Barycentric Coordinate Time

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<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">Calculations pertaining to orbits</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Barycentric_Coordinate_Time" title="Special:EditPage/Barycentric Coordinate Time">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Barycentric+Coordinate+Time%22">"Barycentric Coordinate Time"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Barycentric+Coordinate+Time%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Barycentric+Coordinate+Time%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Barycentric+Coordinate+Time%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Barycentric+Coordinate+Time%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Barycentric+Coordinate+Time%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">November 2007</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p><b>Barycentric Coordinate Time</b> (<b>TCB</b>, from the <a href="/wiki/French_language" title="French language">French</a> <b>Temps-coordonnée barycentrique</b>) is a <a href="/wiki/Coordinate_time" title="Coordinate time">coordinate</a> <a href="/wiki/Time_standard" title="Time standard">time standard</a> intended to be used as the independent variable of time for all calculations pertaining to orbits of <a href="/wiki/Planet" title="Planet">planets</a>, <a href="/wiki/Asteroid" title="Asteroid">asteroids</a>, <a href="/wiki/Comet" title="Comet">comets</a>, and interplanetary <a href="/wiki/Spacecraft" title="Spacecraft">spacecraft</a> in the <a href="/wiki/Solar_System" title="Solar System">Solar System</a>. It is equivalent to the <a href="/wiki/Proper_time" title="Proper time">proper time</a> experienced by a clock at rest in a coordinate frame <a href="/wiki/Proper_frame" title="Proper frame">co-moving</a> with the <a href="/wiki/Barycenter" class="mw-redirect" title="Barycenter">barycenter</a> (center of mass) of the Solar System <sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2023)">citation needed</span></a></i>]</sup>: that is, a clock that performs exactly the same movements as the Solar System but is outside the system's <a href="/wiki/Gravity_well" class="mw-redirect" title="Gravity well">gravity well</a>. It is therefore not influenced by the <a href="/wiki/Gravitational_time_dilation" title="Gravitational time dilation">gravitational time dilation</a> caused by the <a href="/wiki/Sun" title="Sun">Sun</a> and the rest of the system. TCB is the time coordinate for the <a href="/wiki/Barycentric_Celestial_Reference_System" class="mw-redirect" title="Barycentric Celestial Reference System">Barycentric Celestial Reference System</a> (BCRS). </p><p>TCB was defined in 1991 by the <a href="/wiki/International_Astronomical_Union" title="International Astronomical Union">International Astronomical Union</a>, in Recommendation III of the XXIst General Assembly.<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> It was intended as one of the replacements for the problematic 1976 definition of <a href="/wiki/Barycentric_Dynamical_Time" title="Barycentric Dynamical Time">Barycentric Dynamical Time</a> (TDB). Unlike former astronomical time scales, TCB is defined in the context of the <a href="/wiki/General_relativity" title="General relativity">general theory of relativity</a>. The relationships between TCB and other relativistic time scales are defined with fully <a href="/wiki/Metric_tensor_(general_relativity)" title="Metric tensor (general relativity)">general relativistic metrics</a>. The transformation between TCB and <a href="/wiki/Geocentric_Coordinate_Time" title="Geocentric Coordinate Time">Geocentric Coordinate Time</a> (TCG) may be approximated with an uncertainty not larger than <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 5\times 10^{-18}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>18</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5\times 10^{-18}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c38651a0b7eed073b54f203b6fe6ec599b9c37de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.483ex; height:2.676ex;" alt="{\displaystyle 5\times 10^{-18}}"></span> in rate as:<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> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}TCB-TCG&=c^{-2}\left[\int _{t_{0}}^{t}\left({\frac {v_{E}^{2}}{2}}+w_{0ext}(\mathbf {x} _{E})\right)dt+v_{E}^{i}r_{E}^{i}\right]\\&-c^{-4}\left[\int _{t_{0}}^{t}\left(-{\frac {1}{8}}v_{E}^{4}-{\frac {3}{2}}v_{E}^{2}w_{0ext}(\mathbf {x} _{E})+4v_{E}^{i}w_{ext}^{i}(\mathbf {x} _{E})+{\frac {1}{2}}w_{0ext}^{2}(\mathbf {x} _{E})\right)dt\right.