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ΔT (timekeeping) - Wikipedia
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id="toc-Earth's_rate_of_rotation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Values_prior_to_1955" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Values_prior_to_1955"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Values prior to 1955</span> </div> </a> <ul id="toc-Values_prior_to_1955-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Current_values" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Current_values"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Current values</span> </div> </a> <ul id="toc-Current_values-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geological_evidence" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Geological_evidence"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Geological evidence</span> </div> </a> <ul id="toc-Geological_evidence-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span 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href="https://el.wikipedia.org/wiki/%CE%94%CE%AD%CE%BB%CF%84%CE%B1_%CE%A4" title="Δέλτα Τ – Greek" lang="el" hreflang="el" data-title="Δέλτα Τ" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Delta_T" title="Delta T – Spanish" lang="es" hreflang="es" data-title="Delta T" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/%CE%94T" title="ΔT – Malay" lang="ms" hreflang="ms" data-title="ΔT" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%CE%94T" title="ΔT – Japanese" lang="ja" hreflang="ja" data-title="ΔT" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%94%D0%B5%D0%BB%D1%8C%D1%82%D0%B0_T" title="Дельта T – Russian" lang="ru" hreflang="ru" data-title="Дельта T" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%CE%94T" title="ΔT – Turkish" lang="tr" hreflang="tr" data-title="ΔT" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%B8%96%E7%95%8C%E6%97%B6%E6%94%B9%E6%AD%A3%E6%95%B0" title="世界时改正数 – Chinese" lang="zh" 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<div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Measure of variation of solar time from atomic time</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about long-term drift in the length of a day. For related shorter-term variations, see <a href="/wiki/Day_length_fluctuations" title="Day length fluctuations">Day length fluctuations</a>. For other meanings of the mathematical notation ΔT, see <a href="/wiki/%CE%94T_(disambiguation)" class="mw-redirect mw-disambig" title="ΔT (disambiguation)">ΔT (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:TT-UT1_2000%2B.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/TT-UT1_2000%2B.svg/220px-TT-UT1_2000%2B.svg.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/TT-UT1_2000%2B.svg/330px-TT-UT1_2000%2B.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/TT-UT1_2000%2B.svg/440px-TT-UT1_2000%2B.svg.png 2x" data-file-width="640" data-file-height="480" /></a><figcaption>TT-UT1 2000+</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Delta_T_1657-2022.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Delta_T_1657-2022.svg/220px-Delta_T_1657-2022.svg.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Delta_T_1657-2022.svg/330px-Delta_T_1657-2022.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Delta_T_1657-2022.svg/440px-Delta_T_1657-2022.svg.png 2x" data-file-width="640" data-file-height="480" /></a><figcaption>Δ<i>T</i> vs. time from 1657 to 2022<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>In precise <a href="/wiki/Time_standard#Time_standards_based_on_Earth_rotation" title="Time standard">timekeeping</a>, <b>Δ<i>T</i></b> (<b>Delta <i>T</i></b>, <b>delta-<i>T</i></b>, <b>delta<i>T</i></b>, or <b>D<i>T</i></b>) is a measure of the cumulative effect of the departure of the <a href="/wiki/Earth%27s_rotation" title="Earth's rotation">Earth's rotation</a> period from the fixed-length day of <a href="/wiki/International_Atomic_Time" title="International Atomic Time">International Atomic Time</a> (86,400 seconds). Formally, Δ<i>T</i> is the time difference <span class="texhtml">Δ<i>T</i> = TT − UT</span> between <a href="/wiki/Universal_Time" title="Universal Time">Universal Time</a> (UT, defined by Earth's rotation) and <a href="/wiki/Terrestrial_Time" title="Terrestrial Time">Terrestrial Time</a> (TT, independent of Earth's rotation). The value of ΔT for the start of 1902 was approximately zero; for 2002 it was about 64 seconds. So Earth's rotations over that century took about 64 seconds longer than would be required for days of atomic time. As well as this long-term drift in the length of the day there are short-term <a href="/wiki/Day_length_fluctuations" title="Day length fluctuations">fluctuations in the length of day</a> (<span class="texhtml">Δ<i>τ</i></span>) which are dealt with separately. </p><p>Since early 2017, the <a href="/wiki/Day_length_fluctuations" title="Day length fluctuations">length of the day</a> has happened to be very close to the conventional value, and ΔT has remained within half a second of 69 seconds.