Editing Terrestrial Time

{{Short description|Time standard for astronomical observations from the Earth}}
{{Use dmy dates|date=July 2021}}
'''Terrestrial Time''' ('''TT''') is a modern astronomical [[time standard]] defined by the [[IAU|International Astronomical Union]], primarily for time-measurements of astronomical observations made from the surface of Earth.<ref>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 [http://iau.org/static/resolutions/IAU1991_French.pdf IAU 1991 XXIst General Assembly (Buenos Aires) Resolutions], Resolution A.4 (Recommendation IV).  A redefinition by [http://syrte.obspm.fr/IAU_resolutions/Resol-UAI.htm 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.</ref>
For example, the [[Astronomical Almanac]] uses TT for its tables of positions ([[ephemeris|ephemerides]]) of the Sun, Moon and planets as seen from Earth. In this role, TT continues '''Terrestrial Dynamical Time''' (TDT or TD),<ref name=iau1991-4-n4>TT is equivalent to TDT, see IAU conference 1991, Resolution A4, recommendation IV, note 4.</ref> which succeeded [[Ephemeris time|ephemeris time (ET)]]. TT shares the original purpose for which ET was designed, to be free of the [[ΔT (timekeeping)|irregularities in the rotation of Earth]].

The unit of TT is the [[SI second]], the definition of which is based currently on the caesium [[atomic clock]],<ref name=iau1991-4-2>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'.</ref> 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, 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 [[International Astronomical Union]] (IAU) in 1976 at its XVI General Assembly and later named ''Terrestrial Dynamical Time'' (TDT). It was the counterpart to [[Barycentric Dynamical Time]] (TDB), 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 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]]",<ref>{{cite web |title=IAU(1991) RECOMMENDATION IV |url=https://www.iers.org/IERS/EN/Science/Recommendations/recommendation4.html |website=IERS}}</ref> 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 <math>1-L_\mathrm{G}</math>, where <math>L_\mathrm{G} = U_\mathrm{G} / c^2</math> was a constant and <math>U_\mathrm{G}</math> was the [[gravitational potential]] at the geoid surface, a value measured by [[physical geodesy]]. In 1991 the best available estimate of <math>L_\mathrm{G}</math> was {{val|6.969291|e=−10}}.

In 2000, the IAU very slightly altered the definition of TT by adopting an exact value, {{math | 1=''L''<sub>G</sub> = {{val|6.969290134|e=−10}}}}.<ref>{{cite web| url = http://chiron.mtk.nao.ac.jp/~toshio/iaudiv1/IAU_resolutions/Resol-UAI.htm| title = Resolution B1.9 of the IAU XXIV General Assembly, 2000}}</ref>

==Current definition==

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

<math display="block">\mathrm{TT} = \bigl(1-L_\mathrm{G}\bigr) \times \mathrm{TCG} + E,</math>

where TT and TCG are linear counts of [[SI]] [[second]]s in Terrestrial Time and Geocentric Coordinate Time respectively, <math>L_\mathrm{G}</math> is the constant difference in the rates of the two time scales, and <math>E</math> is a constant to resolve the [[epoch (reference date)|epoch]]s (see below). <math>L_\mathrm{G}</math> is defined as exactly {{val|6.969290134|e=−10}}. Due to the term <math>1-L_\mathrm{G}</math> 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,

<math display="block">\mathrm{TT} = \mathrm{TCG} - L_\mathrm{G} \times \bigl(\mathrm{JD_{TCG}} - 2443144.5003725\bigr) \times 86400,</math>

where <math>\mathrm{JD_{TCG}}</math> is the TCG time expressed as a [[Julian day|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 [[Computer algebra#Simplification|simplified]]. The use of a Julian Date specifies the [[Epoch (astronomy)|epoch]] fully. The above equation is often given with the Julian Date {{gaps|2443|144.5}} for the epoch, but that is inexact (though inappreciably so, because of the small size of the multiplier <math>L_\mathrm{G}</math>). The value {{gaps|2443|144.500|3725}} 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 [[Gregorian calendar]] are used. For continuity with their predecessor [[Ephemeris Time]] (ET), TT and TCG were set to match ET at around Julian Date {{gaps|2443|144.5}} {{nowrap|(1977-01-01T00Z).}} More precisely, it was defined that TT instant {{nowrap|1977-01-01T00:00:32.184}} and TCG instant {{nowrap|1977-01-01T00:00:32.184}} exactly correspond to the [[International Atomic Time]] (TAI) instant {{nowrap|1977-01-01T00:00:00.000.}} 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

