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Relativity in the global positioning system. (English) Zbl 1023.83005
Summary: The Global Positioning System (GPS) uses accurate, stable atomic clocks in satellites and on the ground to provide world-wide position and time determination. These clocks have gravitational and motional frequency shifts which are so large that, without carefully accounting for numerous relativistic effects, the system would not work. This paper discusses the conceptual basis, founded on special and general relativity, for navigation using GPS. Relativistic principles and effects which must be considered include the constancy of the speed of light, the equivalence principle, the Sagnac effect, time dilation, gravitational frequency shifts, and relativity of synchronization. Experimental tests of relativity obtained with a GPS receiver aboard the TOPEX/POSEIDON satellite will be discussed. Recently frequency jumps arising from satellite orbit adjustments have been identified as relativistic effects. These will be explained and some interesting applications of GPS will be discussed.

MSC:
83B05 Observational and experimental questions in relativity and gravitational theory
83C10 Equations of motion in general relativity and gravitational theory
83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
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[1] ”IAU Resolutions adopted at the 24th General Assembly (Manchester, August 2000)”, project homepage, L’Observatoire de Paris: Le Bureau National de Métrologie – Systèmes de Référence Temps Espace (BNM – SYRTE), (2000). URL (cited on 20 December 2002): http://syrte.obspm.fr/IAU_resolutions/Resol-UAI.htm. 3
[2] NAVSTAR GPS Space Segment and Navigation User Interfaces, Interface Control Document, ICD-GPS-200C, (ARINC Research Corporation, Fountain Valley, CA, 1993). Related online version (cited on 11 June 2007): http://www.navcen.uscg.gov/pubs/gps/icd200/. 5, 9
[3] Department of Defense World Geodetic System 1984 – Its Definition and Relationships with Local Geodetic Systems, NIMA Technical Report, TR8350.2, (National Imagery and Mapping Agency, Bethesda, MD, 2004), 3rd corr. edition. Related online version (cited on 11 June 2007): http://earth-info.nga.mil/GandG/publications/tr8350.2/tr8350_2.html. 2
[4] Allan, D.W., Weiss, M., and Ashby, N., ”Around-the-World Relativistic Sagnac Experiment”, Science, 228, 69–70, (1985). [DOI]. 2
[5] Alley, C., ”Proper time experiments in gravitational fields with atomic clocks, aircraft, and laser light pulses”, in Meystre, P., and Scully, M.O., eds., Quantum Optics, Experimental Gravitation, and Measurement Theory, Proceedings of the NATO Advanced Study Institute on Quantum Optics and Experimental General Relativity, August 1981, Bad Windsheim, Germany, NATO Science Series: B, vol. 94, pp. 363–427, (Plenum Press, New York, 1983). 5
[6] Ashby, N., An Earth-Based Coordinate Clock Network, NBS Technical Note, 659; S.D. Catalog # C13:46:659, (U.S. Dept. of Commerce, U.S. Government Printing Office, Washington, DC, 1975). 2
[7] Ashby, N., and Allan, D.W., ”Practical Implications of Relativity for a Global Coordinate Time Scale”, Radio Sci., 14, 649–669, (1979). [DOI]. 4
[8] Ashby, N., and Bertotti, B., ”Relativistic Effects in Local Inertial Frames”, Phys. Rev. D, 34, 2246–2258, (1986). [DOI]. 10
[9] Ashby, N., and Spilker Jr, J.J., ”Introduction to Relativistic Effects on the Global Positioning System”, in Parkinson, B.W., and Spilker Jr, J.J., eds., Global Positioning System: Theory and Applications, Vol. 1, Progress in Astronautics and Aeronautics, vol. 163, 18, pp. 623–697, (American Institute of Aeronautics and Astronautics, Washington, DC, 1996). 3, 9