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Calculation">Calculation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%94T_(timekeeping)&action=edit&section=1" title="Edit section: Calculation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Earth's <a href="/wiki/Rotational_speed" class="mw-redirect" title="Rotational speed">rotational speed</a> is <span class="texhtml"><i>ν</i> = <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2π</span></span>⁠</span><span style="white-space: nowrap;"> </span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>dθ</i></span><span class="sr-only">/</span><span class="den"><i>dt</i></span></span>⁠</span></span>, and a day corresponds to one period <span class="texhtml"><i>P</i> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den"><i>ν</i></span></span>⁠</span></span>. A <a href="/wiki/Rotational_acceleration" class="mw-redirect" title="Rotational acceleration">rotational acceleration</a> <span class="texhtml"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>dν</i></span><span class="sr-only">/</span><span class="den"><i>dt</i></span></span>⁠</span></span> gives a rate of change of the period of <span class="texhtml"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>dP</i></span><span class="sr-only">/</span><span class="den"><i>dt</i></span></span>⁠</span> = −<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den"><i>ν</i><sup>2</sup></span></span>⁠</span><span style="white-space: nowrap;"> </span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>dν</i></span><span class="sr-only">/</span><span class="den"><i>dt</i></span></span>⁠</span></span>, which is usually expressed as <span class="texhtml"><i>α</i> = <i>ν</i><span style="white-space: nowrap;"> </span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>dP</i></span><span class="sr-only">/</span><span class="den"><i>dt</i></span></span>⁠</span> = −<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den"><i>ν</i></span></span>⁠</span><span style="white-space: nowrap;"> </span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>dν</i></span><span class="sr-only">/</span><span class="den"><i>dt</i></span></span>⁠</span></span>. This has <a href="/wiki/Dimension_(physics)" class="mw-redirect" title="Dimension (physics)">dimension</a> of <a href="/wiki/Reciprocal_time" class="mw-redirect" title="Reciprocal time">reciprocal time</a> and is commonly reported in <a href="/wiki/Unit_of_measurement" title="Unit of measurement">units</a> of milliseconds-per-day per century, symbolized as ms/day/cy (understood as (ms/day)/cy). Integrating <span class="texhtml"><i>α</i></span> gives an expression for Δ<i>T</i> against time. </p> <div class="mw-heading mw-heading3"><h3 id="Universal_time">Universal time</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%94T_(timekeeping)&action=edit&section=2" title="Edit section: Universal time"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Universal Time is a time scale based on the <a href="/wiki/Earth%27s_rotation" title="Earth's rotation">Earth's rotation</a>, which is somewhat irregular over short periods (days up to a century), thus any time based on it cannot have an accuracy better than 1 in 10<sup>8</sup>. However, a larger, more consistent effect has been observed over many centuries: Earth's rate of rotation is inexorably <a href="/wiki/Tidal_acceleration#Effects_of_Moon's_gravity" title="Tidal acceleration">slowing down</a>. This observed change in the rate of rotation is attributable to two primary forces, one decreasing and one increasing the Earth's rate of rotation. Over the long term, the dominating force is <a href="/wiki/Tidal_acceleration" title="Tidal acceleration">tidal friction</a>, which is slowing the rate of rotation, contributing about <span class="texhtml"><i>α</i> = +2.3</span> ms/day/cy or <span class="texhtml"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>dP</i></span><span class="sr-only">/</span><span class="den"><i>dt</i></span></span>⁠</span> = +2.3</span> ms/cy, which is equal to the very small fractional change <span class="nowrap"><span data-sort-value="6987730000000000000♠"></span>+7.3<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−13</sup></span> day/day. The most important force acting in the opposite direction, to speed up the rate, is believed to be a result of the melting of continental ice sheets at the end of the <a href="/wiki/Last_glacial_period" class="mw-redirect" title="Last glacial period">last glacial period</a>. This removed their tremendous weight, allowing the land under them to begin to rebound upward in the polar regions, an effect that is still occurring today and will continue until isostatic equilibrium is reached. This "<a href="/wiki/Post-glacial_rebound" title="Post-glacial rebound">post-glacial rebound</a>" brings mass closer to the rotational axis of the Earth, which makes the Earth spin faster, according to the law of <a href="/wiki/Angular_momentum" title="Angular momentum">conservation of angular momentum</a>, similar to an ice skater pulling their arms in to spin faster. Models estimate this effect to contribute about −0.6 ms/day/cy. Combining these two effects, the net acceleration (actually a deceleration) of the rotation of the Earth, or the change in the length of the mean solar day (LOD), is +1.7 ms/day/cy or +62 s/cy<sup>2</sup> or +46.5 ns/day<sup>2</sup>. This matches the average rate derived from astronomical records over the past 27 centuries.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Terrestrial_time">Terrestrial time</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%94T_(timekeeping)&action=edit&section=3" title="Edit section: Terrestrial time"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Terrestrial Time is a theoretical uniform time scale, defined to provide continuity with the former <a href="/wiki/Ephemeris_Time" class="mw-redirect" title="Ephemeris Time">Ephemeris Time</a> (ET). ET was an independent time-variable, proposed (and its adoption agreed) in the period 1948–1952<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> with the intent of forming a gravitationally uniform time scale as far as was feasible at that time, and depending for its definition on <a href="/wiki/Simon_Newcomb" title="Simon Newcomb">Simon Newcomb</a>'s <i><a href="/wiki/Newcomb%27s_Tables_of_the_Sun" title="Newcomb's Tables of the Sun">Tables of the Sun</a></i> (1895), interpreted in a new way to accommodate certain observed discrepancies.