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General Relativity and Space Geodesy

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Sciences of Geodesy - II

Abstract

Newton’s final version (published in 1726) of Philosophiae Naturalis Principia Mathematica was a great scientific achievement of the time and contained sufficient information to allow calculation of the dynamics of terrestrial and celestial bodies; it also expounded on the absolute nature of time and space. As examples, Newton’s statements (Newton in Principia: the mathematical principles of natural philosophy, New York, 1726) that “Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external” and “Absolute space, in its own nature, without regard to anything external, remains always similar and immovable” were fundamental to Newtonian calculations. These Newtonian concepts of space and time were challenged and proven to be only approximate by Einstein through his 1905 paper on special relativity, as well as his discovery of general relativity in 1915. The implications for and applications of general relativity within the fields of space geodesy is discussed in this chapter.

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References

  • Ashby N, Shahid-Saless B (1990) Geodetic precession or dragging of inertial frames? Phys Rev D 42:1118–1122

    Article  Google Scholar 

  • Ashby N (2002) Relativity and the global positioning system. Phys Today 55(5):41–47

    Article  Google Scholar 

  • Ashby N (2003) Relativity in the global positioning system. Living Rev Relativ, vol 6, p 1 [http://www.livingreviews.org/Articles/Volume6/2003-1ashby, online article: cited on 7 July 2010]

  • Ashby N (2004) The sagnac effect in the global positioning system. In: Rizzi G, Ruggiero ML (eds) Relativity in rotating frames, Kluwer Academic Publishers, Dordrecht, The Netherlands, pp 11–28

    Google Scholar 

  • Ashby N (2005) Relativity in the global positioning system. In: Ashtekar A (ed) 100 years of relativity space-tine structure: Einstein and beyond. World Scientific Publishing Co, Singapore, pp 257–289

    Chapter  Google Scholar 

  • Ashby N (2006) Relativistic effects in the global positioning system. http://www.aapt.org/doorway/tgru/articles/Ashbyarticle.pdf, online article: cited on 1 May 2011

  • Ashby N, Nelson RA (2009) The global positioning system, relativity and extraterrestrial navigation, in relativity. In: lioner SA, Seidelmann PK, Soffel MH (eds) Fundamental astronomy: dynamics, reference frames, and data analysis proceedings IAU symposium no. 261, Cambridge University Press, pp 22–30

    Google Scholar 

  • Bertotti B, Iess L, Tortora P (2003) A test of general relativity using radio links with the cassini spacecraft. Nature 425:374–376

    Article  Google Scholar 

  • Beutler G, Drewes H, Verdun A (2005a) The integrated global geodetic observing system (IGGOS) viewed from the perspective of history. J Geodyn 40(4–5):414–431

    Article  Google Scholar 

  • Beutler G, Mervart L, Verdun A (2005b) Methods of celestial mechanics: application to planetary system, geodynamics and satellite geodesy, vol II. Springer, Germany

    Google Scholar 

  • Botai OJ, Combrinck L, Sivakumar V, Schuh H, Böhm J (2010) Extracting independent local oscillatory geophysical signals by geodetic tropospheric delay. In: IVS 2010 general meeting proceedings, pp 345–354. http://ivscc.gsfc.nasa.gov/publications/gm2010/botai.pdf

  • Burša M, Kenyon S, Kouba J, Šíma Z, Vatrt V, Vítek V, Vojtíšková M (2007) The geopotential value w 0 for specifying the relativistic atomic time scale and a global vertical reference system. J Geod 81:103–110

    Article  Google Scholar 

  • Carter WE, Robertson DS, MacKay JR (1985) Geodetic radio interferometric surveying: applications and results. J Geophys Res 90(B6):4577–4587

    Article  Google Scholar 

  • Cazenave A (1995) Geoid, topography and distribution of landforms, in global earth physics; a handbook of physical constants, American Geophysical Union

    Google Scholar 

  • Ciufolini I (1986) Measurement of the lense-thirring drag on high-altitude laser- ranged artificial satellites. Phys Rev Lett 56:278–281

    Article  Google Scholar 

  • Ciufolini I, Wheeler JA (1995) Gravitation and inertia. Princeton University Press, Princeton

    Google Scholar 

  • Ciufolini I, Lucchesi DM, Vespe F, Mandiello A (1996) Measurement of dragging of inertial frames and gravitomagnetic field using laser-ranged satellites, Il. Nuovo Cimento A 109:575–590

