Terrestrial Time

Terrestrial Time

Terrestrial Time (TT) is the modern astronomical standard for the passage of time on the surface of the Earth (for civil purposes, Coordinated Universal Time (UTC) is standard). Since time moves at different rates for observers in different locations (due to relativity), and "the surface of the Earth" is not a single point in space, TT is a theoretical ideal; its measurement is approximated by the International Atomic Time (TAI) + 32.184 seconds.

In technical terms, TT is the proper time experienced by a clock located on the geoid. It is formally defined by its relationship to Geocentric Coordinate Time (TCG), which is the standard for the passage of time at the "center" of the Earth, used in astronomical calculations. In order to simplify calculations involving multiple astronomical bodies (each with their own gravity wells), TCG is defined as an approximation of time as it would pass "without" the relativistic effects of gravity; it therefore ticks by faster than TT.


The approximate concept of TT was standardised by the International Astronomical Union (IAU) in 1976 at its XVI General Assembly, under the name "Terrestrial Dynamical Time" (TDT). It was the counterpart to Barycentric Dynamical Time (TDB), which was a time standard for Solar system ephemerides, based on a Dynamical time scale. Both of these time standards turned out to be poorly defined, and TDT was also misnamed, having nothing dynamical about it.

In 1991, in [http://www.iers.org/MainDisp.csl?pid=98-134 Recommendation IV of the XXI General Assembly] , the IAU redefined TDT more precisely, renaming it to "Terrestrial Time". TT was defined in terms of Geocentric Coordinate Time, which was defined by the same General Assembly. TT was defined to be a linear transformation of TCG, such that TT agrees with proper time on the geoid. This left the exact ratio between TT time and TCG time as something to be determined by experiment. The determination of the gravitational potential at the geoid is a task in physical geodesy.

In 2000, in [http://chiron.mtk.nao.ac.jp/~toshio/iaudiv1/IAU_resolutions/Resol-UAI.htm Resolution B1.9 of the XXIV General Assembly] , the IAU refined the definition of TT by specifying the exact ratio between TT and TCG time as 1 − 6.969290134 × 10−10. This has the effect of redefining the geoid in terms of a precise gravitational potential, thus removing the need for horologists to study sea levels.


TT differs from TCG by a constant rate. Formally it is defined by the equation

:TT = (1 − LG) TCG + E

where TT and TCG are linear counts of SI seconds in Terrestrial Time and Geocentric Coordinate Time respectively, LG is the constant difference in the rates of the two time scales, and E is a constant to resolve the epochs (see below). LG is defined as exactly 6.969290134 × 10−10. (In 1991 when TT was first defined, LG was to be determined by experiment, and the best available estimate was 6.969291 × 10−10.)

The equation linking TT and TCG is more commonly seen in the form

:TT = TCG − LG × (JDTCG − 2443144.5003725) × 86400

where JDTCG is the TCG time expressed as a Julian Date. This is just a transformation of the raw count of seconds represented by the variable TCG, so this form of the equation is needlessly complex. The use of a Julian Date does specify the epoch fully, however (see next paragraph). The above equation is often given with the Julian Date 2443144.5 for the epoch, but that is wrong; the value given above is exactly correct.

Time coordinates on the TT and TCG scales are conventionally specified using traditional means of specifying days, carried over from non-uniform time standards based on the rotation of the Earth. Specifically, both Julian Dates and the Gregorian calendar are used. For continuity with their predecessor Ephemeris Time, TT and TCG were set to match ET at around Julian Date 2443144.5 (1977-01-01T00Z). More precisely, it was defined that TT instant 1977-01-01T00:00:32.184 exactly and TCG instant 1977-01-01T00:00:32.184 exactly correspond to the International Atomic Time (TAI) instant 1977-01-01T00:00:00.000 exactly. This is also the instant at which TAI introduced corrections for gravitational time dilation.

TT and TCG expressed as Julian Dates can be related precisely and most simply by the equation

:JDTT = EJD + (JDTCG − EJD) (1 − LG)

where EJD is 2443144.5003725 exactly.


TT is a theoretical ideal, not dependent on a particular realisation. For practical purposes, TT must be realised by actual clocks in the Earth system.

The main realisation of TT is supplied by TAI. The TAI service, running since 1958, attempts to match the rate of proper time on the geoid, using an ensemble of atomic clocks spread over the surface and low orbital space of the Earth. TAI is canonically defined retrospectively, in monthly bulletins, in relation to the readings that particular groups of atomic clocks showed at the time. Estimates of TAI are also provided in real time by the institutions that operate the participating clocks. Because of the historical difference between TAI and ET when TT was introduced, the TAI realisation of TT is defined thus:

:TT(TAI) = TAI + 32.184 s

Because TAI is never revised once published, it is possible for errors in it to become known and remain uncorrected. It is thus possible to produce a better realisation of TT based on reanalysis of historical TAI data. The BIPM has done this approximately annually since 1992. These realisations of TT are named in the form "TT(BIPM07)", with the digits indicate the year of publication. They are published in the form of table of differences from TT(TAI). The latest as of March 2008 is [ftp://ftp2.bipm.fr/pub/tai/scale/ttbipm.07 TT(BIPM07)] .

The international communities of precision timekeeping, astronomy, and radio broadcasts have considered creating a new precision time scale based on observations of an ensemble of pulsars. This new pulsar time scale will serve as an independent means of computing TT, and it may eventually be useful to identify defects in TAI.

ee also

*Time standard
*International Atomic Time

External links

* [http://www.bipm.org/en/scientific/tai/ BIPM]
* [http://tf.nist.gov/general/glossary.htm Time and Frequency from A to Z]
* [http://scienceworld.wolfram.com/astronomy/InternationalAtomicTime.html Time in Astronomy]

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