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Newcomb's tables formed the basis of all astronomical ephemerides of the Sun from 1900 through 1983: they were originally expressed (and published) in terms of Greenwich Mean Time and the mean solar day,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> but later, in respect of the period 1960–1983, they were treated as expressed in terms of ET,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> in accordance with the adopted ET proposal of 1948–52. ET, in turn, can now be seen (in light of modern results)<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> as close to the average mean solar time between 1750 and 1890 (centered on 1820), because that was the period during which the observations on which Newcomb's tables were based were performed. While TT is strictly uniform (being based on the <a href="/wiki/SI" class="mw-redirect" title="SI">SI</a> <a href="/wiki/Second" title="Second">second</a>, every second is the same as every other second), it is in practice realised by <a href="/wiki/International_Atomic_Time" title="International Atomic Time">International Atomic Time</a> (TAI) with an accuracy of about 1 part in 10<sup>14</sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Earth's_rate_of_rotation"><span id="Earth.27s_rate_of_rotation"></span>Earth's rate of rotation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%94T_(timekeeping)&action=edit&section=4" title="Edit section: Earth's rate of rotation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Earth's rate of rotation must be integrated to obtain time, which is Earth's angular position (specifically, the orientation of the meridian of Greenwich relative to the fictitious <a href="/wiki/Mean_sun" class="mw-redirect" title="Mean sun">mean sun</a>). Integrating +1.7 ms/d/cy and centering the resulting parabola on the year 1820 yields (to a first approximation) <span class="nowrap">32 × <big>(</big><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">year − 1820</span><span class="sr-only">/</span><span class="den">100</span></span>⁠</span><big>)</big><span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:0.8em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sub></span></span> - 20</span> seconds for Δ<i>T</i>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> Smoothed historical measurements of Δ<i>T</i> using total <a href="/wiki/Solar_eclipse" title="Solar eclipse">solar eclipses</a> are about +17190 s in the year −500 (501 <a href="/wiki/Before_Christ" class="mw-redirect" title="Before Christ">BC</a>), +10580 s in 0 (1 BC), +5710 s in 500, +1570 s in 1000, and +200 s in 1500. After the invention of the telescope, measurements were made by observing occultations of stars by the <a href="/wiki/Moon" title="Moon">Moon</a>, which allowed the derivation of more closely spaced and more accurate values for Δ<i>T</i>. Δ<i>T</i> continued to decrease until it reached a plateau of +11 ± 6 s between 1680 and 1866. For about three decades immediately before 1902 it was negative, reaching −6.64 s. Then it increased to +63.83 s in January 2000 and +68.97 s in January 2018<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> and +69.361 s in January 2020, after even a slight decrease from 69.358 s in July 2019 to 69.338 s in September and October 2019 and a new increase in November and December 2019. This will require the addition of an ever-greater number of <a href="/wiki/Leap_second" title="Leap second">leap seconds</a> to <a href="/wiki/Coordinated_Universal_Time" title="Coordinated Universal Time">UTC</a> as long as UTC tracks UT1 with one-second adjustments. (The SI second as now used for UTC, when adopted, was already a little shorter than the current value of the second of mean solar time.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup>) Physically, the meridian of Greenwich in Universal Time is almost always to the east of the meridian in Terrestrial Time, both in the past and in the future. +17190 s or about <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac">4<span class="sr-only">+</span><span class="num">3</span>⁄<span class="den">4</span></span> h corresponds to 71.625°E. This means that in the year −500 (501 <a href="/wiki/Before_Christ" class="mw-redirect" title="Before Christ">BC</a>), Earth's faster rotation would cause a total solar eclipse to occur 71.625° to the east of the location calculated using the uniform TT. </p> <div class="mw-heading mw-heading2"><h2 id="Values_prior_to_1955">Values prior to 1955</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%94T_(timekeeping)&action=edit&section=5" title="Edit section: Values prior to 1955"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>All values of Δ<i>T</i> before 1955 depend on observations of the Moon, either via eclipses or occultations. The angular momentum lost by the Earth due to friction induced by the Moon's tidal effect is transferred to the Moon, increasing its angular momentum, which means that its moment arm (approximately its distance from the Earth, i.e. precisely the semi-major axis of the Moon's orbit) is increased (for the time being about +3.8 cm/year), which via <a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws of planetary motion</a> causes the Moon to revolve around the Earth at a slower rate. The cited values of Δ<i>T</i> assume that the lunar acceleration (actually a deceleration, that is a negative acceleration) due to this effect is <span class="texhtml"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>d</i><b>n</b></span><span class="sr-only">/</span><span class="den"><i>dt</i></span></span>⁠</span></span> = −26″/cy<sup>2</sup>, where <span class="texhtml"><b>n</b></span> is the mean sidereal angular motion of the Moon. This is close to the best estimate for <span class="texhtml"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>d</i><b>n</b></span><span class="sr-only">/</span><span class="den"><i>dt</i></span></span>⁠</span></span> as of 2002 of −25.858 ± 0.003″/cy<sup>2</sup>,<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> so Δ<i>T</i> need not be recalculated given the uncertainties and