    Article  Google Scholar 

  • Ciufolini I, Pavlis E, Chieppa F, Fernandes-Vieira E, Pérez-Mercader J (1998) Test of general relativity and measurement of the lense-thirring effect with two earth satellites. Science 279:2100–2103

    Article  Google Scholar 

  • Ciufolini I, Pavlis EC (2004) A confirmation of the general relativistic prediction of the lense–thirring effect. Nature 431:958–960

    Article  Google Scholar 

  • Ciufolini I, Pavlis EC, Peron R (2006) Determination of frame-dragging using earth gravity models from CHAMP and GRACE. New Astron 11:527–550

    Article  Google Scholar 

  • Ciufolini I (2007) Gravitomagnetism, frame-dragging and lunar laser ranging, arXiv:0704.3338v2 [gr-qc], 10 May 2007

    Google Scholar 

  • Combrinck L (2008) Evaluation of PPN parameter gamma as a test of general relativity using SLR data. In: 16th international laser ranging workshop, (Poznan (PL) 13–17 Oct 2008), available at http://cddis.gsfc.nasa.gov/lw16/docs/papers/sci_6_Combrinck_p.pdf

  • Combrinck L (2010) Satellite laser ranging. In: Xu Guochang (ed) Sciences of Geodesy I, advances and future directions. Springer, Germany, pp 301–336

    Chapter  Google Scholar 

  • Combrinck L (2011) Testing general relativity theory through the estimation of PPN parameters γ and β using satellite laser ranging data. S Afr J Geol 114(3–4):549–560

    Article  Google Scholar 

  • Counselman CC, Kent SM, Knight CA, Shapiro II, Clark TA, Hinteregger HF, Rogers AEE, Whitney AR (1974) Solar gravitational deflection of radio waves measured by very-long-baseline interferometry. Phys Rev Lett 33(27):1621–1623

    Article  Google Scholar 

  • Crelinsten J (2006) Einstein’s jury: the race to test relativity. Princeton University Press, Princeton

    Google Scholar 

  • Cugusi L, Proverbio E (1977) Relativistic effects on the motion of the earth’s satellites. In: Paper presented at the international symposium on satellite geodesy in Budapest from 28 June to 1 July 1977, J Geodesy, vol 51, pp 249–252

    Google Scholar 

  • Cugusi L, Proverbio E (1978) Relativistic effects on the motion of earth’s artificial satellites. Astron Astrophys 69:321–325

    Google Scholar 

  • Damour T, Soffel M, Xu C (1994) General-relativistic celestial mechanics IV. Theory of satellite motion. Phys. Rev. D 49:618–635

    Article  Google Scholar 

  • de Sitter W (1916) On Einstein’s theory of gravitation and its astronomical consequences. Mon Not Roy Astron Soc 77:155184

    Google Scholar 

  • Drewes H (2007) science rationale of the global geodetic observing system (GGOS), in dynamic planet, monitoring and understanding a dynamic planet with geodetic and oceanographic tools. In: Tregoning P, Rizos C (eds) Planet earth. IAG Symposia, vol 130. Springer, pp 703–710

    Google Scholar 

  • Dyson FW, Eddington AS, Davidson C (1920) A determination of the deflection of light by the sun’s gravitational field, from observations made at the total eclipse of 29 May 1919. Phil Trans R Soc Lond A 220:291–333

    Article  Google Scholar 

  • Eddington AS (1923) The mathematical theory of relativity. Cambridge University Press, UK

    Google Scholar 

  • Einstein A (1920) Relativity: the special and general theory. Henry Holt and Company, NY

    Google Scholar 

  • Eubanks TM (1991) A consensus model for relativistic effects in geodetic VLBI. In: Eubanks TM (ed) Proceedings of the USNO workshop on relativistic models for use in space geodesy, pp 60–82

    Google Scholar 

  • Eubanks TM, Matsakis DN, Martin JO, Archinal BA, McCarthy DD, Klioner SA, Shapiro S, Shapiro II (1997) Advances in solar system tests of gravity, American Physical Society, APS/AAPT Joint Meeting, 18–21 April, 1997 abstract #K11.05

    Google Scholar 

  • Fomalont EB, Sramek RA (1975) A confirmation of Einstein’s general theory of relativity by measuring the bending of microwave radiation in the gravitational field of the Sun. Astron J 199(3):749–755

    Google Scholar 

  • Fomalont EB, Sramek RA (1976) Measurement of the solar gravitational deflection of radio waves in agreement with general relativity. Phys Rev Lett 36(25):1475–1478