<math display="block">\mathrm{JD_{TT}} = E_\mathrm{JD} + \bigl(\mathrm{JD_{TCG}} - E_\mathrm{JD}\bigr) \times \bigl(1 - L_\mathrm{G}\bigr),</math>

where <math>E_\mathrm{JD}</math> is {{gaps|2443|144.500|3725}} 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.<ref name="Guinot1988"/>

=== TAI ===
{{Main|International Atomic Time}}

The main realization of TT is supplied by TAI. The [[BIPM]] TAI service, performed since 1958, estimates TT using measurements from an ensemble of [[atomic clock]]s spread 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:<ref>IAU conference 1991, Resolution A4, recommendation IV, note 9.</ref>

<math display="block">\mathrm{TT(TAI) = TAI + 32.184 ~ s}.</math>

The offset 32.184&nbsp;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,<ref>L Essen, [http://www.leapsecond.com/history/1968-Metrologia-v4-n4-Essen.pdf "Time Scales"], Metrologia, vol.4 (1968), 161-165, at 163</ref> when [[ΔT (timekeeping)|Δ''T'']] {{nobr|(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".<ref>IAU Commission 4 (Ephemerides), Recommendations to IAU General Assembly 1976, Notes on Recommendation 5, note 2</ref>

TAI is never revised once published and TT(TAI) has small errors relative to TT(BIPM),<ref name="Guinot1988">{{cite journal |last1=Guinot |first1=B. |title=Atomic time scales for pulsar studies and other demanding applications |journal=Astronomy and Astrophysics |date=1 March 1988 |volume=192 |issue=1–2 |pages=370–373 |bibcode=1988A&A...192..370G |url=https://articles.adsabs.harvard.edu/pdf/1988A%26A...192..370G |issn=0004-6361}}</ref> on the order of 10-50 microseconds.<ref>{{cite web |title=TT(BIPM22) |url=https://webtai.bipm.org/ftp/pub/tai/ttbipm/TTBIPM.2022 |access-date=14 December 2023}}</ref>

The [[GPS time]] scale has a nominal difference from atomic time {{nobr|1=(TAI − GPS time = +19 seconds)}},<ref>{{cite web |url=http://www.ucolick.org/~sla/leapsecs/timescales.html |author=Steve Allen |title=Time Scales |publisher=[[Lick Observatory]] |access-date=2017-08-13}}</ref> so that {{nobr|TT ≈ 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.<ref>{{cite web|url=http://www.atomic-clock.galleon.eu.com/support/gps-time-accuracy.html|title=GPS time accurate to 100 nanoseconds|publisher=Galleon|access-date=October 12, 2012|archive-url=https://web.archive.org/web/20120514001920/http://www.atomic-clock.galleon.eu.com/support/gps-time-accuracy.html|archive-date=May 14, 2012|url-status=live}}</ref>

=== 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|2024|7|lc=on}} is TT(BIPM23).<ref>{{cite web |title=Index of /ftp/pub/tai/ttbipm |url=https://webtai.bipm.org/ftp/pub/tai/ttbipm/ |website=webtai.bipm.org |access-date=8 July 2024}}</ref>