smoothing applied to its current values. Nowadays, UT is the observed orientation of the Earth relative to an inertial reference frame formed by extra-galactic radio sources, modified by an adopted ratio between <a href="/wiki/Sidereal_time" title="Sidereal time">sidereal time</a> and solar time. Its measurement by several observatories is coordinated by the <a href="/wiki/International_Earth_Rotation_and_Reference_Systems_Service" title="International Earth Rotation and Reference Systems Service">International Earth Rotation and Reference Systems Service</a> (IERS). </p> <div class="mw-heading mw-heading2"><h2 id="Current_values">Current values</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%94T_(timekeeping)&action=edit&section=6" title="Edit section: Current values"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Recall <span class="texhtml">Δ<i>T</i> = TT − UT1</span> by definition. While <a href="/wiki/Terrestrial_Time" title="Terrestrial Time">TT</a> is only theoretical, it is commonly realized as <a href="/wiki/International_Atomic_Time" title="International Atomic Time">TAI</a> + 32.184 seconds where TAI is <a href="/wiki/Coordinated_Universal_Time" title="Coordinated Universal Time">UTC</a> plus the current leap seconds, so <span class="texhtml">Δ<i>T</i> = UTC − UT1 + (leap seconds) + 32.184 s</span>. </p><p>This can be rewritten as <span class="texhtml">Δ<i>T</i> = (leap seconds) + 32.184 s − DUT1</span>, where <a href="/wiki/DUT1" title="DUT1">DUT1</a> is UT1 − UTC. The value of DUT1 is sent out in the weekly <a href="/wiki/IERS" class="mw-redirect" title="IERS">IERS</a> <a rel="nofollow" class="external text" href="https://datacenter.iers.org/data/latestVersion/bulletinA.txt">Bulletin A</a>, as well as several <a href="/wiki/Time_signal_service" class="mw-redirect" title="Time signal service">time signal services</a>, and by extension serve as a source of the current <span class="texhtml">Δ<i>T</i></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Geological_evidence">Geological evidence</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%94T_(timekeeping)&action=edit&section=7" title="Edit section: Geological evidence"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Tidal_acceleration" title="Tidal acceleration">Tidal deceleration</a> rates have varied over the history of the Earth-Moon system. Analysis of layering in fossil <a href="/wiki/Mollusc_shell" title="Mollusc shell">mollusc shells</a> from 70 million years ago, in the <a href="/wiki/Late_Cretaceous" title="Late Cretaceous">Late Cretaceous</a> period, shows that there were 372 days a year, and thus that the day was about 23.5 hours long then.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> Based on geological studies of <a href="/wiki/Rhythmites#Tidal_rhythmites" class="mw-redirect" title="Rhythmites">tidal rhythmites</a>, the day was 21.9±0.4 hours long 620 million years ago and there were 13.1±0.1 synodic months/year and 400±7 solar days/year. The average recession rate of the Moon between then and now has been 2.17±0.31 cm/year, which is about half the present rate. The present high rate may be due to near <a href="/wiki/Resonance" title="Resonance">resonance</a> between natural ocean frequencies and tidal frequencies.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%94T_(timekeeping)&action=edit&section=8" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">IERS Rapid Service/Prediction Center (c. 1986). <a rel="nofollow" class="external text" href="http://maia.usno.navy.mil/ser7/historic_deltat.data"><i>Historic Delta T and LOD</i></a>. Source attributed data to McCarthy and Babcock (1986). Retrieved April 2022.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">IERS Rapid Service/Prediction Center. <a rel="nofollow" class="external text" href="http://maia.usno.navy.mil/ser7/deltat.data"><i>Delta T determinations</i></a>. Retrieved April 2022.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://cddis.nasa.gov/archive/products/iers/deltat.data">"deltat.data"</a>. <i>urs.earthdata.nasa.gov</i><span class="reference-accessdate">. Retrieved <span class="nowrap">September 19,</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=urs.earthdata.nasa.gov&rft.atitle=deltat.data&rft_id=https%3A%2F%2Fcddis.nasa.gov%2Farchive%2Fproducts%2Fiers%2Fdeltat.data&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%CE%94T+%28timekeeping%29" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://DLMcN.com/deltaT_March_2023_Short.pdf">"Current values and short term predictions of Delta T (2000 to 2024)"</a> <span class="cs1-format">(PDF)</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Current+values+and+short+term+predictions+of+Delta+T+%282000+to+2024%29&rft_id=http%3A%2F%2FDLMcN.com%2FdeltaT_March_2023_Short.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%CE%94T+%28timekeeping%29" class="Z3988"></span>(diagram constructed by the UK Hydrographic Office).</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">McCarthy & Seidelmann 2009, 88–89.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Naval Oceanography Portal <a rel="nofollow" class="external text" href="https://www.usno.navy.mil/USNO/earth-orientation/eo-products/long-term">"Long-term Delta T"</a></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Naval Meteorology and Oceanography Command <a rel="nofollow" class="external text" href="https://www.cnmoc.usff.navy.mil/Organization/United-States-Naval-Observatory/Earth-Orientation-Department/Earth-Orientation-Information-Center/Frequently-Asked-Questions-About-Earth-Orientation/Suggested-Reading/">"Suggested Reading"</a>, Delta T information - McCarthy, D.D. and A.K. Babcock, Physics of the Earth and Planetary Interiors, Vol. 44, 1986, 281-292</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><i>Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac</i>, Nautical Almanac Offices of UK and US (1961), at pp. 9 and 71.