    Article  Google Scholar 

  • Fomalont EB, Kopeikin SM (2003) The measurement of the light deflection from jupiter: experimental results. arXiv:astro-ph/0302294v2, pp 1–10

    Google Scholar 

  • Heinkelmann R, Schuh H (2009) Very long baseline interferometry: accuracy limits and relativistic tests, In: Klioner SA, Seidelmann PK, Soffel MH (eds) Relativity in fundamental astronomy: dynamics, reference frames, and data analysis proceedings IAU symposium no. 261, Cambridge University Press

    Google Scholar 

  • Hugentobler U (2008) Orbit Perturbations due to Relativistic Corrections. Unpublished notes available at ftp://maia.usno.navy.mil/conv2010/chapter10/add_info/

  • Huang C, Ries JC, Tapley BD, Watkins MM (1990) Relativistic effects for near-earth satellite orbit determination. Celest Mech Dyn Astron 48:167–185

    Google Scholar 

  • Huang C, Liu L (1992) Analytical solutions to the four post-newtonian effects in a near-earth satellite orbit. Celest Mech Dyn Astron 53:293–307

    Article  Google Scholar 

  • Hoffman-Wellenhof B, Moritz H (2005) Physical geodesy. Springer-Verlag, Wien

    Google Scholar 

  • Holdridge D (1967) An alternate expression for light time using general relativity, space programs, vol III. NASA, Washington, pp 2–4 (Summary 37–48)

    Google Scholar 

  • Iorio L (2006) A critical analysis of a recent test of the lense–thirring effect with the LAGEOS satellites. J Geod 80:128–136

    Article  Google Scholar 

  • Iorio L (2007) The lense-thirring effect on orbits. In: Iorio L (ed) The measurement of gravitomagnetism. Nova Science Publishers Inc, NY, pp 73–86

    Google Scholar 

  • Iorio L (2010a) On possible a priori “imprinting” of general relativity itself on the performed lense-thirring tests with LAGEOS satellites, communication and network, 2010, vol 2, pp 26–30. doi: 10.4236/cn.2010.21003 (Published Online February 2010 http://www.scirp.org/journal/cn)

  • Iorio L (2010b) Conservative evaluation of the uncertainty in the LAGEOS–LAGEOS II lense-thirring test. Cent Eur J Phys 8(1):25–32

    Article  Google Scholar 

  • Iorio L (2011) Effects of standard and modified gravity on interplanetary ranges. Int J Mod Phys D 20:181–232 (arXiv:1002.4585v5 [gr-qc])

    Article  Google Scholar 

  • Kaplan GH (2005) The IAU resolutions on astronomical reference systems time scales, and earth rotation models, explanation and implementation, United States Naval Observatory Circular No. 179, USNO, Washington

    Google Scholar 

  • Kouba J (2004) Improved relativistic transformations in GPS. GPS Solutions 8:170–180

    Article  Google Scholar 

  • Klioner SA (1991) Proceedings of AGU chapman conference on geodetic VLBI: monitoring global change. In: Carter WE (ed) (NOAA Tech. Rep. NOS 137, NGS 49; Washington, DC: AGU), p 188

    Google Scholar 

  • Klioner SA, Kopeikin SM (1992) Microarcsecond astrometry in space—relativistic effects and reduction of observations. Astron J 104:897–914

    Article  Google Scholar 

  • Klioner SA (2003) A practical relativistic model for microarcsecond astrometry in space. Astron J 125:1580–1597

    Article  Google Scholar 

  • Kopeikin SM (2001) Testing the relativistic effect of the propagation of gravity by very long baseline interferometry. Astrophys J 556:L1–L5

    Article  Google Scholar 

  • Kopeikin SM, Schäfer G (1999) Lorentz covariant theory of light propagation in gravitational fields of arbitrary-moving bodies. Phys Rev D 60:124002 (arXiv:gr-qc/9902030v5)

    Article  Google Scholar 

  • Lambert SB, Le Poncin-Lafitte C (2009) Determining the relativistic parameter γ using very long baseline interferometry. Astron Astrophys 499:331–335 (arXiv:0903.1615v1)

    Article  Google Scholar 

  • Larson KL, Ashby N, Hackman C, Bertiger W (2007) An assessment of relativistic effects for low earth orbiters: the GRACE satellites. Metrologia 44:484–490

