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# Atomic Time

Fundamentals
Title Atomic Time
Author(s) J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
Level Basic
Year of Publication 2011

## TAI

TAI stands for International Atomic Time and was established as a reference time by the Bureau International de l'Heure. Its initial epoch was matched to the $0^{h}0^{m}0^{s}$ of UT2 scale of January 1$^{st}$, 1958, so the difference between TAI and UT2 was $0$ in this epoch.

The TAI second duration was defined in 1967 as the same as the ET second, according to the following sentence: The TAI second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Cesium 133 atom.

It is realized from several high-precision atomic clocks held at standards institutes in various countries, it is, therefore, a statistical time. There is an elaborate process of continuous intercomparison, leading to a weighted average of all the clocks involved.

After this definition had been done, the TAI second substituted for ET second as the SI second in 1967. With the next three points in mind, one can obtain the relationship between ET and TAI:

• TAI second = ET second
• The difference between ET time and UT2 time at $0^{h}0^{m}0^{s}$ of UT2 scale of January 1$^{st}$, 1958 was $32.184$ seconds.
• TAI time = UT2 time at $0^{h}0^{m}0^{s}$ of UT2 scale of January 1$^{st}$, 1958.

Obviously the relationship between TAI scale and ET scale (or TDT scale afterwards) is a constant offset of $32.184$ seconds.

## UTC

UTC stands for Universal Time Coordinated and is the compromise between TAI and UT1. In fact UTC, as an atomic time, is as uniform as the TAI scale can be, but it is always kept closer than $0.9$ seconds with respect to UT1, in order to follow earth's rotation variations. This is accomplished by adding (or subtracting) a certain number of Leap Seconds to TAI. This number, which is refreshed periodically, is provided by the IERS (International Earth Rotation Service) [footnotes 1].

This time is very important since all currently used time signals are synchronised with UTC.

Official Time is the one used by all nations of the world. It usually differs by an integer number of hours or half an hours with regard to UTC. This difference is given by time zones and the proper adjustments in summer and winter.

## GNSS Time

The GPST, GLONASST, GST and BDT are the reference times used in GPS, GLONASS, Galileo and BeiDou systems, respectively.

GPS Time (GPST) is a continuous time scale (no leap seconds) defined by the GPS Control segment on the basis of a set of atomic clocks at the Monitor Stations and onboard the satellites. It starts at 0h UTC (midnight) of January 5th to 6th 1980 (6.d0). At that epoch, the difference TAI−UTC was 19 seconds, thence GPS−UTC=n − 19s. GPS time is synchronised with the UTC(USNO) at 1 microsecond level (modulo one second), but actually is kept within 25 ns.

GLONASS Time (GLONASST) is generated by the GLONASS Central Synchroniser and the difference between the UTC(SU) and GLONASST should not exceed 1 millisecond plus three hours[footnotes 2] (i.e.,$GLONASST=UTC(SU)+3^h-\tau$, where $|\tau|\lt 1 milisec.$), but $\tau$ is typically better than 1 microsecond. Note: Unlike GPS, Galileo or BeiDou, GLONASS time scale implements leap seconds, like UTC.

Galileo System Time (GST) is a continuous time scale maintained by the Galileo Central Segment and synchronised with TAI with a nominal offset below 50 ns. The GST start epoch is 0h UTC on Sunday, 22 August 1999 (midnight between 21 and 22 August).

BeiDou Time (BDT) is a continuous time scale starting at 0h UTC on January 1st, 2006 and is synchronised with UTC within 100 ns< (modulo one second), [BeiDou-SIS-ICD-Test, 2011].

## Notes

1. ^ The fact that a certain number of seconds are added to TAI in order to obtain UTC may indicate that the earth rotation speed is slowing down, but the conclusion that the earth will stop rotating is absolutely wrong. Although since 1972 the earth's rotation rate has been slowing down (that is the same to say that leap seconds are being added during last years) this tendency may change in the future.
2. ^ The difference between Moscow Time and Greenwich Mean Time (GMT).

## References

• BeiDou-SIS-ICD-Test, 2011. Technical report. BeiDou Navigation Satellite System Signal In Space. Interface Control Document (Test version), December 2011.