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">See G M Clemence's proposal of 1948, contained in his paper: "<a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1948AJ.....53..169C">On the System of Astronomical Constants</a>", <i>Astronomical Journal</i> (1948) vol.53 (6), issue #1170, pp 169–179; also G M Clemence (1971), "<a rel="nofollow" class="external text" href="http://articles.adsabs.harvard.edu/full/1971JHA.....2...73C">The Concept of Ephemeris Time</a>", in <i>Journal for the History of Astronomy</i> v2 (1971), pp. 73–79 (giving details of the genesis and adoption of the ephemeris time proposal); also article <a href="/wiki/Ephemeris_time" title="Ephemeris time">Ephemeris time</a> and references therein.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=j8MRAAAAYAAJ&pg=PT6#PPT18,M1">Newcomb's <i>Tables of the Sun</i></a> (Washington, 1895), Introduction, I. Basis of the Tables, pp. 9 and 20, citing time units of Greenwich Mean Noon, Greenwich Mean Time, and mean solar day</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">W de Sitter, on p. 38 of <i>Bulletin of the Astronomical Institutes of the Netherlands</i>, v4 (1927), pp.21–38, "<a rel="nofollow" class="external text" href="http://articles.adsabs.harvard.edu/full/1927BAN.....4...21D">On the secular accelerations and the fluctuations of the moon, the sun, Mercury and Venus</a>", which refers to "the 'astronomical time', given by the earth's rotation, and used in all practical astronomical computations", and states that it "differs from the 'uniform' or 'Newtonian' time".</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">See p. 612 in <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=uJ4JhGJANb4C">Explanatory Supplement to the Astronomical Almanac</a></i>, ed. P K Seidelmann, 1992, confirming introduction of ET in the 1960 edition of the ephemerides.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">See especially F R Stephenson (1997), and Stephenson & Morrison (1995), book and papers cited below.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">A similar parabola is plotted on p. 54 of McCarthy & Seidelmann (2009).</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://eclipse.gsfc.nasa.gov/SEhelp/deltat2004.html">"NASA.gov"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=NASA.gov&rft_id=https%3A%2F%2Feclipse.gsfc.nasa.gov%2FSEhelp%2Fdeltat2004.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%CE%94T+%28timekeeping%29" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.usno.navy.mil/USNO/earth-orientation/eo-products/long-term">"Long-term Delta T — Naval Oceanography Portal"</a>. c. 2018<span class="reference-accessdate">. Retrieved <span class="nowrap">September 29,</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Long-term+Delta+T+%E2%80%94+Naval+Oceanography+Portal&rft_id=https%3A%2F%2Fwww.usno.navy.mil%2FUSNO%2Fearth-orientation%2Feo-products%2Flong-term&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%CE%94T+%28timekeeping%29" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">In "The Physical Basis of the Leap Second", by D D McCarthy, C Hackman and R A Nelson, in <i>Astronomical Journal</i>, vol.136 (2008), pages 1906–1908, it is stated (page 1908), that "the SI second is equivalent to an older measure of the second of UT1, which was too small to start with and further, as the duration of the UT1 second increases, the discrepancy widens."</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">In the late 1950s, the caesium standard was used to measure both the current mean length of the second of mean solar time (UT2) (result: 9192631830 cycles) and also the second of ephemeris time (ET) (result: 9192631770 ± 20 cycles), see "Time Scales", by L Essen, in <i>Metrologia</i>, vol.4 (1968), pp.161–165, on p.162. The ephemeris figure was chosen for the <a href="/wiki/Second" title="Second">SI second</a>. Essen in the same 1968 article (p.162) stated that this "seemed reasonable in view of the variations in UT2".</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text">J.Chapront, M.Chapront-Touzé, G.Francou (2002): "<a rel="nofollow" class="external text" href="http://www.aanda.org/articles/aa/full/2002/20/aa2201/aa2201.html">A new determination of lunar orbital parameters, precession constant, and tidal acceleration from LLR measurements</a>" (also <a rel="nofollow" class="external text" href="http://www.aanda.org/articles/aa/pdf/2002/20/aa2201.pdf">in PDF</a>). <i>Astronomy & Astrophysics</i> <b>387</b>, 700–709.</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.sciencedaily.com/releases/2020/03/200309135410.htm">"Ancient shell shows days were half-hour shorter 70 million years ago: Beer stein-shaped distant relative of modern clams captured snapshots of hot days in the late Cretaceous"</a>. <i>ScienceDaily</i><span class="reference-accessdate">. Retrieved <span class="nowrap">March 14,</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=ScienceDaily&rft.atitle=Ancient+shell+shows+days+were+half-hour+shorter+70+million+years+ago%3A+Beer+stein-shaped+distant+relative+of+modern+clams+captured+snapshots+of+hot+days+in+the+late+Cretaceous&rft_id=https%3A%2F%2Fwww.sciencedaily.com%2Freleases%2F2020%2F03%2F200309135410.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%CE%94T+%28timekeeping%29" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWinterGoderisMalderenSinnesael2020" class="citation journal cs1">Winter, Niels J. de; Goderis, Steven; Malderen, Stijn J. M. Van; Sinnesael, Matthias; Vansteenberge, Stef; Snoeck, Christophe; Belza, Joke; Vanhaecke, Frank; Claeys, Philippe (2020). <a rel="nofollow" class="external text" href="https://doi.org/10.1029%2F2019PA003723">"Subdaily-Scale Chemical Variability in a Torreites Sanchezi Rudist Shell: Implications for Rudist Paleobiology and the Cretaceous Day-Night Cycle"</a>. <i>Paleoceanography and Paleoclimatology</i>. <b>35</b> (2): e2019PA003723. