Editing Time standard

{{Use American English|date=May 2025}}
{{Short description|Specification for measuring time}}A '''time standard''' is a specification for measuring time: either the rate at which time passes or points in time or both. In modern times, several time specifications have been officially recognized as standards, where formerly they were matters of custom and practice. An example of a kind of time standard can be a time scale, specifying a method for measuring divisions of time.  A standard for civil time can specify both time intervals and time-of-day.

Standardized time measurements are made using a [[clock]] to count periods of some period changes, which may be either the changes of a natural phenomenon or of an artificial machine.

Historically, time standards were often based on the Earth's rotational period. From the late 18 century to the 19th century it was assumed that the Earth's daily rotational rate was constant. Astronomical observations of several kinds, including eclipse records, studied in the 19th century, raised suspicions that the rate at which [[Earth]] rotates is gradually slowing and also shows small-scale irregularities, and this was confirmed in the early twentieth century. Time standards based on [[Earth's rotation|Earth rotation]] were replaced (or initially supplemented) for astronomical use from 1952 onwards by an ''[[ephemeris time]]'' standard based on the Earth's orbital period and in practice on the motion of the Moon. The invention in 1955 of the caesium [[atomic clock]] has led to the replacement of older and purely astronomical time standards, for most practical purposes, by newer time standards based wholly or partly on atomic time.

Various types of second and day are used as the basic time interval for most time scales. Other intervals of time (minutes, hours, and years) are usually defined in terms of these two.

== Terminology ==
The term "time" is generally used for many close but different concepts, including:
* [[instant]]<ref>IEC 60050-113:2011, item 113-01-08</ref> as an object&nbsp;– one point on the time axis. Being an object, it has no value;
** [[Calendar date|date]]<ref>IEC 60050-113:2011, item 113-01-012: "mark attributed to an instant by means of a specified time scale</ref> as a quantity characterizing an instant. As a quantity, it has a value which may be expressed in a variety of ways, for example "2014-04-26T09:42:36,75" in [[ISO 8601|ISO standard]] format, or more colloquially such as "today, 9:42&nbsp;a.m.";
* time interval<ref>IEC 60050-113:2011, item 113-01-010; ISO 80000-3:2006, item 3–7</ref> as an object&nbsp;– part of the time axis limited by two instants. Being an object, it has no value;
** duration<ref>IEC 60050-113:2011, item 113-01-013: "range of a time interval (113-01-10)"</ref> as a quantity characterizing a time interval.<ref>ISO 80000-3:2006, item 3–7</ref> As a quantity, it has a value, such as a number of minutes, or may be described in terms of the quantities (such as times and dates) of its beginning and end.
* [[chronology]], an ordered sequence of events in the [[past]]. Chronologies can be put into chronological groups ([[periodization]]). One of the most important systems of periodization is the [[geologic time scale]], which is a system of periodizing the events that shaped the [[Earth]] and its life. Chronology, periodization, and interpretation of the past are together known as the study of [[history]].

== Definitions of the second ==
{{Main|Second#History of definition}}

There have only ever been three definitions of the second: as a fraction of the day, as a fraction of an extrapolated year, and as the microwave frequency of a caesium atomic clock.<ref>{{cite web |author1=U.S. Naval Observatory |title=Leap Seconds |url=https://tycho.usno.navy.mil/leapsec.html |archive-url=https://web.archive.org/web/20191019051714/https://tycho.usno.navy.mil/leapsec.html |access-date=19 October 2019|archive-date=2019-10-19 }}</ref>

In early history, clocks were not accurate enough to track seconds. After the invention of mechanical clocks, the [[CGS|CGS system]] and [[MKS system of units]] both defined the second as {{frac|86,400}} of a [[mean solar day]]. MKS was adopted internationally during the 1940s.

