Relativistic Theory for Syntonization of Clocks in the Vicinity of the Earth

G. Petit, P. Wolf

Abstract:	A well known prediction of Einstein's general theory of relativity states that two ideal clocks that move with a relative velocity, and are submitted to different gravitational fields will, in general, be observed to run at different rates. Similarly the rate of a clock with respect to the coordinate time of some spacetime reference system is dependent on the velocity of the clock in that reference system and on the gravitational fields it is submitted to. For the syntonization of clocks and the realization of coordinate times (like TM) this rate shift has to be taken into account at an accuracy level which should be below the frequency stability of the clocks in question, i.e. all terms that are larger than the instability of the clocks should be corrected for. We present a theory for the calculation of the relativistic rate shift for clocks in the vicinity of the Earth, including all terms larger than one part in 10^18. This, together with previous work on clock synchronization (Petit & Wolf 1993, 1994), amounts to a complete relativistic theory for the realization of coordinate time scales at picosecond synchronization and 10^-18 syntonization accuracy, which should be sufficient lo accommodate future developments in time transfer and clock technology.
Published in:	Proceedings of the 26th Annual Precise Time and Time Interval Systems and Applications Meeting December 6 - 8, 1994 Hyatt Regency Reston Town Center Reston, Virginia
Pages:	381 - 392
Cite this article:	Petit, G., Wolf, P., "Relativistic Theory for Syntonization of Clocks in the Vicinity of the Earth," Proceedings of the 26th Annual Precise Time and Time Interval Systems and Applications Meeting, Reston, Virginia, December 1994, pp. 381-392.
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