Abstract
The problem of synchronization of the Earth-based clocks has been discussed in the framework of General Relativity Theory. The synchronization is considered as the transformation of the observers' proper time scales to the coordinate time scale of local inertial geocentric reference system, which is single for all the observers. The formulas for the relativistic corrections occurring in some methods of Earth-based clock synchronization (transported clock, duplex communication via geostationary satellite and meteor-burst link, LASSO experiments) have been derived enabling one to attain the accuracy of 0.1 ns.
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References
Allan, D.W.: 1981, ‘Some methods of maintaining and/or generating time and frequency at arbitrary points on surface of the Earth’, J. of the Institution of Electronics and Telecommunication Engineers, 27(10), 383–388.
Allan, D.W. and Ashby, N.: 1986, ‘Coordinate time in the vicinity of the Earth.’ In: Relativity in Celestial mechanics and Astrometry, (J. Kovalevsky and V.A. Brumberg (eds.)), Reidel, Dordrecht, 299–313.
Alley, C.O.: 1983, ‘Proper time experiments in gravitational fields with atomic clocks, aircraft, and laser light pulses.’ In: Quantum Opt., Exp. Gravity, and Meas. Theory, Plenum, New York.
Ashby, N. and Allan, D.W.: 1979, ‘Practical implications of relativity for a global coordinate time scale.’ Radio Science, 14(4), 649–669.
Ashby, N. and Allan, D.W: 1984, ‘Coordinate time on and near the Earth.’ Phys. Rev. Lett., 53(19), 1858; 54(3), 254, 1985.
Ashby, N. and Bertotti, B.: 1986, ‘Relativistic effects in local inertial frames.’ Phys. Rev., D34(8), 2246–2259.
Ashtekar, A. and Magnon, A.: 1975, ‘The Sagnac effect in general relativity.’ Jour. of Math. Phys., 16(2), 341–344.
Bjerhammar, A.: 1985, ‘On a relativistic geodesy.’ Bulletin Géodésique, 59(3), 207–220.
Borisova, L.B., Bronnikov, K.A. and Melnikov, V.N.: 1988, ‘Accounting for gravitational relativistic effects in the definition of single time scale on the Earth and in near-earth space.’ Izmeritelnaya Technika, No.5, 31–33. (in Russian).
Born, M.: 1962, Einstein's theory of relativity. Dover Publ., New York.
Brumberg, V.A.: 1972, Relativistic Celestial Mechanics. Nauka, Moscow. (in Russian).
Brumberg, V.A.: 1987, ‘Post-post-Newtonian propagation of light in the Schwarzschild field.’ Kinematica i Fizika Neb. Tel, 3(1), 8–13. (in Russian).
Brumberg, VA.: 1991, ‘Relativistic hierarchy of reference systems and time scales.’ In: Proc. IAU Colloquium No.127, in press.
Brumberg, V.A. and Kopejkin, S.M.: 1989, ‘Relativistic theory of celestial reference frames.’ In: Reference Systems (J. Kovalevsky, I.I. Muller, B. Kolaczek (eds.)), Kluwer, Dordrecht, 115.
Brumberg, V.A. and Kopejkin, S.M.: 1990, ‘Relativistic time scales in the Solar system’. Celestial Mechanics, 48, 23–44.
Clark, T.A., Counselman III, C.C. et al.: 1979, ‘Synchronization of clocks by very long baseline interferometry’. IEEE Trans. on instrum. and measur., IM-28(3), 184–187.
Cohen, J.M. and Moses, H.E.: 1977, ‘New test of the synchronization procedure in noninertial systems’. Phys. Rev. Lett., 39(26), 1641–1643.
Cohen, J.M., Moses, H.E. and Rosenblum, A.: 1983b, ‘Clock-transport synchronization in noninertial frames and gravitational fields’. Phys. Rev. Lett., 51(17), 1501–1502.
Cohen, J.M., Moses, H.E. and Rosenblum, A.: 1983b, ‘Accurate time-keeping and accurate navigation’. In: Proc. of IEEE Military Communications Conference', 3, New York, 729–730.
Cohen, J.M., Moses, H.E. and Rosenblum, A.: 1984, ‘Electromagnetic synchronization of clocks with finite separation in a rotating system’. Classical and Quantum Gravity, 1(6), L57-L59.
Counselman III, C.C., Shapiro, I.I., Rogers, A.E.E., et al.: 1977, ‘ VLBI clock synchronization’. Proc. IEEE, 65(11), 1622–1623.
Einstein, A.: 1953, The meaning of relativity. Princeton.
Fock, A.V.: 1959, Theory of Space, Time and Gravitation. Pergamon Press, London.
Fukushima, T.: 1990, Circular 13, Sub-Group on Astronomical Constants, IAU Working Group on Reference Systems.
Fukushima, T., Fujimoto, M.-K., Kinoshita, H. and Aoki, S.: 1986b, ‘A system of astronomical constants in the relativistic framework’. Celestial Mechanics, 38 (3), 215–230.
Fukushima, T., Fujimoto, M.-K., Kinoshita, H. and Aoki, S.: 1986b, ‘Coordinate systems in the general relativistic framework’. In: Reference Systems (J. Kovalevsky, I.I. Muller, B. Kolaczek (eds.)), Kluwer, Dordrecht, 145–168.