In the late 1940s, quartz crystal oscillator clocks could measure time more accurately than the rotation of the Earth. [[Time metrology|Metrologists]] also knew that Earth's orbit around the Sun (a year) was much more stable than Earth's rotation. This led to the definition of [[ephemeris time]] and the [[tropical year]], and the ephemeris second was defined as "the fraction {{frac|31,556,925.9747}} of the tropical year for 1900 [[January 0]] at 12 hours ephemeris time".<ref>''Whitaker's Almanac 2013'' (ed. Ruth Northey), London 2012, p. 1131, {{isbn|978-1-4081-7207-0}}.</ref><ref name="USNO">{{cite web
 | title=Leap Seconds
 | publisher=Time Service Department, [[United States Naval Observatory]]
 | url=http://tycho.usno.navy.mil/leapsec.html
 | access-date=November 22, 2015
 | archive-url=https://web.archive.org/web/20150312003149/http://tycho.usno.navy.mil/leapsec.html
 | archive-date=March 12, 2015
 | url-status=dead
 }}</ref> This definition was adopted as part of the [[International System of Units]] in 1960.<ref>{{cite web
 |title=SI Brochure (2006)
 |work=SI Brochure 8th Edition
 |url=https://www.bipm.org/utils/common/pdf/si_brochure_8.pdf
 |page=112
 |publisher=[[BIPM]]
 |access-date=May 23, 2019
 |archive-url=https://web.archive.org/web/20190503133741/https://www1.bipm.org/utils/common/pdf/si_brochure_8.pdf
 |archive-date=May 3, 2019
 |url-status=live
 }}</ref>

Most recently, atomic clocks have been developed that offer improved accuracy. Since 1967, the [[SI base unit]] for time is the [[SI]] second, defined as exactly "the duration of 9,192,631,770 [[frequency|periods]] of the radiation corresponding to the transition between the two [[Hyperfine structure|hyperfine levels]] of the ground state of the [[caesium-133]] atom" (at a temperature of [[Absolute zero|0&nbsp;K]] and at mean [[sea level]]).<ref>{{cite book |last1=McCarthy |first1=Dennis D. |author-link1=Dennis McCarthy (scientist) |last2=Seidelmann |first2=P. Kenneth |title=Time: From Earth Rotation to Atomic Physics |pages=231&ndash;232 |year=2009 |location=Weinheim |publisher=Wiley}}</ref><ref name="second">{{cite web |title=Base unit definitions: Second |url=http://physics.nist.gov/cuu/Units/second.html |publisher=[[NIST]] |access-date=9 April 2011 |url-status=live |archive-url=https://web.archive.org/web/20110417135428/http://physics.nist.gov/cuu/Units/second.html |archive-date=17 April 2011}}</ref> The SI second is the basis of all atomic timescales, e.g. coordinated universal time, GPS time, International Atomic Time, etc.

== Current time standards ==

[[Geocentric Coordinate Time]] (TCG) is a [[coordinate time]] having its spatial origin at the center of Earth's mass. TCG is a theoretical ideal, and any particular realization will have [[measurement error]].

[[International Atomic Time]] (TAI)<ref>[http://www.bipm.org/en/scientific/tai/tai.html TAI]</ref> is the primary physically realized time standard. TAI is produced by the [[International Bureau of Weights and Measures]] (BIPM), and is based on the combined input of many [[atomic clock]]s around the world,<ref>{{cite web | url=https://www.bipm.org/en/bipm/tai/clock_comparisons.html | archive-url=https://web.archive.org/web/20190810172820/https://www.bipm.org/en/bipm/tai/clock_comparisons.html | archive-date=2019-08-10 | title=BIPM - clock comparisons }}</ref> each corrected for environmental and relativistic effects (both gravitational and because of speed, like in [[Satellite navigation|GNSS]]). TAI is not related to [[Geocentric Coordinate Time|TCG]] directly but rather is a realization of [[Terrestrial Time]] (TT), a theoretical timescale that is a rescaling of TCG such that the time rate approximately matches [[proper time]] at [[mean sea level]].