    Article  Google Scholar 

  • Lebach DE, Corey BE, Shapiro II, Ratner MI, Webber JC, Rogers AEE, Davis JL, Herring TA (1995) Measurement of the solar gravitational deflection of radio waves using very-long-baseline interferometry. Phys Rev Lett 75(8):1439–1442

    Article  Google Scholar 

  • Lense J, Thirring H (1918) Uber die Einfluss der Eigenrotation der Zentralkorper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Phys Zeitschr, vol 19, p 156. English edition: Lense J, Thirring H (1984) Gen Relativ Gravitation (trans: Mashoon B, Hehl FW, Theiss DS (eds)), vol 16, p 711

    Google Scholar 

  • Lindegren L (2009) Gaia: Astrometric performance and current status of the project, in: relativity in fundamental astronomy. In: Klioner SA, Seidelmann PK, Soffel MH Proceedings IAU symposium: dynamics, reference frames, and data analysis, proceedings IAU symposium no. 261, Cambridge University Press

    Google Scholar 

  • Lucchesi DM (2003) LAGEOS II perigee shift and Schwarzschild gravitoelectric field. Phys Lett A 318:234–240

    Article  Google Scholar 

  • Lucchesi DM, 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 non-newtonian gravity. Phys Rev Lett 105:231103

    Article  Google Scholar 

  • MacMillan D, Petrachenko W, Niell A, Corey B, Behrend D, Schuh H (2011) VLBI2010: next generation VLBI System for geodesy and astrometry, Geophysical Research Abstracts, Vol. 13, EGU2011-13547, 2011, EGU General Assembly 2011

    Google Scholar 

  • Margot J, Giorgini JD (2009) Probing general relativity with radar astrometry in the inner solar system. In: Klioner SA, Seidelmann PK, Soffel MH (eds) Relativity in fundamental astronomy: dynamics, reference frames, and data analysis, proceedings IAU symposium no. 261, Cambridge University Press

    Google Scholar 

  • McCarthy DD, Petit G (2003) IERS conventions (2003), (IERS technical note; 32) Frankfurt am Maim: Verlag des Bundesamts für Kartographie und Geodäsie. Available at http://www.iers.org/nn_11216/IERS/EN/Publications/TechnicalNotes/tn32.html

  • Merkowitz SM (2010) Tests of gravity using lunar laser ranging. Living Rev Relativ, vol 13, p 7. Available at http://www.livingreviews.org/lrr-2010-7 (Online Article: cited on 12 Sep 2011)

  • Misner CW, Thorne KS, Wheeler JA (1973) Gravitation. W. H Freeman and Company, San Francisco

    Google Scholar 

  • Moran J (1989) Introduction to VLBI. In: Felli M, Spencer RE (eds) Very long baseline interferometry, techniques and applications. Kluwer Academic Publishers, Dordrecht, pp 27–45

    Chapter  Google Scholar 

  • Moyer TD (2000) DESCANSO book series, deep space communications and navigation series. In: Yuen JH (ed) Formulation for observed and computed values of deep space network data types for navigation, vol 2

    Google Scholar 

  • Montenbruck O, Gill E (2001) Satellite orbits: models, methods and applications. Springer-Verlag, Berlin

    Google Scholar 

  • Müller J, Soffel M, Klioner SA (2008) Geodesy and relativity. J Geod 82:133–145

    Article  Google Scholar 

  • Murphy TW Jr, Adelberger EG, Battat JBR, Carey LN, Hoyle CD, LeBlanc P, Michelsen EL, Nordtvedt K, Orin AE, Strasburg CW, Stubss CW, Swanson HE, Williams E (2007) APOLLO: the apache point observatory lunar laser-ranging operation: instrument description and first detections. Publ Astron Soc Pac 120:20–37 2008 (arXiv:0710.0890v2)

    Article  Google Scholar 

  • Murphy T Jr (2009) Lunar ranging, gravitomagnetism, and APOLLO. Space Sci Rev 148:217–223

    Article  Google Scholar 

  • Newton I (1726) Principia: the mathematical principles of natural philosophy. English edition: (Motte A, Adee D), New York

    Google Scholar 

  • Nelson RA, Ely TA (2006) Relativistic transformations for time synchronization and dissemination in the solar system. In: Proceedings of 38th annual precise time and time interval (PTTI) meeting. http://www.pttimeeting.org/archivemeetings/ptti2006.html, online article: cited on 9 May 2011

