Terrestrial Time
Terrestrial Time (TT) is a modern astronomical
The unit of TT is the
TT is distinct from the time scale often used as a basis for civil purposes, Coordinated Universal Time (UTC). TT is indirectly the basis of UTC, via International Atomic Time (TAI). Because of the historical difference between TAI and ET when TT was introduced, TT is 32.184 s ahead of TAI.
History
A definition of a terrestrial time standard was adopted by the
In 1991, in Recommendation IV of the XXI General Assembly, the IAU redefined TDT, also renaming it "Terrestrial Time". TT was formally defined in terms of Geocentric Coordinate Time (TCG), 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",[4] i.e. the rate approximately matched the rate of proper time on the Earth's surface at mean sea level. Thus the exact ratio between TT time and TCG time was , where was a constant and was the gravitational potential at the geoid surface, a value measured by physical geodesy. In 1991 the best available estimate of was 6.969291×10−10.
In 2000, the IAU very slightly altered the definition of TT by adopting an exact value, LG = 6.969290134×10−10.[5]
Current definition
TT differs from Geocentric Coordinate Time (TCG) by a constant rate. Formally it is defined by the equation
where TT and TCG are linear counts of
The equation linking TT and TCG more commonly has the form given by the IAU,
where is the TCG time expressed as a Julian date (JD). The Julian Date is a linear transformation of the raw count of seconds represented by the variable TCG, so this form of the equation is not simplified. The use of a Julian Date specifies the epoch fully. The above equation is often given with the Julian Date 2443144.5 for the epoch, but that is inexact (though inappreciably so, because of the small size of the multiplier ). The value 2443144.5003725 is exactly in accord with the definition.
Time coordinates on the TT and TCG scales are specified conventionally using traditional means of specifying days, inherited from non-uniform time standards based on the rotation of Earth. Specifically, both Julian Dates and the
TT and TCG expressed as Julian Dates can be related precisely and most simply by the equation
where is 2443144.5003725 exactly.
Realizations
TT is a theoretical ideal, not dependent on a particular realization. For practical use, physical clocks must be measured and their readings processed to estimate TT. A simple offset calculation is sufficient for most applications, but in demanding applications, detailed modeling of relativistic physics and measurement uncertainties may be needed.[6]
TAI
The main realization of TT is supplied by TAI. The
The offset 32.184 s arises from history. The atomic time scale A1 (a predecessor of TAI) was set equal to UT2 at its conventional starting date of 1 January 1958,[8] when ΔT (ET − UT) was about 32 seconds. The offset 32.184 seconds was the 1976 estimate of the difference between Ephemeris Time (ET) and TAI, "to provide continuity with the current values and practice in the use of Ephemeris Time".[9]
TAI is never revised once published and TT(TAI) has small errors relative to TT(BIPM),[6] on the order of 10-50 microseconds.[10]
The
TT(BIPM)
Approximately annually since 1992, the International Bureau of Weights and Measures (
Pulsars
Researchers from the
Other standards
TT is in effect a continuation of (but is more precisely uniform than) the former
TT is slightly ahead of
Relativistic relationships
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 (even as a theoretical ideal) does not match the proper time of all observers.
In relativistic terms, TT is described as the
The present definition of TT is a linear scaling of Geocentric Coordinate Time (TCG), which is the proper time of a notional observer who is infinitely far away (so not affected by gravitational time dilation) and at rest relative to Earth. TCG is used to date 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.
See also
References
- ^ The 1991 definition refers to the scale agreeing with the SI second "on the geoid", i.e. close to mean sea level on Earth's surface, see IAU 1991 XXIst General Assembly (Buenos Aires) Resolutions, Resolution A.4 (Recommendation IV). A redefinition by resolution of the IAU 2000 24th General Assembly (Manchester), at Resolution B1.9, is in different terms intended for continuity and to come very close to the same standard.
- ^ TT is equivalent to TDT, see IAU conference 1991, Resolution A4, recommendation IV, note 4.
- ^ IAU conference 1991, Resolution A4, recommendation IV, part 2 states that the unit for TT is to agree with the SI second 'on the geoid'.
- ^ "IAU(1991) RECOMMENDATION IV". IERS.
- ^ "Resolution B1.9 of the IAU XXIV General Assembly, 2000".
- ^ ISSN 0004-6361.
- ^ IAU conference 1991, Resolution A4, recommendation IV, note 9.
- ^ L Essen, "Time Scales", Metrologia, vol.4 (1968), 161-165, at 163
- ^ IAU Commission 4 (Ephemerides), Recommendations to IAU General Assembly 1976, Notes on Recommendation 5, note 2
- ^ "TT(BIPM22)". Retrieved 14 December 2023.
- ^ Steve Allen. "Time Scales". Lick Observatory. Retrieved 13 August 2017.
- ^ "GPS time accurate to 100 nanoseconds". Galleon. Archived from the original on 14 May 2012. Retrieved 12 October 2012.
- ^ "Index of /ftp/pub/tai/ttbipm". webtai.bipm.org. Retrieved 24 April 2022.
- S2CID 204961320.
- ^ P K Seidelmann (ed.) (1992), 'Explanatory Supplement to the Astronomical Almanac', at p.42; also IAU Commission 4 (Ephemerides), Recommendations to IAU General Assembly 1976, Notes on Recommendation 5, note 2.
- .
- ^ "Delta T: Past, Present and Future". The Astronomical Almanac Online. 2020. Archived from the original on 18 September 2022.
- ^ For example, IAU Commission 4 (Ephemerides), Recommendations to IAU General Assembly 1976, Notes on Recommendation 5, note 1, as well as other sources, indicate the time scale for apparent geocentric ephemerides as a proper time.
- ^ B Guinot (1986), "Is the International Atomic Time a Coordinate Time or a Proper Time?", Celestial Mechanics, 38 (1986), pp.155-161.
- ^ IAU General Assembly 1991, Resolution A4, Recommendations III and IV, define TCB and TCG as coordinate time scales, and TT as a linear scaling of TCG, hence also a coordinate time.