[[Universal Time]] (UT1) is the [[Earth Rotation Angle]] (ERA) linearly scaled to match historical definitions of [[#Mean solar time|mean solar time]] at 0° longitude. At high precision, Earth's rotation is irregular and is determined from the positions of distant quasars using long baseline interferometry, laser ranging of the Moon and artificial satellites, as well as GPS satellite orbits.

[[Coordinated Universal Time]] (UTC) is an atomic time scale designed to approximate UT1. UTC differs from TAI by an integral number of seconds. UTC is kept within 0.9 second of UT1 by the introduction of one-second steps to UTC, the "[[leap second]]". To date these steps (and difference "TAI-UTC") have always been positive.

The [[Global Positioning System]] broadcasts a very precise [[time signal]] worldwide, along with instructions for converting [[GPS time]] (GPST) to UTC. It was defined with a constant offset from TAI: GPST = TAI - 19 s. The GPS time standard is maintained independently but regularly synchronized with or from, UTC time.

[[Standard time]] or [[civil time]] in a [[time zone]] deviates a fixed, round amount, usually a whole number of hours, from some form of [[Universal Time]], usually UTC.  The offset is chosen such that a new day starts approximately while the Sun is crossing the [[nadir]] meridian. Alternatively the difference is not really fixed, but it changes twice a year by a round amount, usually one hour, see [[Daylight saving time]].

[[Julian day|Julian day number]] is a count of days elapsed since Greenwich mean noon on 1 January 4713 B.C., Julian proleptic calendar. The Julian Date is the Julian day number followed by the fraction of the day elapsed since the preceding noon. Conveniently for astronomers, this avoids the date skip during an observation night. Modified Julian day (MJD) is defined as MJD = JD - 2400000.5. An MJD day thus begins at midnight, civil date. Julian dates can be expressed in UT1, TAI, TT, etc. and so for precise applications the timescale should be specified, e.g. MJD 49135.3824 TAI.<ref>{{cite web |last1=Matsakis |first1=Demetrios |title=Systems of time |url=https://tycho.usno.navy.mil/systime.html |archive-url=https://web.archive.org/web/20190930064831/https://tycho.usno.navy.mil/systime.html |access-date=30 September 2019|archive-date=2019-09-30 }}</ref>

[[Barycentric Coordinate Time]] (TCB) is a [[coordinate time]] having its spatial origin at the center of mass of the [[Solar System]], which is called the barycenter.

