites: a high-accuracy scientific tool. Journal of Geodesy, 93:2181–2194, doi:10.1007/s00190-019-01228-y.
 
34.
Pearlman, M. R., Noll, C. E., Pavlis, E. C., Lemoine, F. G., Combrink, L., Degnan, J. J., Kirchner, G., and Schreiber, U. (2019b). The ILRS: approaching 20 years and planning for the future. Journal of Geodesy, 93:2161–2180, doi:10.1007/s00190-019-01241-1.
 
35.
Petit, G. and Luzum, B. (2010). IERS Technical Note No. 36. Technical report, Bureau International Des Poids Et Mesures Sevres (France), 1–179.
 
36.
Rutkowska, M. and Jagoda, M. (2010). Estimation of the elastic Earth parameters (h2, l2) using SLR data. Advances in space research, 46(7):859–871, doi:10.1016/j.asr.2010.04.010.
 
37.
Rutkowska, M. and Jagoda, M. (2015). SLR technique used for description of the Earth elasticity. Artificial Satellites, 50(3):127–141, doi:10.1515/arsa-2015-0010.
 
38.
Schillak, S., Lejba, P., and Michałek, P. (2021). Analysis of the quality of SLR station coordinates determined from Laser Ranging to the LARES satellite. Sensors, 21(3):737, doi:10.3390/s21030737.
 
39.
Schwarzschild, K. (2003). On the gravitational field of a mass point according to Einstein’s theory. Gen. Relativ. Gravit, 35(5):951–959, doi:10.1023/A:1022971926521.
 
40.
Seeber, G. (2003). Satellite geodesy, 2nd ed. Walter de gruyter, doi:10.1515/9783110200089.
 
41.
Shen, Y., Guo, J., Zhao, C., Yu, X., and Li, J. (2015). Earth rotation parameter and variation during 2005–2010 solved with LAGEOS SLR data. Geodesy and Geodynamics, 6(1):55–60, doi:10.1016/j.geog.2014.12.002.
 
42.
Sośnica, K. (2014). Determination of precise satellite orbits and geodetic parameters using Satellite Laser Ranging. Astronomical Institute, University of Bern, Switzerland, doi:10.7892/boris.53915.
 
43.
Sośnica, K. and Bosy, J. (2019). Global Geodetic Observing System 2015–2018. Advances in Geodesy and Geoinformation, 68(1):121–144, doi:10.24425/gac.2019.126090.
 
44.
Sośnica, K., Bury, G., Zajdel, R., Kazmierski, K., Ventura-Traveset, J., Prieto-Cerdeira, R., and Mendes, L. (2021). General relativistic effects acting on the orbits of Galileo satellites. Celestial Mechanics and Dynamical Astronomy, 133:14, doi:10.1007/s10569-021-10014-y.
 
45.
Sośnica, K., Jäggi, A., Meyer, U., Thaller, D., Beutler, G., Arnold, D., and Dach, R. (2015). Time variable Earth’s gravity field from SLR satellites. Journal of Geodesy, 89:945–960, doi:10.1007/s00190-015-0825-1.
 
46.
Specht, M. (2022). Experimental studies on the relationship between HDOP and position error in the GPS system. Metrology and Measurement Systems, 29(1):17–36, doi:10.24425/mms.2022.138549.
 
47.
Strugarek, D., Sośnica, K., Arnold, D., Jäggi, A., Zajdel, R., and Bury, G. (2021). Determination of SLR station coordinates based on LEO, LARES, LAGEOS, and Galileo satellites. Earth, Planets and Space, 73:87, doi:10.1186/s40623-021-01397-1.
 
48.
Williams, J. G., Turyshev, S. G., and Boggs, D. H. (2004). Progress in lunar laser ranging tests of relativistic gravity. Physical Review Letters, 93(26):261101, doi:10.1103/PhysRevLett.93.261101.
 
49.
Zelensky, N. P., Lemoine, F. G., Chinn, D. S., Melachroinos, S., Beckley, B. D., Beall, J. W., and Bordyugov, O. (2014). Estimated SLRstation position and network frame sensitivity to time-varying gravity. Journal of Geodesy, 88:517–537, doi:10.1007/s00190-014-0701-4.
 
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