Terrestrial Time

Terrestrial Time(TT) is a modern astronomicaltime standarddefined by theInternational Astronomical Union,primarily for time-measurements of astronomical observations made from the surface of Earth. For example, theAstronomical Almanacuses TT for its tables of positions (ephemerides) of the Sun, Moon and planets as seen from Earth. In this role, TT continuesTerrestrial Dynamical Time(TDT or TD),which succeededephemeris time (ET).TT shares the original purpose for which ET was designed, to be free of theirregularities in the rotation of Earth.

The unit of TT is theSI second,the definition of which is based currently on the caesiumatomic 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(UTC). TT is indirectly the basis of UTC, viaInternational 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 theInternational Astronomical Union(IAU) in 1976 at its XVI General Assembly and later namedTerrestrial Dynamical Time(TDT). It was the counterpart toBarycentric Dynamical Time(TDB), which was a time standard for Solar systemephemerides,to be based on adynamical 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 Recommendation IV of the XXI General Assembly, the IAU redefined TDT, also renaming it "Terrestrial Time". TT was formally defined in terms ofGeocentric 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 thegeoid",i.e. the rate approximately matched the rate ofproper timeon the Earth's surface at mean sea level. Thus the exact ratio between TT time and TCG time was$1-L_{\mathrm {G} }$,where$L_{\mathrm {G} }=U_{\mathrm {G} }/c^{2}$was a constant and$U_{\mathrm {G} }$was thegravitational potentialat the geoid surface, a value measured byphysical geodesy.In 1991 the best available estimate of$L_{\mathrm {G} }$was6.969291×10⁻¹⁰.

In 2000, the IAU very slightly altered the definition of TT by adopting an exact value,L_G=6.969290134×10⁻¹⁰.

Current definition

TT differs from Geocentric Coordinate Time (TCG) by a constant rate. Formally it is defined by the equation

$$\mathrm {TT} ={\bigl (}1-L_{\mathrm {G} }{\bigr )}\times \mathrm {TCG} +E,$$

where TT and TCG are linear counts ofSIsecondsin Terrestrial Time and Geocentric Coordinate Time respectively,$L_{\mathrm {G} }$is the constant difference in the rates of the two time scales, and$E$is a constant to resolve theepochs(see below).$L_{\mathrm {G} }$is defined as exactly6.969290134×10⁻¹⁰.Due to the term$1-L_{\mathrm {G} }$the rate of TT is very slightly slower than that of TCG.

The equation linking TT and TCG more commonly has the form given by the IAU,

$$\mathrm {TT} =\mathrm {TCG} -L_{\mathrm {G} }\times {\bigl (}\mathrm {JD_{TCG}} -2443144.5003725{\bigr )}\times 86400,$$

where$\mathrm {JD_{TCG}}$is the TCG time expressed as aJulian 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 notsimplified.The use of a Julian Date specifies theepochfully. The above equation is often given with the Julian Date2443144.5for the epoch, but that is inexact (though inappreciably so, because of the small size of the multiplier$L_{\mathrm {G} }$). The value2443144.5003725is 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 theGregorian calendarare used. For continuity with their predecessorEphemeris Time(ET), TT and TCG were set to match ET at around Julian Date2443144.5(1977-01-01T00Z).More precisely, it was defined that TT instant1977-01-01T00:00:32.184and TCG instant1977-01-01T00:00:32.184exactly correspond to theInternational Atomic Time(TAI) instant1977-01-01T00:00:00.000.This is also the instant at which TAI introduced corrections forgravitational time dilation.

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

$$\mathrm {JD_{TT}} =E_{\mathrm {JD} }+{\bigl (}\mathrm {JD_{TCG}} -E_{\mathrm {JD} }{\bigr )}\times {\bigl (}1-L_{\mathrm {G} }{\bigr )},$$

where$E_{\mathrm {JD} }$is2443144.5003725exactly.

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.

TAI

Main article:International Atomic Time

The main realization of TT is supplied by TAI. TheBIPMTAI service, performed since 1958, estimates TT using measurements from an ensemble ofatomic clocksspread over the surface and low orbital space of Earth. TAI is canonically defined retrospectively, in monthly bulletins, in relation to the readings shown by that particular group of atomic clocks 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:

$$\mathrm {TT(TAI)=TAI+32.184~s}.$$

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,whenΔT(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".

TAI is never revised once published and TT(TAI) has small errors relative to TT(BIPM),on the order of 10-50 microseconds.

TheGPS timescale has a nominal difference from atomic time(TAI − GPS time = +19 seconds),so thatTT ≈ GPS time + 51.184 seconds.This realization introduces up to a microsecond of additional error, as the GPS signal is not precisely synchronized with TAI, but GPS receiving devices are widely available.

TT(BIPM)

Approximately annually since 1992, the International Bureau of Weights and Measures (BIPM) has produced better realizations of TT based on reanalysis of historical TAI data. BIPM's realizations of TT are named in the form "TT(BIPM08)", with the digits indicating the year of publication. They are published in the form of a table of differences from TT(TAI), along with an extrapolation equation that may be used for dates later than the table. The latest as of July 2024is TT(BIPM23).

Pulsars

Researchers from theInternational Pulsar Timing Arraycollaboration have created a realization TT(IPTA16) of TT based on observations of an ensemble ofpulsarsup to 2012. This new pulsar time scale is an independent means of computing TT. The researchers observed that their scale was within 0.5 microseconds of TT(BIPM17), with significantly lower errors since 2003. The data used was insufficient to analyze long-term stability, and contained several anomalies, but as more data is collected and analyzed, this realization may eventually be useful to identify defects in TAI and TT(BIPM).

Other standards

TT is in effect a continuation of (but is more precisely uniform than) the formerEphemeris Time(ET). It was designed for continuity with ET,and it runs at the rate of the SI second, which was itself derived from a calibration using the second of ET (see, under Ephemeris time,Redefinition of the secondandImplementations). TheJPL ephemeris time argument T_ephis within a few milliseconds of TT.

TT is slightly ahead ofUT1(a refined measure of mean solar time at Greenwich) by an amount known asΔT= TT − UT1.ΔTwas measured at +67.6439 seconds (TT ahead of UT1) at 0 hUTCon 1 January 2015;and by retrospective calculation, ΔTwas close to zero about the year 1900. ΔTis expected to continue to increase, with UT1 becoming steadily (but irregularly) further behind TT in the future. In fine detail, ΔTis somewhat unpredictable, with 10-year extrapolations diverging by 2-3 seconds from the actual value.

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 thetheory 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 theproper timeof a clock located on thegeoid(essentiallymean sea level). However, TT is now actually defined as acoordinate time scale. The redefinition did not quantitatively change TT, but rather made the existing definition more precise. In effect it defined the geoid (mean sea level) in terms of a particular level ofgravitational time dilationrelative to a notional observer located at infinitely high altitude.

The present definition of TT is a linear scaling ofGeocentric 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

• Barycentric Coordinate Time
• Geocentric Coordinate Time

External links

• BIPM technical services: Time Metrology
• Time and Frequency from A to Z