=== Conversions ===
Conversions between atomic time systems (TAI, GPST, and UTC) are for the most part exact. However, GPS time is a measured value as opposed to a computed "paper" scale.<ref name=Timescales/> As such it may differ from UTC(USNO) by a few hundred nanoseconds,<ref>{{cite web |title=USNO GPS Time Transfer — Naval Oceanography Portal |url=https://www.cnmoc.usff.navy.mil/Our-Commands/United-States-Naval-Observatory/Precise-Time-Department/Global-Positioning-System/USNO-GPS-Time-Transfer/ |url-status=live |archive-url=https://web.archive.org/web/20220819222419/https://www.cnmoc.usff.navy.mil/Our-Commands/United-States-Naval-Observatory/Precise-Time-Department/Global-Positioning-System/USNO-GPS-Time-Transfer/ |archive-date=2022-08-19 |access-date=2025-01-23 |website=www.cnmoc.usff.navy.mil |quote=GPS time is automatically steered to UTC(USNO) on a daily basis to keep system time within one microsecond of UTC(USNO), but during the last several years has been within a few hundred nanoseconds.}}</ref> which in turn may differ from official UTC by as much as 26 nanoseconds.<ref name="Timescales">{{cite web |title=International Time Scales and the B.I.P.M. — Naval Oceanography Portal |url=https://www.cnmoc.usff.navy.mil/Our-Commands/United-States-Naval-Observatory/Precise-Time-Department/The-USNO-Master-Clock/International-Time-Scales-and-the-BIPM/ |archive-url=https://web.archive.org/web/20220819222318/https://www.cnmoc.usff.navy.mil/Our-Commands/United-States-Naval-Observatory/Precise-Time-Department/The-USNO-Master-Clock/International-Time-Scales-and-the-BIPM/ |archive-date=2022-08-19 |access-date=2025-01-23 |website=www.cnmoc.usff.navy.mil}}</ref> Conversions for UT1 and TT rely on published difference tables which {{as of|2022|lc=y}} are specified to 10 microseconds and 0.1 nanoseconds respectively.
{| class="wikitable"
|-
! System
! Description
! UT1
! UTC
! TT
! TAI
! GPS
|-
| UT1
| Mean Solar Time
| UT1
| UTC = UT1 − DUT1
| TT = UT1 − DUT1 + LS + 32.184 s + DTT
| TAI = UT1 − DUT1 + LS
| GPS = UT1 − DUT1 + LS − 19 s
|-
| UTC
| Civil Time
| UT1 = UTC + DUT1
| UTC
| TT = UTC + LS + 32.184 s + DTT
| TAI = UTC + LS
| GPS = UTC + LS − 19 s
|-
| TT
| Terrestrial Time
| UT1 = TT − 32.184 s − DTT − LS + DUT1
| UTC = TT − 32.184 s − DTT − LS
| TT
| TAI = TT − 32.184 s − DTT
| GPS = TT − 51.184 s − DTT
|-
| TAI
| Atomic Time
| UT1 = TAI − LS + DUT1
| UTC = TAI − LS
| TT = TAI + 32.184 s + DTT
| TAI
| GPS = TAI − 19 s
|-
| GPS
| GPS Time
| UT1 = GPS + 19 s − LS + DUT1
| UTC = GPS + 19 s − LS
| TT = GPS + 51.184 s + DTT
| TAI = GPS + 19 s
| GPS
|}
Definitions:
# LS = TAI − UTC = leap seconds from USNO Table of Leap Seconds<ref>[https://maia.usno.navy.mil/products/leap-second navy.mil]</ref>
# [[DUT1]] = UT1 − UTC published in IERS Bulletins<ref>{{cite web | url=https://www.iers.org/IERS/EN/Publications/Bulletins/bulletins.html | title=IERS - IERS Bulletins }}</ref> or U.S. Naval Observatory EO<ref>[https://maia.usno.navy.mil/products/eo-products navy.mil]</ref>
# DTT = TT − TAI − 32.184 s published in [[BIPM]]'s TT(BIPM) tables.<ref>{{cite web | url=https://webtai.bipm.org/ftp/pub/tai/ttbipm/ | title=Index of /FTP/Pub/Tai/Ttbipm }}</ref>

TCG is linearly related to TT as: TCG − TT = <var>L<sub>G</sub></var> × (JD − 2443144.5) × 86400 seconds, with the scale difference <var>L<sub>G</sub></var> defined as 6.969290134{{e|-10}} exactly.

TCB is a linear transformation of [[Barycentric Dynamical Time|TDB]] and TDB differs from TT in small, mostly periodic terms. Neglecting these terms (on the order of 2 milliseconds for several millennia around the present epoch),<ref name="IAU2006_B3"/> TCB is related to TT by: TCB − TT = <var>L<sub>B</sub></var> × (JD − 2443144.5) × 86400 seconds.<ref>{{cite web |title=IAU (1991) RECOMMENDATION III |url=https://www.iers.org/IERS/EN/Science/Recommendations/recommendation3.html |website=www.iers.org|at=Note 1}}</ref> The scale difference <var>L<sub>B</sub></var> has been defined by the IAU to be 1.550519768e-08 exactly.<ref name="IAU2006_B3">{{cite web |title=IAU 2006 Resolution B3: Re-definition of Barycentric Dynamical Time, TDB |url=https://www.iau.org/static/resolutions/IAU2006_Resol3.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.iau.org/static/resolutions/IAU2006_Resol3.pdf |archive-date=2022-10-09 |url-status=live |access-date=4 April 2022 |page=2}}</ref>

