Editing Terrestrial Time (section)

=== 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>