Measurement Techniques

, Volume 57, Issue 8, pp 891–897 | Cite as

Relativistic Effects on Moving Clocks

  • V. F. Fateev
  • V. P. Sysoev

Using the general theory of relativity we obtain practical formulas for calculating relativistic effects on clocks moving in the anomalous gravitational field of the Earth. We examine compensation methods for these effects and determine the compensation error using the orbital parameters of the motion path for clocks in GLONASS/GPS systems


moving clocks relativistic effects gravitational potential,compensation methods 


  1. 1.
    J. Hafele and R. Keating, “Around-the-World Atomic Clocks: Predicted Relativistic Time Gains,” Science, 177, 166–168 (1972).ADSCrossRefGoogle Scholar
  2. 2.
    R. Vessot and M. A. Levine, “Test of the Equivalence Principle Using a Space-Borne Clock,” Gen. Rel. Grav., 10, No. 3, 181–204 (1979).ADSCrossRefGoogle Scholar
  3. 3.
    L. B. Borisova and V. N. Melnikov, “Relativistic corrections to readings from a portable clock,” Izmer. Tekhn., No. 4, 13–15 (1988); Measur. Techn., 31, No. 4, 323–327 (1988).Google Scholar
  4. 4.
    V. F. Fateev, Relativistic Theory of Navigation and Timing, Mozhaiskii VKA, Leningrad (1988).Google Scholar
  5. 5.
    Yu. N. Medvedev and Yu. F. Smirnov, “Evaluating relativistic and gravitational corrections when moving transportable quantum clocks,” Metrology of Time and Space: Proc. 5th Russ. Symp., VNIIFTRI, Moscow (1994), pp. 342–343.Google Scholar
  6. 6.
    G. Petit and P. Wolf, “Relativistic theory for time comparisons: a review,” Metrologia, 42 , 138–144 (2005).ADSCrossRefGoogle Scholar
  7. 7.
    B. A. Gaygerov and V. P. Sysoev, “Relativistic effects in comparisons of time scales by means of transportable quantum clocks,” Izmer. Tekhn., No. 2, 25–29 (2012); Measur. Techn., 55, No. 2, 143–150 (2012).Google Scholar
  8. 8.
    K. Muller, Theory of Relativity, Atomizdat, Moscow (1975).Google Scholar
  9. 9.
    S. Kopeikin, M. Efroimsky, and G. Kaplan, Relativistic Celestial Mechanics of the Solar System, WILEY-VCH, Berlin (2011).CrossRefMATHGoogle Scholar
  10. 10.
    Recommendation ITU-R TF.2018 (08/2012), Relativistic Time Transfer in the Vicinity of Earth and in the Solar System,, accessed 03.28.2014.
  11. 11.
    N. P. Grushinskij, Theory of the Figure of the Earth, Nauka, Moscow (1976).Google Scholar
  12. 12.
    V. P. Sysoev et al., “Transportable quantum clock based on a hydrogen generator,” Metrology of Time and Space: Proc. 6th Int. Symp., VNIIFTRI, Moscow (2012), pp. 31–33.Google Scholar
  13. 13.
    I. A. Andronov and G. B. Malykin, “Physical problems of a fiber gyroscope and the Sagnac effect,” Usp. Phys. Nauk, 172, No. 8, 849–873 (2002).CrossRefGoogle Scholar
  14. 14.
    N. Ashby, “Relativity in the Global Positioning System,” Liv. Rev. Relat., 6, 1–42 (2003).Google Scholar
  15. 15.
    N. K. Pavlis et al., “The development and evaluation of the Earth Gravitational Model 2008 (EGM2008),” J. Geophys. Res., 117, B04406 (2012).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.All-Russia Research Institute of Physicotechnical and Radio Measurements (VNIIFTRI)MendeleevoRussia

Personalised recommendations