== Time standards based on Earth rotation ==
[[Apparent solar time]] or true solar time is based on the solar day, which is the period between one solar noon (passage of the real Sun across the [[meridian (geography)|meridian]]) and the next. A solar day is approximately 24 hours of mean time. Because the Earth's orbit around the Sun is elliptical, and because of the obliquity of the Earth's axis relative to the [[ecliptic|plane of the orbit (the ecliptic)]], the apparent solar day varies a few dozen seconds above or below the mean value of 24 hours. As the variation accumulates over a few weeks, there are differences as large as 16 minutes between apparent solar time and mean solar time (see [[Equation of time]]). However, these variations cancel out over a year. There are also other perturbations such as Earth's wobble, but these are less than a second per year.

[[Sidereal time]] is time by the stars. A sidereal rotation is the time it takes the Earth to make one revolution with rotation to the stars, approximately 23 hours 56 minutes 4 seconds. A mean solar day is about 3 minutes 56 seconds longer than a mean sidereal day, or {{fract|1|366}} more than a mean sidereal day. In [[astronomy]], sidereal time is used to predict when a [[star]] will reach its [[culmination|highest point]] in the sky. For accurate astronomical work on land, it was usual to observe sidereal time rather than solar time to measure mean solar time, because the observations of 'fixed' stars could be measured and reduced more accurately than observations of the Sun (in spite of the need to make various small compensations, for refraction, aberration, precession, nutation and proper motion).  It is well known that observations of the Sun pose substantial obstacles to the achievement of accuracy in measurement.<ref>See H A Harvey, [http://adsabs.harvard.edu/full/1936PA.....44..533H "The Simpler Aspects of Celestial Mechanics"], in Popular Astronomy 44 (1936), 533-541.</ref> In former times, before the distribution of accurate time signals, it was part of the routine work at any observatory to observe the sidereal times of meridian transit of selected 'clock stars' (of well-known position and movement), and to use these to correct observatory clocks running local mean sidereal time; but nowadays local sidereal time is usually generated by computer, based on time signals.<ref>A E Roy, D Clarke, [https://books.google.com/books?id=v2S6XV8dsIAC&pg=PA89 'Astronomy: Principles and Practice' (4th edition, 2003) at p.89].</ref>

{{Anchor|Mean solar time}}[[Mean solar time]] was a time standard used especially at sea for navigational purposes, calculated by observing apparent solar time and then adding to it a correction, the [[equation of time]], which compensated for two known irregularities in the length of the day, caused by the ellipticity of the Earth's orbit and the obliquity of the Earth's equator and polar axis to the [[ecliptic]] (which is the plane of the Earth's orbit around the sun). It has been superseded by [[Universal Time]].

[[Greenwich Mean Time]] was originally mean time deduced from meridian observations made at the [[Royal Greenwich Observatory]] (RGO). The principal meridian of that observatory was chosen in 1884 by the [[International Meridian Conference]] to be the [[Prime Meridian]].  GMT either by that name or as 'mean time at Greenwich' used to be an international time standard, but is no longer so; it was initially renamed in 1928 as Universal Time (UT) (partly as a result of ambiguities arising from the changed practice of starting the astronomical day at midnight instead of at noon, adopted as from 1 January 1925).  [[UT1]] is still in reality mean time at Greenwich. Today, GMT is a [[time zone]] but is still the legal time in the UK in winter (and as adjusted by one hour for summer time).  But [[Coordinated Universal Time]] (UTC) (an atomic-based time scale which is always kept within 0.9 second of UT1) is in common actual use in the UK, and the name GMT is often used to refer to it. (See articles [[Greenwich Mean Time]], [[Universal Time]], [[Coordinated Universal Time]] and the sources they cite.)