[10] Ashby, N., and Weiss, M., Global Positioning System Receivers and Relativity, NIST Technical Note, TN 1385, (National Institute of Standards and Technology, Boulder, CO, 1999). 2
[11] Buisson, J.A., Easton, R.L., and McCaskill, T.B., ”Initial Results of the NAVSTAR GPS NTS-2 Satellite”, in Rueger, L.J. et al., ed., 9th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting, Proceedings of the meeting, held at NASA Goddard Space Flight Center, November 29–December 1, 1977, pp. 177–200, (Technical Information and Administrative Support Division, Goddard Space Flight Center, Greenbelt, MD, 1978). 5
[12] Epstein, M., Stoll, E., and Fine, J., ”Observable Relativistic Frequency Steps Induced by GPS Orbit Changes”, in Breakiron, L.A., ed., 33rd Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting, Proceedings of a meeting held at Long Beach, California, 27–29 November 2001, (U.S. Naval Observatory, Washington, DC, 2002). Related online version (cited on 11 June 2007): http://tycho.usno.navy.mil/ptti/index1.html. 9, 9, 9, 9, 9
[13] Fitzpatrick, P., The Principles of Celestial Mechanics, (Academic Press, New York, 1970). 5, 9, 9, 9, 9 · Zbl 0214.23804
[14] Fliegel, H.F., and DiEsposti, R.S., GPS and Relativity: an Engineering Overview, The Aerospace Corporation Report, ATR-97(3389)-1, (The Aerospace Corporation, El Segundo, CA, 1996). 6
[15] Garland, G.D., The Earth’s Shape and Gravity, (Pergamon Press, New York, 1965). 3
[16] Hulse, R.A., and Taylor, J.H., ”Discovery of a pulsar in a binary system”, Astrophys. J., 195, L51–L53, (1975). [DOI], [ADS]. 13
[17] Kraus, J.D., Antennas, (McGraw-Hill, New York, 1988), 2nd edition. 10
[18] Lambeck, K., in Geophysical Geodesy: The Slow Deformations of the Earth, pp. 13–18, Oxford Science Publications, (Clarendon Press, Oxford; New York, 1988). 3
[19] Malys, S., and Slater, J., ”Maintenance and Enhancement of the World Geodetic System 1984”, in Proceedings of the 7th International Technical Meeting of The Satellite Division of The Institute of Navigation (ION GPS-94), September 20–23, 1994, Salt Palace Convention Center - Salt Lake City, UT, pp. 17–24, (Institute of Navigation, Fairfax, VA, 1994). 2
[20] Mashhoon, B., ”Nonlocal Theory of Accelerated Observers”, Phys. Rev. A, 47, 4498–4501, (1993). [DOI]. 10
[21] Mashhoon, B., ”On the Coupling of Intrinsic Spin with the Rotation of the Earth”, Phys. Lett. A, 198, 9–13, (1995). [DOI]. 10
[22] Parkinson, B.W., and Spilker Jr, J.J., ”Overview of GPS Operation and Design”, in Parkinson, B.W., and Spilker Jr, J.J., eds., Global Positioning System: Theory and Applications, Vol. 1, Progress in Astronautics and Aeronautics, vol. 163, 2, pp. 29–56, (American Institute of Aeronautics and Astronautics, Washington, DC, 1996). 6
[23] Taylor, J.H., ”Binary Pulsars and Relativistic Gravity”, Rev. Mod. Phys., 66, 711–719, (1994). [DOI]. 13
[24] Tetewsky, A.K., and Mullen, F.E., ”Effects of Platform Rotation on GPS with Implications for GPS Simulators”, in Proceedings of the 9th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GPS-96), September 17–20, 1996, Kansas City Convention Center, Kansas City, Missouri, pp. 1917–1925, (Institute of Navigation, Fairfax, VA, 1996). 10
[25] Galileo Open Service Signal In Space Interface Control Document (SIS ICD), (European Space Agency / Galileo Joint Undertaking, Brussels, 2006). Related online version (cited on 6 November 2009): http://www.gsa.europa.eu/go/galileo/os-sis-icd. (document), 12
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