  • Neumann GA, Cavanaugh JF, Coyle DB, McGarry J, Smith DE, Sun X, Torrence M, Zagwodzki TW, Zuber MT (2006) Laser ranging at interplanetary distances. http://cddis.gsfc.nasa.gov/lw15/docs/papers/Laser Ranging at Interplanetary Distances.pdf, online article: cited on 11 Sept 2011. In: Proceedings of the 15th international workshop on laser ranging, Canberra, Australia

  • Pavlis DE, Poulose SG, Deng C, McCarthy JJ (2007) GEODYN II system documentation. SGT-Inc., Greenbelt, MD, contractor report

    Google Scholar 

  • Perryman MAC, de Boer KS, Gilmore G, Høg E, Lattanzi MG, Lindegren L, Luri X, Mignard F, Pace O, de Zeeuw PT (2001) GAIA: composition, formation and evolution of the galaxy. Astron Astrophys 369:339–363

    Article  Google Scholar 

  • Petit G (2009) Relativity in the IERS conventions. In: Klioner SA, Seidelmann PK, and Soffel MH (eds) Relativity in fundamental astronomy: dynamics, reference frames, and data analysis. In: Proceedings IAU symposium no. 261, Cambridge University Press

    Google Scholar 

  • Petit G, Luzum B (2010) IERS conventions (2010). In: Petit G, Luzum B (eds) (IERS Technical Note; No. 36). Bundesamts für Kartographie und Geodäsie, Frankfurt am Main. Available at http://www.iers.org/nn_11216/IERS/EN/Publications/TechnicalNotes/tn36.html

  • Pitjeva EV (2005) Relativistic effects and solar oblateness from radar observations of planets and spacecraft. Astron Lett 31:340–349

    Article  Google Scholar 

  • Robertson HP (1962) Relativity and cosmology. In: Deutsch AJ, Klemperer WB (eds) Space age astronomy. Academic, NY, pp 228–235

    Google Scholar 

  • Robertson DS, Carter WE (1984) Relativistic deflection of radio signals in the solar gravitational field measured with VLBI. Nature 310:572–574

    Article  Google Scholar 

  • Robertson DS, Carter WE, Dillinger WH (1991) New measurement of the solar gravitational deflection of radio signals using VLBI. Nature 349:768–770

    Article  Google Scholar 

  • Ries JC, Huang C, Watkins MM (1988) Effect of general relativity on a near-earth satellite in the geocentric and barycentric reference frames. Phys Rev Lett 61:903–906

    Article  Google Scholar 

  • Riley WJ (2007) Handbook of frequency stability analysis. Hamilton Technical Services, USA, pp 22–23

    Google Scholar 

  • Schuh H, Fellbaum M, Campbell J, Soffel M, Ruder H, Schneider M (1988) On the deflection of radio signals in the gravitational field of Jupiter. Phys Lett A 129:299–300

    Article  Google Scholar 

  • Schwarzschild K (1916) On the gravitational field of a mass point according to Einstein’s theory. Sitzungsber Preuss AkadWiss, Phys Math Kl, vol 189, arXiv:physics/9905030v1, translated by S. Antoci and A. Loinger

    Google Scholar 

  • Senior KL, Ray JR, Beard RL (2008) Characterization of periodic variations in the GPS satellite clocks. GPS Solut 12:211–225

    Article  Google Scholar 

  • Shapiro II (1964) Fourth test of general relativity. Phys Rev Lett 13:789–791

    Article  Google Scholar 

  • Shapiro II (1967) New method for the detection of light deflection by solar gravity. Science 157:806–808

    Article  Google Scholar 

  • Shapiro II, Pettengill GH, Ash ME, Stone ML, Smith WB, Ingalls RP, Brockelman RA (1968) Fourth test of general relativity: preliminary results. Phys Rev Lett 20:266

    Google Scholar 

  • Shapiro SS, Davis JL, Lebach DE, Gregory JS (2004) Measurement of the solar gravitational deflection of radio waves using geodetic very-long-baseline interferometry data, 1979–1999. Phys Rev Lett 92(12):1–4 121101

    Article  Google Scholar 

  • Smith DE, Zuber MT, Xiaoli S, Neumann GA, Cavanaugh JF, McGarry JF, Zagwodzki TW (2006) Two-way laser link over interplanetary distance. Science 311:53