\\&\qquad \qquad \left.-\left(3w_{0ext}(\mathbf {x} _{E})+{\frac {v_{E}^{2}}{2}}\right)v_{E}^{i}r_{E}^{i}\right]\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>T</mi> <mi>C</mi> <mi>B</mi> <mo>−</mo> <mi>T</mi> <mi>C</mi> <mi>G</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mrow> <mo>[</mo> <mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mn>2</mn> </mfrac> </mrow> <mo>+</mo> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>+</mo> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> </mrow> <mo>]</mo> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>4</mn> </mrow> </msup> <mrow> <mo>[</mo> <mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>8</mn> </mfrac> </mrow> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msubsup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mn>4</mn> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> <msubsup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msubsup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> </mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mspace width="2em" /> <mspace width="2em" /> <mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> <mrow> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mn>3</mn> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> </mrow> <mo>]</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}TCB-TCG&=c^{-2}\left[\int _{t_{0}}^{t}\left({\frac {v_{E}^{2}}{2}}+w_{0ext}(\mathbf {x} _{E})\right)dt+v_{E}^{i}r_{E}^{i}\right]\\&-c^{-4}\left[\int _{t_{0}}^{t}\left(-{\frac {1}{8}}v_{E}^{4}-{\frac {3}{2}}v_{E}^{2}w_{0ext}(\mathbf {x} _{E})+4v_{E}^{i}w_{ext}^{i}(\mathbf {x} _{E})+{\frac {1}{2}}w_{0ext}^{2}(\mathbf {x} _{E})\right)dt\right.\\&\qquad \qquad \left.-\left(3w_{0ext}(\mathbf {x} _{E})+{\frac {v_{E}^{2}}{2}}\right)v_{E}^{i}r_{E}^{i}\right]\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aca6c04f6a2b6501e3225db5bac77e43d6d18fe7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -10.088ex; margin-bottom: -0.25ex; width:85.015ex; height:21.843ex;" alt="{\displaystyle {\begin{aligned}TCB-TCG&=c^{-2}\left[\int _{t_{0}}^{t}\left({\frac {v_{E}^{2}}{2}}+w_{0ext}(\mathbf {x} _{E})\right)dt+v_{E}^{i}r_{E}^{i}\right]\\&-c^{-4}\left[\int _{t_{0}}^{t}\left(-{\frac {1}{8}}v_{E}^{4}-{\frac {3}{2}}v_{E}^{2}w_{0ext}(\mathbf {x} _{E})+4v_{E}^{i}w_{ext}^{i}(\mathbf {x} _{E})+{\frac {1}{2}}w_{0ext}^{2}(\mathbf {x} _{E})\right)dt\right.\\&\qquad \qquad \left.-\left(3w_{0ext}(\mathbf {x} _{E})+{\frac {v_{E}^{2}}{2}}\right)v_{E}^{i}r_{E}^{i}\right]\end{aligned}}}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{E}^{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{E}^{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82d4030851bb27f8ee7bc4af1c286443c82a6fd1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.817ex; height:3.176ex;" alt="{\displaystyle x_{E}^{i}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{E}^{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{E}^{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b48cf9e0669ff1d4e336a23c6ae62a0f00c43f4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.615ex; height:3.176ex;" alt="{\displaystyle v_{E}^{i}}"></span> are the barycentric coordinate position and velocity of the geocenter, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{E}^{i}=x^{i}-x_{E}^{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msup> <mo>−</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{E}^{i}=x^{i}-x_{E}^{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458b71531a1d67fc64c2ed400cba97b55d33110e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.422ex; height:3.343ex;" alt="{\displaystyle r_{E}^{i}=x^{i}-x_{E}^{i}}"></span> with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be8cd88951c7c0e3b181f956531b0a878bbed203" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.129ex; height:2.676ex;" alt="{\displaystyle x^{i}}"></span> the barycentric position of the observer, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t=TCB}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mi>T</mi> <mi>C</mi> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t=TCB}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c71301cde40b9873ae4566395391b278d84fac75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.105ex; height:2.176ex;" alt="{\displaystyle