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1029%2F2019PA003723">10.1029/2019PA003723</a></span>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/1854%2FLU-8685501">1854/LU-8685501</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2572-4525">2572-4525</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Paleoceanography+and+Paleoclimatology&rft.atitle=Subdaily-Scale+Chemical+Variability+in+a+Torreites+Sanchezi+Rudist+Shell%3A+Implications+for+Rudist+Paleobiology+and+the+Cretaceous+Day-Night+Cycle&rft.volume=35&rft.issue=2&rft.pages=e2019PA003723&rft.date=2020&rft_id=info%3Ahdl%2F1854%2FLU-8685501&rft.issn=2572-4525&rft_id=info%3Adoi%2F10.1029%2F2019PA003723&rft.aulast=Winter&rft.aufirst=Niels+J.+de&rft.au=Goderis%2C+Steven&rft.au=Malderen%2C+Stijn+J.+M.+Van&rft.au=Sinnesael%2C+Matthias&rft.au=Vansteenberge%2C+Stef&rft.au=Snoeck%2C+Christophe&rft.au=Belza%2C+Joke&rft.au=Vanhaecke%2C+Frank&rft.au=Claeys%2C+Philippe&rft_id=https%3A%2F%2Fdoi.org%2F10.1029%252F2019PA003723&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%CE%94T+%28timekeeping%29" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilliams2000" class="citation journal cs1">Williams, George E. (2000). "Geological constraints on the Precambrian history of Earth's rotation and the Moon's orbit". <i>Reviews of Geophysics</i>. <b>38</b> (1): 37–60. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000RvGeo..38...37W">2000RvGeo..38...37W</a>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.597.6421">10.1.1.597.6421</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1029%2F1999RG900016">10.1029/1999RG900016</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:51948507">51948507</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Reviews+of+Geophysics&rft.atitle=Geological+constraints+on+the+Precambrian+history+of+Earth%27s+rotation+and+the+Moon%27s+orbit&rft.volume=38&rft.issue=1&rft.pages=37-60&rft.date=2000&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.597.6421%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A51948507%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1029%2F1999RG900016&rft_id=info%3Abibcode%2F2000RvGeo..38...37W&rft.aulast=Williams&rft.aufirst=George+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%CE%94T+%28timekeeping%29" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%94T_(timekeeping)&action=edit&section=9" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Dennis_McCarthy_(scientist)" title="Dennis McCarthy (scientist)">McCarthy, D.D.</a> & Seidelmann, P.K. <i>TIME: From Earth Rotation to Atomic Physics.</i> Weinheim: Wiley-VCH. (2009). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-527-40780-4" title="Special:BookSources/978-3-527-40780-4">978-3-527-40780-4</a></li> <li>Morrison, L.V. & Stephenson, F. R. "<a rel="nofollow" class="external text" href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?2004JHA....35..327M&data_type=PDF_HIGH&type=PRINTER&filetype=.pdf">Historical values of the Earth's clock error Δ<i>T</i> and the calculation of eclipses</a>" (pdf, 862 KB), <i>Journal for the History of Astronomy</i> <b>35</b> (2004) 327–336.</li> <li>Stephenson, F.R. <i>Historical Eclipses and Earth's Rotation</i>. Cambridge University Press, 1997. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-46194-4" title="Special:BookSources/0-521-46194-4">0-521-46194-4</a></li> <li>Stephenson, F. R. & Morrison, L.V. "Long-term fluctuations in the Earth's rotation: 700 BC to AD 1990". <i><a href="/wiki/Philosophical_Transactions_of_the_Royal_Society_of_London" class="mw-redirect" title="Philosophical Transactions of the Royal Society of London">Philosophical Transactions of the Royal Society of London</a></i>, Series A <b>351</b> (1995) 165–202. <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/54464">JSTOR link</a>. Includes evidence that the 'growth' in Delta-T is being modified by an oscillation with a wavelength around 1500 years; if that is true, then during the next few centuries Delta-T values will increase more slowly than is envisaged.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%CE%94T_(timekeeping)&action=edit&section=10" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://maia.usno.navy.mil/products/deltaT">IERS Rapid Service-Prediction Center</a> Values for Delta T.</li> <li><a rel="nofollow" class="external text" href="https://webspace.science.uu.nl/~gent0113/deltat/deltat.htm">Delta T webpage by Robert van Gent</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20150226203358/http://user.online.be/felixverbelen/dt.htm">Delta T webpage by Felix Verbelen</a> (archived from the original dead URL)</li> <li><a rel="nofollow" class="external text" href="https://archive.today/20120716020131/sunearth.gsfc.nasa.gov/eclipse/SEhelp/rotation.html">Eclipse Predictions and Earth's Rotation by Fred Espenak</a> (archived from the original dead URL)</li> <li><a rel="nofollow" class="external text" href="https://eclipse.gsfc.nasa.gov/SEhelp/deltatpoly2004.html">Polynomial expressions for Delta T (Δ<i>T</i>) Espenak and Meeus</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20200917092531/http://www.astro-stuff.com/">Delta-T Charts and data software</a> (archived from the original dead URL)</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist 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title="Chronometry">Chronometry</a></li> <li><a href="/wiki/Orders_of_magnitude_(time)" title="Orders of magnitude (time)">Orders of magnitude</a></li> <li><a href="/wiki/Time_metrology" class="mw-redirect" title="Time metrology">Metrology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">International standards</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Coordinated_Universal_Time" title="Coordinated Universal Time">Coordinated Universal Time</a> <ul><li><a href="/wiki/UTC_offset" title="UTC offset">offset</a></li></ul></li> <li><a