    Article  Google Scholar 

  • Soffel M, Klioner SA, Petit G, Wolf P, Kopeikin SM, Bretagnon P, Brumberg VA, Capitaine N, Damour T, Fukushima T, Guinot B, Huang T-Y, Lindegren L, Ma C, Nordtvedt K, Ries JC, Seidelmann PK, Vokrouhlicky′ D, Will CM, Xu C (2003) The IAU 2000 resolutions for astrometry, celestial mechanics, and metrology in the relativistic framework: explanatory supplement. Astron J 126:2687–2706

    Article  Google Scholar 

  • Sovers O, Fanselow J, Jacobs C (1998) Astrometry and geodesy with radio interferometry: experiments, models, results. Rev Mod Phys 70:1393–1454

    Article  Google Scholar 

  • Tapley BD, Schutz BE, Born GH (2004) Statistical orbit determination. Elsevier Academic Press, London

    Google Scholar 

  • Turon C, O’Flaherty KS, Perryman MAC (eds) (2005) The three-dimensional universe with GAIA, ESA SP-576

    Google Scholar 

  • Turyshev SG (2009) Experimental tests of general relativity: recent progress and future directions. Uspekhi Fizicheskikh Nauk, vol 179, p 3. arXiv:0809.3730 [gr-qc]

    Google Scholar 

  • Turyshev SG, Farr W, Folkner WM, Girerd AR, Hemmti H, Murphy TW, Williams JG, Degnan JJ (2010) Advancing tests of relativistic gravity via laser ranging to Phobos. Experim Astron 28(2–3):209–249 (arXiv:1003.4961v2)

    Article  Google Scholar 

  • Vecchiato A, Lattanzi MG, Bucciarelli B, Crosta M, de Felice F, Gai M (2003) Testing general relativity by micro-arcsecond global astrometry. Astron Astrophys 399:337–342

    Article  Google Scholar 

  • Vallado DA (2001) Fundamentals of astrodynamics and applications, 2nd edn., Space technology libraryMicrocosm Press, California

    Google Scholar 

  • Wei-qun Z, Chuan-fu L, Shuang-lin Y, Guan-zhong W, Yi-ping Z, Pei-hong Y, Jian Z (2001) A study and performance evaluation of hydrogen maser used in Chinese mobile VLBI stations. Chin Astron Astrophys 25(3):390–397

    Article  Google Scholar 

  • Will CM, Nordtvedt K Jr (1972) Conservation laws and preferred frames in relativistic gravity. I. Preferred-frame theories and an extended PPN formalism. Astrophys J 177:757–774

    Article  Google Scholar 

  • Will CM (2006) The confrontation between general relativity and experiment. Liv Rev Relativ. http://relativity.livingreviews.org/Articles/lrr-2006-3/, online article: cited on 12 Sep 2011, (arXiv:gr-qc/0510072v2)

  • Williams JG, Newhall XX, Dickey JO (1996) Relativity parameters determined from lunar laser ranging. Phys Rev D 53:6730–6739

    Article  Google Scholar 

  • Williams JG, Turyshev SG, Boggs DH (2004) Progress in lunar laser ranging tests of relativistic gravity. Phys Rev Lett 93:261101 (arXiv:gr-qc/0411113v2)

    Article  Google Scholar 

  • Williams JG, Turyshev SG, Boggs DH (2009) Lunar laser ranging tests of the equivalence principle with the earth and moon. Int J Mod Phys D 18:1129–1175 (arXiv:gr-qc/0507083v2)

    Article  Google Scholar 

  • Xu G (2007) GPS, theory, algorithms and applications, 2nd edn. Springer, Berlin

    Google Scholar 

  • Zhang J, Zhang K, Grenfell R, Deakin R (2006) Short note: on the relativistic doppler effect for precise velocity determination using GPS. J Geod 80:104–110

    Article  Google Scholar 

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Acknowledgements

A script to generate Fig. 2.1 was kindly provided by Urs Hugentobler, Institute of Astronomical and Physical Geodesy, Technische Universität München. The comments and suggestions by Roberto Peron of Istituto di Fisica dello Spazio Interplanetario (IFSI-INAF) were very valuable and contributed to the readability of this chapter. This work is based on research supported by the National Research Foundation of South Africa under grant IFR2011041500034.

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    Ludwig Combrinck

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  1. Abt. 1 Geodäsie und Fernerkundung, GeoForschungsZentrum Potsdam, Telegrafenberg A 17, Potsdam, 14473, Brandenburg, Germany

    Guochang Xu

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Combrinck, L. (2013). General Relativity and Space Geodesy. In: Xu, G. (eds) Sciences of Geodesy - II. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28000-9_2

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