Terrestrial Time

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This article is about Terrestrial Time; for other meanings of TT, see TT (disambiguation).

Terrestrial Time (TT) is the modern time standard for time on the surface of the Earth. It is the proper time experienced by a clock located on the geoid. In astronomy it is used as the time coordinate for apparent ephemerides for an Earthbound viewer. It is directly related to Geocentric Coordinate Time (TCG), which is the astronomical time standard for the Earth system. TT ticks slower than TCG by a constant rate, due to gravitational time dilation.

History

The approximate concept of TT was standardised by the International Astronomical Union (IAU) in 1976 at its XVIth 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. Both of these time standards turned out to be poorly defined, and TDT was also misnamed, having nothing dynamical about it.

In 1991, in [Recommendation IV of the XXIst 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 [Resolution B1.9 of the XXIVth 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.

Definition

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

TT = (1 - L_G) TCG + E

where TT and TCG are linear counts of SI seconds in Terrestrial Time and Geocentric Coordinate Time respectively, L_G is the constant difference in the rates of the two time scales, and E is a constant to resolve the epochs (see below). L_G is defined as exactly 6.969290134 × 10^-10. (In 1991 when TT was first defined, L_G 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 - L_G x (JD_TCG - 2443144.5003725) x 86400

where JD_TCG 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

JD_TT = E_JD + (JD_TCG - E_JD) (1 - L_G)

where E_JD is 2443144.5003725 exactly.

Realisation

TT is a Platonic time scale: 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(BIPM05)", 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 April 2006 is [TT(BIPM05)].

The international communities of precision timekeeping, astronomy, and radio broadcasts are preparing to create 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.

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