Versions of [[Universal Time]] such as UT0 and UT2 have been defined but are no longer in use.{{sfn|Urban|Seidelmann|2013|page=81}}<ref>{{cite web |last1=Schlyter |first1=Paul |title=Time Scales: UT1, UTC, TAI, ET, TT, GPS time |url=https://www.stjarnhimlen.se/comp/time.html |url-status=live |archive-url=https://web.archive.org/web/20250102032517/http://stjarnhimlen.se/comp/time.html |archive-date=2025-01-02 |access-date=2025-01-23 |website=www.stjarnhimlen.se |quote=UT2 is nowadays considered obsolete.}}</ref>

==Time standards for planetary motion calculations==
[[Ephemeris time]] (ET) and its successor time scales described below have all been intended for astronomical use, e.g. in planetary motion calculations, with aims including uniformity, in particular, freedom from irregularities of Earth rotation. Some of these standards are examples of [[dynamical time scale]]s and/or of [[coordinate time]] scales. Ephemeris Time was from 1952 to 1976 an official time scale standard of the [[International Astronomical Union]]; it was a [[dynamical time scale]] based on the orbital motion of the Earth around the Sun, from which the ephemeris second was derived as a defined fraction of the tropical year. This ephemeris second was the standard for the [[SI]] second from 1956 to 1967, and it was also the source for calibration of the [[atomic clock|caesium atomic clock]];  its length has been closely duplicated, to within 1 part in 10<sup>10</sup>, in the size of the current SI second referred to atomic time.<ref>{{cite journal | last1=Markowitz | first1=W. |author-link1=William Markowitz| last2=Hall | first2=R. Glenn | last3=Essen | first3=L. |author-link3=Louis Essen| last4=Parry | first4=J. V. L. | title=Frequency of Cesium in Terms of Ephemeris Time | journal=Physical Review Letters | volume=1 | issue=3 | date=1958-08-01 | issn=0031-9007 | doi=10.1103/PhysRevLett.1.105 | pages=105–107| bibcode=1958PhRvL...1..105M }}</ref><ref>[[William Markowitz|Wm Markowitz]] (1988) 'Comparisons of ET(Solar), ET(Lunar), UT and TDT', in (eds.) A K Babcock & G A Wilkins, 'The Earth's Rotation and Reference Frames for Geodesy and Geophysics', IAU Symposia #128 (1988), at pp 413-418.</ref>  This Ephemeris Time standard was non-relativistic and did not fulfil growing needs for relativistic [[coordinate time]] scales.  It was in use for the official almanacs and planetary ephemerides from 1960 to 1983, and was replaced in official almanacs for 1984 and after, by numerically integrated [[Jet Propulsion Laboratory Development Ephemeris]] DE200 (based on the JPL relativistic coordinate time scale [[Ephemeris time#JPL ephemeris time argument Teph|T<sub>eph</sub>]]).

For applications at the Earth's surface, ET's official replacement was [[Terrestrial Dynamical Time]] (TDT), which maintained continuity with it. TDT is a uniform atomic time scale, whose unit is the SI second. TDT is tied in its rate to the SI second, as is International Atomic Time (TAI), but because TAI was somewhat arbitrarily defined at its inception in 1958 to be initially equal to a refined version of UT, TDT was offset from TAI, by a constant 32.184 seconds. The offset provided a continuity from Ephemeris Time to TDT. TDT has since been redefined as [[Terrestrial Time]] (TT).