=== Pulsars ===

Researchers from the [[International Pulsar Timing Array]] collaboration have created a realization TT(IPTA16) of TT based on observations of an ensemble of [[rotation-powered pulsar#History|pulsar]]s up 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).<ref>{{Cite journal|arxiv = 1910.13628|doi = 10.1093/mnras/stz3071|doi-access=free|title = A pulsar-based time-scale from the International Pulsar Timing Array|year = 2020|last1 = Hobbs|first1 = G.|last2 = Guo|first2 = L.|last3 = Caballero|first3 = R. N.|last4 = Coles|first4 = W.|last5 = Lee|first5 = K. J.|last6 = Manchester|first6 = R. N.|last7 = Reardon|first7 = D. J.|last8 = Matsakis|first8 = D.|last9 = Tong|first9 = M. L.|last10 = Arzoumanian|first10 = Z.|last11 = Bailes|first11 = M.|last12 = Bassa|first12 = C. G.|last13 = Bhat|first13 = N D R.|last14 = Brazier|first14 = A.|last15 = Burke-Spolaor|first15 = S.|last16 = Champion|first16 = D. J.|last17 = Chatterjee|first17 = S.|last18 = Cognard|first18 = I.|last19 = Dai|first19 = S.|last20 = Desvignes|first20 = G.|last21 = Dolch|first21 = T.|last22 = Ferdman|first22 = R. D.|last23 = Graikou|first23 = E.|last24 = Guillemot|first24 = L.|last25 = Janssen|first25 = G. H.|last26 = Keith|first26 = M. J.|last27 = Kerr|first27 = M.|last28 = Kramer|first28 = M.|last29 = Lam|first29 = M. T.|last30 = Liu|first30 = K.|journal = Monthly Notices of the Royal Astronomical Society|volume = 491|issue = 4|pages = 5951–5965|bibcode = 2020MNRAS.491.5951H|s2cid = 204961320|display-authors = 29}}</ref>

=== Other standards ===

TT is in effect a continuation of (but is more precisely uniform than) the former [[Ephemeris Time]] (ET).  It was designed for continuity with ET,<ref>P K Seidelmann (ed.) (1992), [https://books.google.com/books?id=uJ4JhGJANb4C&pg=PA42 '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.</ref> 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, [[Ephemeris time#Redefinition of the second|Redefinition of the second]] and [[Ephemeris time#Implementations|Implementations]]). The [[Ephemeris time#JPL ephemeris time argument Teph|JPL ephemeris time argument T<sub>eph</sub>]] is within a few milliseconds of TT.

TT is slightly ahead of [[UT1]] (a refined measure of mean solar time at Greenwich) by an amount known as {{nobr|1=[[ΔT (timekeeping)|Δ''T'']] = TT − UT1.}}  Δ''T'' was measured at +67.6439 seconds (TT ahead of UT1) at 0&nbsp;h [[UTC]] on 1&nbsp;January 2015;<ref>[[US Naval Observatory]] ([[USNO]]) data file online at [https://web.archive.org/web/20190808224315/http://maia.usno.navy.mil:80/ser7/deltat.data https://web.archive.org/web/20190808224315/http://maia.usno.navy.mil:80/ser7/deltat.data (accessed 27 October 2015)].</ref> and by retrospective calculation, Δ''T'' was close to zero about the year 1900. Δ''T'' is expected to continue to increase, with UT1 becoming steadily (but irregularly) further behind TT in the future. In fine detail, Δ''T'' is somewhat unpredictable, with 10-year extrapolations diverging by 2-3 seconds from the actual value.<ref>{{cite web |title=Delta T: Past, Present and Future |url=http://asa.hmnao.com/SecK/DeltaT.html |website=The Astronomical Almanac Online |archive-url=https://web.archive.org/web/20220918033245/http://asa.hmnao.com/SecK/DeltaT.html |archive-date=18 September 2022 |date=2020 |url-status=dead}}</ref>

==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 [[proper time]] of a clock located on the [[geoid]] (essentially [[mean sea level]]).<ref>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.</ref>
However,<ref name=guin86>B Guinot (1986), [http://adsabs.harvard.edu/abs/1986CeMec..38..155G "Is the International Atomic Time a Coordinate Time or a Proper Time?"], Celestial Mechanics, 38 (1986), pp.155-161.</ref>
TT is now actually defined as a [[coordinate time scale]].<ref>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.</ref>
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 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]] (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]]

==References==
{{Reflist}}

==External links==
*[https://www.bipm.org/en/time-metrology BIPM technical services: Time Metrology]
*[https://www.nist.gov/pml/time-and-frequency-division/popular-links/time-frequency-z Time and Frequency from A to Z]

{{Time measurement and standards}}

[[Category:Time scales]]
[[Category:Earth]]
[[Category:Time in astronomy]]