href="/wiki/Universal_Time" title="Universal Time">UT</a></li> <li><a class="mw-selflink selflink">ΔT</a></li> <li><a href="/wiki/DUT1" title="DUT1">DUT1</a></li> <li><a href="/wiki/International_Earth_Rotation_and_Reference_Systems_Service" title="International Earth Rotation and Reference Systems Service">International Earth Rotation and Reference Systems Service</a></li> <li><a href="/wiki/ISO_31-1" title="ISO 31-1">ISO 31-1</a></li> <li><a href="/wiki/ISO_8601" title="ISO 8601">ISO 8601</a></li> <li><a href="/wiki/International_Atomic_Time" title="International Atomic Time">International Atomic Time</a></li> <li><a href="/wiki/12-hour_clock" title="12-hour clock">12-hour clock</a></li> <li><a href="/wiki/24-hour_clock" title="24-hour clock">24-hour clock</a></li> <li><a href="/wiki/Barycentric_Coordinate_Time" title="Barycentric Coordinate Time">Barycentric Coordinate Time</a></li> <li><a href="/wiki/Barycentric_Dynamical_Time" title="Barycentric Dynamical Time">Barycentric Dynamical Time</a></li> <li><a href="/wiki/Civil_time" title="Civil time">Civil time</a></li> <li><a href="/wiki/Daylight_saving_time" title="Daylight saving time">Daylight saving time</a></li> <li><a href="/wiki/Geocentric_Coordinate_Time" title="Geocentric Coordinate Time">Geocentric Coordinate Time</a></li> <li><a href="/wiki/International_Date_Line" title="International Date Line">International Date Line</a></li> <li><a href="/wiki/IERS_Reference_Meridian" title="IERS Reference Meridian">IERS Reference Meridian</a></li> <li><a href="/wiki/Leap_second" title="Leap second">Leap second</a></li> <li><a href="/wiki/Solar_time" title="Solar time">Solar time</a></li> <li><a href="/wiki/Terrestrial_Time" title="Terrestrial Time">Terrestrial Time</a></li> <li><a href="/wiki/Time_zone" title="Time zone">Time zone</a></li> <li><a href="/wiki/180th_meridian" title="180th meridian">180th meridian</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="9" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/Hourglass" title="Hourglass"><img alt="template illustration" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Marine_sandglass_MMM.jpg/75px-Marine_sandglass_MMM.jpg" decoding="async" width="75" height="175" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Marine_sandglass_MMM.jpg/113px-Marine_sandglass_MMM.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Marine_sandglass_MMM.jpg/150px-Marine_sandglass_MMM.jpg 2x" data-file-width="1637" data-file-height="3819" /></a></span><br /><span typeof="mw:File"><a href="/wiki/Time_zone" title="Time zone"><img alt="template illustration" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Aleutian_Islands_with_180th_meridian_and_International_Date_Line_%28cropped%29.png/75px-Aleutian_Islands_with_180th_meridian_and_International_Date_Line_%28cropped%29.png" decoding="async" width="75" height="152" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Aleutian_Islands_with_180th_meridian_and_International_Date_Line_%28cropped%29.png/113px-Aleutian_Islands_with_180th_meridian_and_International_Date_Line_%28cropped%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Aleutian_Islands_with_180th_meridian_and_International_Date_Line_%28cropped%29.png/150px-Aleutian_Islands_with_180th_meridian_and_International_Date_Line_%28cropped%29.png 2x" data-file-width="496" data-file-height="1007" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Obsolete standards</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ephemeris_time" title="Ephemeris time">Ephemeris time</a></li> <li><a href="/wiki/Greenwich_Mean_Time" title="Greenwich Mean Time">Greenwich Mean Time</a></li> <li><a href="/wiki/Prime_meridian" title="Prime meridian">Prime meridian</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Time_in_physics" title="Time in physics">Time in physics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Absolute_space_and_time" title="Absolute space and time">Absolute space and time</a></li> <li><a href="/wiki/Spacetime" title="Spacetime">Spacetime</a></li> <li><a href="/wiki/Chronon" title="Chronon">Chronon</a></li> <li><a href="/wiki/Continuous_signal" class="mw-redirect" title="Continuous signal">Continuous signal</a></li> <li><a href="/wiki/Coordinate_time" title="Coordinate time">Coordinate time</a></li> <li><a href="/wiki/Cosmological_decade" title="Cosmological decade">Cosmological decade</a></li> <li><a href="/wiki/Discrete_time_and_continuous_time" title="Discrete time and continuous time">Discrete time and continuous time</a></li> <li><a href="/wiki/Proper_time" title="Proper time">Proper time</a></li> <li><a href="/wiki/Theory_of_relativity" title="Theory of relativity">Theory of relativity</a></li> <li><a href="/wiki/Time_dilation" title="Time dilation">Time dilation</a></li> <li><a href="/wiki/Gravitational_time_dilation" title="Gravitational time dilation">Gravitational time dilation</a></li> <li><a href="/wiki/Time_domain" title="Time domain">Time domain</a></li> <li><a href="/wiki/Time-translation_symmetry" title="Time-translation symmetry">Time-translation symmetry</a></li> <li><a href="/wiki/T-symmetry" title="T-symmetry">T-symmetry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Horology" class="mw-redirect" title="Horology">Horology</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Clock" title="Clock">Clock</a></li> <li><a href="/wiki/Astrarium" title="Astrarium">Astrarium</a></li> <li><a href="/wiki/Atomic_clock" title="Atomic clock">Atomic clock</a></li> <li><a href="/wiki/Complication_(horology)" title="Complication (horology)">Complication</a></li> <li><a href="/wiki/History_of_timekeeping_devices" title="History of timekeeping devices">History of timekeeping devices</a></li> <li><a href="/wiki/Hourglass" title="Hourglass">Hourglass</a></li> <li><a href="/wiki/Marine_chronometer" title="Marine chronometer">Marine chronometer</a></li> <li><a href="/wiki/Marine_sandglass" title="Marine sandglass">Marine sandglass</a></li> <li><a