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Relativistic time scales in the solar system

  • V. A. Brumberg
  • S. M. Kopejkin
Article

Abstract

This paper deals with a self-consistent relativistic theory of time scales in the Solar system based on the construction of the hierarchy of dynamically non-rotating harmonic reference systems for a four-dimensional space-time of general relativity. In our approach barycentric (TB) and terrestrial (TT) times are regarded as the coordinate times of barycentric (BRS) and geocentric (GRS) reference systems, respectively, with an appropriate choice of the units of measurement. This enables us to avoid some of the inconsistencies and ambiguities of the definitions of these scales as these are currently applied. International atomic time (TAI) is shown to be the physical realization of TT on the surface of the Earth. This realization is achieved by a specific procedure to average the readings of atomic clocks distributed over the terrestrial surface, all of them synchronized with respect to TT. Extending TAI beyond the Earth's surface may be performed along a three-dimensional hypersurface TT = const. The unit of measurement of TAI coincides with TB and TT units and is equal to the SI second on the surface of the geoid in rotation. Due to the specific choice of the units of measurement the TB scale differs from the TT (TAI) scale only by relativistic nonlinear and periodic terms resulting from the planetary and lunar theories of motion. The proper time τ0 of any terrestrial observer coincides with the coordinate time τ of the corresponding topocentric reference system (TRS) evaluated at its origin. τ0 is reacted to TT (TAI) by the relativistic transformation involving the GRS velocity of the observer, its height above the geoid and the quadrupole tidal gravitational potential of the external masses. The impact of introducing TB and TT on the units of measurement of length and the basic astronomical constants is discussed.

Keywords

Solar System Gravitational Potential Coordinate Time Atomic Clock Periodic Term 
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References