For the calculation of ephemerides, [[Barycentric Dynamical Time]] (TDB) was officially recommended to replace ET. TDB is similar to TDT but includes relativistic corrections that move the origin to the barycenter, hence it is a dynamical time at the barycenter.<ref>{{cite journal | last1=Brumberg | first1=V. A. |author-link1=Victor A. Brumberg| last2=Kopejkin | first2=S. M. |author-link2=Sergei Kopeikin| title=Relativistic time scales in the solar system | journal=Celestial Mechanics and Dynamical Astronomy | volume=48 | issue=1 | date=1990 | issn=0923-2958 | doi=10.1007/BF00050674 | pages=23–44| bibcode=1990CeMDA..48...23B }}</ref> TDB differs from TT only in periodic terms. The difference is at most 2 milliseconds. Deficiencies were found in the definition of TDB (though not affecting T<sub>eph</sub>), and TDB has been replaced by [[Barycentric Coordinate Time]] (TCB) and [[Geocentric Coordinate Time]] (TCG), and redefined to be [[Ephemeris time#JPL ephemeris time argument Teph|JPL ephemeris time argument T<sub>eph</sub>]], a specific fixed linear transformation of TCB. As defined, TCB (as observed from the Earth's surface) is of divergent rate relative to all of ET, T<sub>eph</sub> and TDT/TT;<ref name=why1992>P K Seidelmann & T Fukushima (1992), [http://articles.adsabs.harvard.edu/full/1992A%26A...265..833S "Why new time scales?"], ''Astronomy & Astrophysics'' vol.265 (1992), pages 833-838, including [http://www.ucolick.org/~sla/leapsecs/deltat.png Fig. 1 at p.835, a graph giving an overview of the rate differences and offsets between various standard time scales], present and past, defined by the IAU.</ref> and the same is true, to a lesser extent, of TCG. The ephemerides of Sun, Moon and planets in current widespread and official use continue to be those calculated at the [[Jet Propulsion Laboratory]] (updated as from 2003 to [[DE405]]) using as argument T<sub>eph</sub>.

==See also==
* [[Atomic clock]]
* [[Clock synchronization]]
* [[Clock signal]]
* [[Epoch (astronomy)]]
* [[Frequency standard]]
* [[Radio clock]]
* [[Time in astronomy]]
* [[Time signal]]
* [[Time metrology]]
* [[Time transfer]]
* [[Timekeeping on Mars]]
* [[Orbital period#Small body orbiting a central body|Orbital period as unit of time]]

== Notes ==
{{NoteFoot}}

== References ==
=== Citations ===
{{Reflist}}

=== Sources ===
{{Refbegin}}
*{{cite book| editor1-last = Urban |editor1-first = Sean | editor2-last = Seidelmann | editor2-first = P. Kenneth | date = 2013 | title = Explanatory Supplement to the Astronomical Almanac | edition = 3rd | location = Mill Valley, California | publisher = University Science Books}}
* ''Explanatory Supplement to the Astronomical Almanac,'' P. K. Seidelmann, ed., University Science Books, 1992, {{ISBN|0-935702-68-7}}.
{{Refend}}

==External links==
* [https://tycho.usno.th.mil/cgi-bin/timer.pl Current time]{{Dead link|date=December 2024 |bot=InternetArchiveBot |fix-attempted=yes }} according to the [[bservatory]] (get the current time)
* [https://tycho.usno.mil/systime.html Systems of Time]{{Dead link|date=December 2024 |bot=InternetArchiveBot |fix-attempted=yes }} by Demetrios Matsakis, Director, Time Service Dept., [[United States Naval Observatory]]
* [http://tycho.usno.navy.mil/leapsec.html USNO article on the definition of seconds and leap seconds] {{Webarchive|url=https://web.archive.org/web/20120611083237/http://tycho.usno.navy.mil/leapsec.html |date=2012-06-11 }}
* [http://www.ucolick.org/~sla/leapsecs/timescales.html A history of astronomical time scales] by Steve Allen
* [http://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/ Why is a minute divided into 60 seconds, an hour into 60 minutes, yet there are only 24 hours in a day] Ask the Experts – March 5, 2021. SCIENTIFIC AMERICAN

{{Time Topics}}
{{Time measurement and standards}}
{{Timezones}}
{{Authority control}}

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