href="/wiki/Radio_clock" title="Radio clock">Radio clock</a></li> <li><a href="/wiki/Watch" title="Watch">Watch</a> <ul><li><a href="/wiki/Stopwatch" title="Stopwatch">stopwatch</a></li></ul></li> <li><a href="/wiki/Water_clock" title="Water clock">Water clock</a></li> <li><a href="/wiki/Sundial" title="Sundial">Sundial</a></li> <li><a href="/wiki/Dialing_scales" title="Dialing scales">Dialing scales</a></li> <li><a href="/wiki/Equation_of_time" title="Equation of time">Equation of time</a></li> <li><a href="/wiki/History_of_sundials" title="History of sundials">History of sundials</a></li> <li><a href="/wiki/Schema_for_horizontal_dials" title="Schema for horizontal dials">Sundial markup schema</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Calendar" title="Calendar">Calendar</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Gregorian_calendar" title="Gregorian calendar">Gregorian</a></li> <li><a href="/wiki/Hebrew_calendar" title="Hebrew calendar">Hebrew</a></li> <li><a href="/wiki/Hindu_calendar" title="Hindu calendar">Hindu</a></li> <li><a href="/wiki/Holocene_calendar" title="Holocene calendar">Holocene</a></li> <li><a href="/wiki/Islamic_calendar" title="Islamic calendar">Islamic</a> (lunar Hijri)</li> <li><a href="/wiki/Julian_calendar" title="Julian calendar">Julian</a></li> <li><a href="/wiki/Solar_Hijri_calendar" title="Solar Hijri calendar">Solar Hijri</a></li> <li><a href="/wiki/Astronomical_year_numbering" title="Astronomical year numbering">Astronomical</a></li> <li><a href="/wiki/Dominical_letter" title="Dominical letter">Dominical letter</a></li> <li><a href="/wiki/Epact" title="Epact">Epact</a></li> <li><a href="/wiki/Equinox" title="Equinox">Equinox</a></li> <li><a href="/wiki/Intercalation_(timekeeping)" title="Intercalation (timekeeping)">Intercalation</a></li> <li><a href="/wiki/Julian_day" title="Julian day">Julian day</a></li> <li><a href="/wiki/Leap_year" title="Leap year">Leap year</a></li> <li><a href="/wiki/Lunar_calendar" title="Lunar calendar">Lunar</a></li> <li><a href="/wiki/Lunisolar_calendar" title="Lunisolar calendar">Lunisolar</a></li> <li><a href="/wiki/Solar_calendar" title="Solar calendar">Solar</a></li> <li><a href="/wiki/Solstice" title="Solstice">Solstice</a></li> <li><a href="/wiki/Tropical_year" title="Tropical year">Tropical year</a></li> <li><a href="/wiki/Determination_of_the_day_of_the_week" title="Determination of the day of the week">Weekday determination</a></li> <li><a href="/wiki/Names_of_the_days_of_the_week" title="Names of the days of the week">Weekday names</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Archaeology and geology</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chronological_dating" title="Chronological dating">Chronological dating</a></li> <li><a href="/wiki/Geologic_time_scale" title="Geologic time scale">Geologic time scale</a></li> <li><a href="/wiki/International_Commission_on_Stratigraphy" title="International Commission on Stratigraphy">International Commission on Stratigraphy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Astronomical_chronology" title="Astronomical chronology">Astronomical chronology</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Galactic_year" title="Galactic year">Galactic year</a></li> <li><a href="/wiki/Nuclear_timescale" title="Nuclear timescale">Nuclear timescale</a></li> <li><a href="/wiki/Precession" title="Precession">Precession</a></li> <li><a href="/wiki/Sidereal_time" title="Sidereal time">Sidereal time</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other <a href="/wiki/Unit_of_time" title="Unit of time">units of time</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Instant" title="Instant">Instant</a></li> <li><a href="/wiki/Flick_(time)" title="Flick (time)">Flick</a></li> <li><a href="/wiki/Shake_(unit)" title="Shake (unit)">Shake</a></li> <li><a href="/wiki/Jiffy_(time)" title="Jiffy (time)">Jiffy</a></li> <li><a href="/wiki/Second" title="Second">Second</a></li> <li><a href="/wiki/Minute" title="Minute">Minute</a></li> <li><a href="/wiki/Moment_(unit)" title="Moment (unit)">Moment</a></li> <li><a href="/wiki/Hour" title="Hour">Hour</a></li> <li><a href="/wiki/Day" title="Day">Day</a></li> <li><a href="/wiki/Week" title="Week">Week</a></li> <li><a href="/wiki/Fortnight" title="Fortnight">Fortnight</a></li> <li><a href="/wiki/Month" title="Month">Month</a></li> <li><a href="/wiki/Year" title="Year">Year</a></li> <li><a href="/wiki/Olympiad" title="Olympiad">Olympiad</a></li> <li><a href="/wiki/Lustrum" title="Lustrum">Lustrum</a></li> <li><a href="/wiki/Decade" title="Decade">Decade</a></li> <li><a href="/wiki/Century" title="Century">Century</a></li> <li><a href="/wiki/Saeculum" title="Saeculum">Saeculum</a></li> <li><a href="/wiki/Millennium" title="Millennium">Millennium</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chronology" title="Chronology">Chronology</a></li> <li><a href="/wiki/Duration_(philosophy)" title="Duration (philosophy)">Duration</a> <ul><li><a href="/wiki/Duration_(music)" title="Duration (music)">music</a></li></ul></li> <li><a href="/wiki/Mental_chronometry" title="Mental chronometry">Mental chronometry</a></li> <li><a href="/wiki/Decimal_time" title="Decimal time">Decimal time</a></li> <li><a href="/wiki/Metric_time" title="Metric time">Metric time</a></li> <li><a href="/wiki/System_time" title="System time">System time</a></li> <li><a href="/wiki/Time_metrology" class="mw-redirect" title="Time metrology">Time metrology</a></li> <li><a href="/wiki/Time_value_of_money" title="Time value of money">Time value of money</a></li> <li><a href="/wiki/Timekeeper" title="Timekeeper">Timekeeper</a></li></ul> </div></td></tr></tbody></table></div> <!-- NewPP limit report Parsed by mw‐web.codfw.main‐f69cdc8f6‐f9ddp Cached time: 20241122145509 Cache expiry: 2592000 Reduced expiry: false Complications: 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