Gubanov, V.S., Kajdanovskij, M.N. and Umarbaeva, N.D., 1989, ‘Application of interferomeri technique in clock comparison via geostationary retranslator’. Kinematica i Fizika Neb. Tel, 5(6), 84–88. (in Russian).
Guinot, B.: 1990, Circular 3, Sub-Group on Time, IAU Working Group on Reference Systems.
Hellings, R.W.: 1986, ‘Relativistic effects in astronomical timing measurements’. Astron. J., 91(3), 650–659; 92 (6), 1446.
Huang, T.-Y, Zhu, J., Xu, B.-X. and Zhang, H.: 1989, ‘The concept of International Atomic Time (TAI) and Terrestrial Dynamic Time (TDT)’. Astronomy and Astrophysics, 220(1–2), 329–334.
Kascheev, B.L. and Bondar, B.G.: 1989, Meteor-Burst Link. UMK VO, Kiev. (in Russian).
Klioner, S.A.: 1989a, ‘Propagation of the Light in the Barycentric Reference System considering the Motion of the Gravitating Masses’ Preprint of the Institute of Applied Astronomy No 6, Leningrad. (in Russian).
Klioner, S.A.: 1989b, ‘Influence of the Quadrupole Field and Rotation of the Bodies on the Light Propagation in the Barycentric Reference System’ Preprint of the Institute of Applied Astronomy No 12, Leningrad. (in Russian).
Klioner, S.A.: 1990a, ‘Motion of photons and relativistic reduction of observations of near-Earth objects’ In: Abstracts ofreports of international symposium ‘Motion of Test Bodies in the Relativistic Gravitational Theory’, 23–26 May, 1990, Vilnius, 34–35. (in Russian).
Klioner, S.A.: 1990b, ‘Relativistic aspect of Earth-based clock synchronization’. Preprint of the Institute of Applied Astronomy No 25, Leningrad. (in Russian).
Kopejkin, S.M.: 1988, ‘Celestial Coordinate Reference Systems in Curved Space-Time’. Celestial Mechanics, 44, 87–115. (in Russian).
Kopejkin, S.M.: 1989, ‘Asymptotic matching of the Solar-system gravitational Fields’. Astron. Zh., 66(6), 1289–1303.
Kopejkin, S.M.: 1991, ‘Relativistic manifestations of gravitational fields in gravimetry and geodesy’. Manuscripta Geodaetica, in press.
Landau, L.D. and Lifshitz, E.M.: 1975, The Classical Theory of Fields, Pergamon Press, Oxford.
Matisson, E.M.: 1989, ‘Ultra stable clocks for use in space’. Advances in space research, 9(9), 13–19.
Møller, C.: 1972, The Theory of Relativity, Clarendon Press, Oxford.
Podlaha, M.F.: 1984, ‘Note on the Cohen, Moses and Rosenblum letter about the slow-clock transport synchronization in noninertial reference systems’. Lettere Nuovo Cimento, 40(7), 223–224.
Post, E.J.: 1967, ‘Sagnac effect’. Reviews of Mod. Phys., 39(2), 475–493.
Richter, G.W. and Matzner, R.A.: 1981, ‘Gravitational Deflection of the Light at 11/2 PPN Order’. Astrophys. and Sp.Sci., 79(1), 119–127.
Richter, G.W. and Matzner, R.A.: 1982a, ‘Second-order contributions to gravitational deflection of light in the parametrized post-Newtonian formalism’. Phys. Rev, D26(6), 1219–1224.
Richter, G.W. and Matzner, R.A.: 1982b, ‘Second-order contributions to gravitational deflection of light in the PPN. H Photon orbits and deflections in three dimensions’. Phys. Rev., D26(10), 2549–2556.
Richter, G.W. and Matzner, R.A.: 1983, ‘Second-order contributions to relativistic time delay in the parametrized post-Newtonian formalism’. Phys. Rev., D28(12), 3007–3012.
Saburi, Y: 1976, ‘Observed time discontinuity of clock synchronization in rotating frame of the Earth’. Journal of Radio Research Laboratories, 23(112), 255–265.
Serene, B.E.H.: 1981, ‘The LASSO experiment and its operational organization’. J. of the Institution of Electronics and Telecommunication Engineers, 27(10), 422–432.
Serene, B.E.H.: 1988, ‘The LASSO experiment onboard Meteosat-P2’. (unpublished)
Skalafuris, A.J.: 1985, ‘Current theoretical attempts toward synchronization of a global satellite network’. Radio Science, 20(6), 1529–1536.
Soffel, M., Herold, H., Ruder, H. and Schneider, M.: 1988, ‘Relativistic theory of gravimetric measurements and definition of the geoid’. Manuscripta Geodaetica, 13(3), 143–146.
Vessot, R.F.C.: 1979, ‘Relativity experiments with clocks’. Radio Science, 14(4), 629–647.
Voinov, A.X.: 1990, ‘Relativistic equations of motion of an Earth satellite’. Manuscripta Geodaetica, 15, 65–73.
Will,C.M.: 1981, Theory and experiment in gravitational physics. Cambridge Univ. Press.
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Klioner, S.A. The problem of clock synchronization: A relativistic approach. Celestial Mech Dyn Astr 53, 81–109 (1992). https://doi.org/10.1007/BF00049363
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DOI: https://doi.org/10.1007/BF00049363