Editing Terrestrial Time (section)

==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>