t=TCB}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02d3006c4190b1939b04d9b9bb21006fb4e6fa4a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.894ex; height:2.343ex;" alt="{\displaystyle t_{0}}"></span> is the origin of TCB and TCG defined so that 1977 January 1, 00:00:00 <a href="/wiki/International_Atomic_Time" title="International Atomic Time">TAI</a> is 1977 January 1, 00:00:32.184 TCG / TCB, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w_{0ext}(\mathbf {x} _{E})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{0ext}(\mathbf {x} _{E})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcbc3ce6b6f1dbc49e770be624051ea8c7337e74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.727ex; height:2.843ex;" alt="{\displaystyle w_{0ext}(\mathbf {x} _{E})}"></span> is the sum <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \sum _{A}{\frac {GM_{A}}{r_{A}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>G</mi> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mrow> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \sum _{A}{\frac {GM_{A}}{r_{A}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/221e83b66677dd5dd10e05ac80e82f0a7b4abaf9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:7.6ex; height:3.843ex;" alt="{\displaystyle \scriptstyle \sum _{A}{\frac {GM_{A}}{r_{A}}}}"></span> of <a href="/wiki/Gravitational_potential" title="Gravitational potential">gravitational potentials</a> for all solar system bodies apart from the Earth evaluated at the geocenter, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w_{ext}^{i}(\mathbf {x} _{E})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> <mi>x</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{ext}^{i}(\mathbf {x} _{E})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5d4179f44f873c5f27446166a634406556aa7d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.905ex; height:3.176ex;" alt="{\displaystyle w_{ext}^{i}(\mathbf {x} _{E})}"></span> is similarly the sum <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle \sum _{A}{\frac {GM_{A}}{r_{A}}}v_{A}^{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="false" scriptlevel="1"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>G</mi> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mrow> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mfrac> </mrow> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \scriptstyle \sum _{A}{\frac {GM_{A}}{r_{A}}}v_{A}^{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c25563dc574ef246734c6ec86cd503d09703c726" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:9.562ex; height:3.843ex;" alt="{\displaystyle \scriptstyle \sum _{A}{\frac {GM_{A}}{r_{A}}}v_{A}^{i}}"></span>. The approximation discards higher powers of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{E}^{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{E}^{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b26073283295f3b92c08667afd5a50f9d8e8fbd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.536ex; height:3.176ex;" alt="{\displaystyle r_{E}^{i}}"></span> as they have been found to be negligible.<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> </p><p>Because the reference frame for TCB is not influenced by the <a href="/wiki/Gravitational_potential" title="Gravitational potential">gravitational potential</a> caused by the Solar System, TCB ticks faster than clocks on the surface of the Earth by 1.550505 × 10<sup>−8</sup> (about 490 milliseconds per year). Consequently, the values of physical constants to be used with calculations using TCB differ from the traditional values of physical constants (The traditional values were in a sense wrong, incorporating corrections for the difference in time scales). Adapting the large body of existing software to change from TDB to TCB is an ongoing task, and as of 2002<sup class="plainlinks noexcerpt noprint asof-tag update" style="display:none;"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Barycentric_Coordinate_Time&action=edit">[update]</a></sup> many calculations continued to use TDB in some form. </p><p>Time coordinates on the TCB scale are specified conventionally using traditional means of specifying days, inherited from slightly non-uniform time standards based on the rotation of the Earth. Specifically, both <a href="/wiki/Julian_Date" class="mw-redirect" title="Julian Date">Julian Dates</a> and the <a href="/wiki/Gregorian_calendar" title="Gregorian calendar">Gregorian calendar</a> are used. For continuity with its predecessor <a href="/wiki/Ephemeris_Time" class="mw-redirect" title="Ephemeris Time">Ephemeris Time</a>, TCB was set to match ET at around Julian Date 2443144.5 (1977-01-01T00Z). More precisely, it was defined that TCB instant 1977-01-01T00:00:32.184 corresponds exactly to the <a href="/wiki/International_Atomic_Time" title="International Atomic Time">International Atomic Time</a> (TAI) instant 1977-01-01T00:00:00.000, at the <a href="/wiki/Geocentric_coordinates" class="mw-redirect" title="Geocentric coordinates">geocenter</a>. This is also the instant at which TAI introduced corrections for gravitational time dilation. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Barycentric_Coordinate_Time&action=edit&section=1" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Terrestrial_Time" title="Terrestrial Time">Terrestrial Time</a></li></ul> <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=Barycentric_Coordinate_Time&action=edit&section=2" title="Edit section: References"><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"><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"><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://web.archive.org/web/20070927234636/http://www.iers.org/MainDisp.csl?pid=98-133">"IAU(1991) Recommendation III"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.iers.org/MainDisp.csl?pid=98-133">the original</a> on 2007-09-27<span class="reference-accessdate">. Retrieved <span class="nowrap">2006-04-28</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=IAU%281991%29+Recommendation+III&rft_id=http%3A%2F%2Fwww.iers.org%2FMainDisp.csl%3Fpid%3D98-133&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABarycentric+Coordinate+Time" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPetit" class="citation web cs1">Petit, Gerard. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220120130229/https://www.iers.org/SharedDocs/Publikationen/EN/IERS/Publications/tn/TechnNote29/tn29_019.pdf;jsessionid=BA47C983D1F7A649FE5F4B0BDEB9F5B6.live2?__blob=publicationFile&v=1">"Comparision [sic] of "Old" and "New" Concepts: Coordinate Times and Time Transformations"</a>. p. 23. Archived from <a rel="nofollow" class="external text" href="https://www.iers.org/SharedDocs/Publikationen/EN/IERS/Publications/tn/TechnNote29/tn29_019.pdf;jsessionid=BA47C983D1F7A649FE5F4B0BDEB9F5B6.live2?__blob=publicationFile&v=1">the original</a> on 2022-01-20.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Comparision+%5Bsic%5D+of+%22Old%22+and+%22New%22+Concepts%3A+Coordinate+Times+and+Time+Transformations&rft.pages=23&rft.aulast=Petit&rft.aufirst=Gerard&rft_id=https%3A%2F%2Fwww.iers.org%2FSharedDocs%2FPublikationen%2FEN%2FIERS%2FPublications%2Ftn%2FTechnNote29%2Ftn29_019.pdf%3Bjsessionid%3DBA47C983D1F7A649FE5F4B0BDEB9F5B6.live2%3F__blob%3DpublicationFile%26v%3D1&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABarycentric+Coordinate+Time" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSoffelKlionerPetitWolf2003" class="citation journal cs1">Soffel, M.; Klioner, S. A.; Petit, G.; Wolf, P.; Kopeikin, S. M.; Bretagnon, P.; Brumberg, V. A.; Capitaine, N.; Damour, T.; Fukushima, T.; Guinot, B.; Huang, T.-Y.; Lindegren, L.; Ma, C.; Nordtvedt, K.; Ries, J. C.; Seidelmann, P. K.; Vokrouhlick, D.; Will, C. M.; Xu, C. (December 2003). <a rel="nofollow" class="external text" href="https://iopscience.iop.org/article/10.1086/378162/fulltext/202343.text.html">"The IAU 2000 Resolutions for Astrometry, Celestial Mechanics, and Metrology in the Relativistic Framework: Explanatory Supplement"</a>. <i>The Astronomical Journal</i>. <b>126</b> (6): 2687–2706. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/astro-ph/0303376">astro-ph/0303376</a></span>. <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/2003AJ....126.2687S">2003AJ....126.2687S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F378162">10.1086/378162</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:32887246">32887246</a>.</cite><span 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measurement</a> and <a href="/wiki/Time_standard" title="Time standard">standards</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><a href="/wiki/Chronometry" 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 href="/wiki/%CE%94T_(timekeeping)" title="ΔT (timekeeping)">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 class="mw-selflink selflink">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 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Barycentric Coordinate Time - Wikipedia