  1. Allan, D. W. and Ashby, N.: 1986, In Relativity in Celestial Mechanics and Astrometry (Eds. J. Kovalevsky and V. A. Brumberg), p. 299, Reidel, Dordrecht.Google Scholar
  2. Ashby, N. and Allan, D. W.: 1979, Radio Sci., 14, 649.Google Scholar
  3. Ashby, N. and Bertotti, B.: 1986, Phys. Rev., D 34, 2246.Google Scholar
  4. Backer, D. C. and Hellings, R. W.: 1986, Ann. Rev. Astron. Astrophys., 24, 537.Google Scholar
  5. Brumberg, V. A.: 1972, Relativistic Celestial Mechanics, Nauka, Moscow (in Russian).Google Scholar
  6. Brumberg, V. A. and Kopejkin, S. M.: 1989a, In. Reference Frames (eds. J. Kovalevsky, I. I. Mueller and B. Kolaczek), p. 115, Kluwer, Dordrecht.Google Scholar
  7. Brumberg, V. A. and Kopejkin, S. M.: 1989b, Nuovo Cim. B 103, 63.Google Scholar
  8. Brumberg, V. A. and Kopejkin, S. M.: 1989c, Kinematika i Fizika Neb. Tel., 5, 3 (in Russian).Google Scholar
  9. Canuto, V. M. and Goldman, I.: 1982, Nature, 296, 709.Google Scholar
  10. Canuto, V. M., Goldman, I. and Shapiro, I. L: 1984, Astrophys. J., 276, 1.Google Scholar
  11. CCIR, 1982. Report 439-3, Recommendations and Reports of the CCIR. XVth Plenary Assembly, Geneva.Google Scholar
  12. Counselman III, C. C. and Shapiro, I. L: 1968, Science, 162, 352.Google Scholar
  13. Damour, T.: 1983, InGravitational Radiation (eds. N. Deruelle and T. Piran), p. 59, North-Holland, Amsterdam.Google Scholar
  14. Damour, T.: 1987, In 300 Years of Gravitation (eds. S. W. Hawking and W. Israel), p. 128, Cambridge Univ. Press, Cambridge.Google Scholar
  15. Fairhead, L., Bretagnon, P. and Lestrade, J. -F.: 1987, In The Earth's Rotation and Reference Frames for Geodesy and Geodynamics (eds. G. Wilkins and A. Babcock), p. 419, Kluwer, Dordrecht.Google Scholar
  16. Fock, A. V.: 1959, Theory of Space, Time and Gravitation, Pergamon Press, London.Google Scholar
  17. Fukushima, T., Fujimoto, M. K., Kinoshita, H. and Aoki, S.: 1986a, In Relativity in Celestial Mechanics and Astrometry (eds. J. Kovalevsky and V. A. Brumberg), p. 145, Reidel, Dordrecht.Google Scholar
  18. Fukushima, T., Fujimoto, M. -K., Kinoshita, H. and Aoki, S.: 1986b, Celes. Mech., 38, 215.Google Scholar
  19. Fukushima, T.: 1989, In. Reference Frames (eds. J. Kovalevsky, I. I. Mueller and B. Kolaczek), p. 417, Kluwer, Dordrecht.Google Scholar
  20. Guinot, B.: 1986, Celest. Mech., 38, 155.Google Scholar
  21. Guinot, B.: 1988, Astron. Astrophys., 192, 370.Google Scholar
  22. Guinot, B. and Seidelmann, P. K.: 1988, Astron. Astrophys., 194, 304.Google Scholar
  23. Hellings, R. W.: 1986, Astron. J., 91, 650; 92, 1446.Google Scholar
  24. Hirayma, Th., Kinoshita, H., Fujimoto, M. -K. and Fukushima, T.: 1988, IUGG XIX Gen. Assembly, Vancouver, 1, 91.Google Scholar
  25. Huang, T. -Y., Zhu, J., Xu, B. -X. and Zhang, H.: 1989, Astron. Astrophys., 220, 329.Google Scholar
  26. IAU: 1977, Transactions of the IAU, 16 B, 60, Reidel, Dordrecht.Google Scholar
  27. Japanese Ephemeris: 1985, Basis of the New Japanese Ephemeris, Tokyo.Google Scholar
  28. Kopejkin, S. M.: 1985, Astron. Zh., 62, 889 (in Russian). English translation in Sov. Astron., 29, No. 5.Google Scholar
  29. Kopejkin, S. M.: 1988, Celest. Mech., 44, 87.Google Scholar
  30. Kopejkin, S. M.: 1989a, Astron. Zh., 66, 1069. (in Russian).Google Scholar
  31. Kopejkin, S. M.: 1989b, Astron. Zh., 66, No. 6. (in Russian).Google Scholar
  32. Kovalevsky, J. and Mueller, I. L: 1981, In Reference Coordinate Systems for Earth Dynamics (eds. E. M. Gaposchkin and B. Kolaczek), p. 375, Reidel, Dordrecht.Google Scholar
  33. Landau, L. D. and Lifshitz, E. M.: 1975, The Classical Theory of Fields, Pergamon Press, Oxford.Google Scholar
  34. Mansfield, V. N.: 1976, Nature, 261, 560.Google Scholar
  35. Misner, C. W., Thorne, K. S. and Wheeler, J. A.: 1973, Gravitation, Freeman, San Francisco.Google Scholar
  36. Moritz, H.: 1980, Advanced Physical Geodesy, Wichmann, Karlsruhe and Abacus Press, Kent.Google Scholar
  37. Moritz, H. and Mueller, I. I.: 1987, Earth Rotation: Theory and Observation, Ungar, New York.Google Scholar
  38. Moyer, T. D.: 1981, Celest. Mech., 23, 33 and 57.Google Scholar
  39. Mulholland, J. D.: 1972, Publ. Astron. Soc. Pacific, 84, 357.Google Scholar
  40. Murray, C. A.: 1983, Vectorial Astrometry, Adam Hilger, Bristol.Google Scholar
  41. Ries, J. C., Huanghand, K. and Watkins, M.: 1988, Phys. Rev. Lett., 61, 903.Google Scholar
  42. Schäfer, G. 1986, Gen. Relativity Gravitation, 18, 255.Google Scholar
  43. Soffel, M., Herold, H., Ruder, H. and Schneider, M.: 1987, Manuscripta Geodaetica, 13, 143.Google Scholar
  44. Soffel, M. H.: 1989, Relativity in Astrometry, Celestial Mechanics and Geodesy, Springer, Berlin.Google Scholar
  45. Soma M., Hyrayama, Th. and Kinoshita, H.: 1987, Celest. Mech., 41, 389.Google Scholar
  46. Thomas, J.: 1975, Astron. J., 80, 405.Google Scholar
  47. Wilkins, G. A.: 1974, In Time Determination, Dissemination and Synchronization (eds. H. Enslin and E. Proverbio), p. 241, Anastatiche 3T, Cagliari.Google Scholar
  48. Will, C. M.: 1981, Theory and Experiment in Gravitational Physics, Cambridge Univ. Press, Cambridge.Google Scholar
  49. Winkler, G. M. R. and Van Flandera, T. C.: 1977, Astron. J., 81, 84.Google Scholar
  50. Zhongolovich, I. D.: 1957, Bull. Inst. Theoret. Astron., 6, 505 (in Russian).Google Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • V. A. Brumberg
    • 1
  • S. M. Kopejkin
    • 2
  1. 1.Institute of Applied AstronomyLeningradU.S.S.R.
  2. 2.Sternberg State Astronomical InstituteMoscowU.S.S.R.

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