Terrestrial Time


Terrestrial Time is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth.
For example, the Astronomical Almanac uses TT for its tables of positions of the Sun, Moon and planets as seen from Earth. In this role, TT continues Terrestrial Dynamical Time, which in turn succeeded ephemeris time. TT shares the original purpose for which ET was designed, to be free of the irregularities in the rotation of Earth.
The unit of TT is the SI second, the definition of which is currently based on the caesium atomic clock, but TT is not itself defined by atomic clocks. It is a theoretical ideal, and real clocks can only approximate it.
TT is distinct from the time scale often used as a basis for civil purposes, Coordinated Universal Time. TT indirectly underlies UTC, via International Atomic Time. Because of the historical difference between TAI and ET when TT was introduced, TT is approximately 32.184 s ahead of TAI.

History

A definition of a terrestrial time standard was adopted by the International Astronomical Union in 1976 at its General Assembly, and later named Terrestrial Dynamical Time. It was the counterpart to Barycentric Dynamical Time, which was a time standard for Solar system ephemerides, to be based on a dynamical time scale. Both of these time standards turned out to be imperfectly defined. Doubts were also expressed about the meaning of 'dynamical' in the name TDT.
In 1991, in , the IAU redefined TDT, also renaming it "Terrestrial Time". TT was formally defined in terms of Geocentric Coordinate Time, defined by the IAU on the same occasion. TT was defined to be a linear scaling of TCG, such that the unit of TT is the SI second on the geoid. This left the exact ratio between TT time and TCG time as something to be determined by experiment. Experimental determination of the gravitational potential at the geoid surface is a task in physical geodesy.
In 2000, the IAU very slightly altered the definition of TT by adopting an exact value for the ratio between TT and TCG time, as .

Current definition

TT differs from Geocentric Coordinate Time by a constant rate. Formally it is defined by the equation
where TT and TCG are linear counts of SI seconds in Terrestrial Time and Geocentric Coordinate Time respectively, is the constant difference in the rates of the two time scales, and is a constant to resolve the epochs. is defined as exactly .
The equation linking TT and TCG is more commonly seen in the form
where 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 specifies the epoch fully. The above equation is often given with the Julian Date for the epoch, but that is inexact. The value is exactly in accord with the definition.
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 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 . 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 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
where is exactly.

Realization

TT is a theoretical ideal, not dependent on a particular realization. For practical purposes, TT must be realized by actual clocks in the Earth system.
The main realization 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 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 realization of TT is defined thus:
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 realization of TT based on reanalysis of historical TAI data. The BIPM has done this approximately annually since 1992. These realizations of TT are named in the form "TT", with the digits indicating the year of publication. They are published in the form of table of differences from TT. The latest is TT.
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.

Approximation

Sometimes times described in TT must be handled in situations where TT's detailed theoretical properties are not significant. Where millisecond accuracy is enough, TT can be summarized in the following ways:
Observers in different locations, that are in relative motion or at different altitudes, can disagree about the rates of each other's clocks, owing to effects described by the theory of relativity. As a result, TT does not match the proper time of all observers.
In relativistic terms, TT is described as the proper time of a clock located on the geoid.
However,
TT is now actually defined as a coordinate time scale.
The redefinition did not quantitatively change TT, but rather made the existing definition more precise. In effect it defined the geoid in terms of a particular level of gravitational time dilation relative to a notional observer located at infinitely high altitude.
The present definition of TT is a linear scaling of Geocentric Coordinate Time, which is the proper time of a notional observer who is infinitely far away and at rest relative to Earth. TCG is used so far mainly for theoretical purposes in astronomy. From the point of view of an observer on Earth's surface the second of TCG passes in slightly less than the observer's SI second. The comparison of the observer's clock against TT depends on the observer's altitude: they will match on the geoid, and clocks at higher altitude tick slightly faster.