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</button> <ul id="toc-Epoch_versus_equinox-sublist" class="vector-toc-list"> <li id="toc-Date-references_for_coordinate_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Date-references_for_coordinate_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Date-references for coordinate systems</span> </div> </a> <ul id="toc-Date-references_for_coordinate_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Epochs_and_periods_of_validity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Epochs_and_periods_of_validity"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Epochs and periods of validity</span> </div> </a> <ul id="toc-Epochs_and_periods_of_validity-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Changing_the_standard_equinox_and_epoch" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Changing_the_standard_equinox_and_epoch"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Changing the standard equinox and epoch</span> </div> </a> <ul id="toc-Changing_the_standard_equinox_and_epoch-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Specifying_an_epoch_or_equinox" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Specifying_an_epoch_or_equinox"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Specifying an epoch or equinox</span> </div> </a> <ul id="toc-Specifying_an_epoch_or_equinox-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Besselian_years" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Besselian_years"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Besselian years</span> </div> </a> <ul id="toc-Besselian_years-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Julian_years_and_J2000" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Julian_years_and_J2000"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Julian years and J2000</span> </div> </a> <ul id="toc-Julian_years_and_J2000-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Epoch_of_the_day" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Epoch_of_the_day"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Epoch of the day</span> </div> </a> <ul id="toc-Epoch_of_the_day-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-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">8</span> <span>References</span> </div> </a> <button aria-controls="toc-References-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle References subsection</span> </button> <ul id="toc-References-sublist" class="vector-toc-list"> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Citations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Citations"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Citations</span> </div> </a> <ul id="toc-Citations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.4</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> </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 class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Epoch (astronomy)</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 55 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-55" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">55 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Epog_(sterrekunde)" title="Epog (sterrekunde) – Afrikaans" lang="af" hreflang="af" data-title="Epog (sterrekunde)" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AD%D9%82%D8%A8%D8%A9_(%D8%B9%D9%84%D9%85_%D8%A7%D9%84%D9%81%D9%84%D9%83)" title="حقبة (علم الفلك) – Arabic" lang="ar" hreflang="ar" data-title="حقبة (علم الفلك)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/D%C3%B3mina_(astronom%C3%ADa)" title="Dómina (astronomía) – Asturian" lang="ast" hreflang="ast" data-title="Dómina (astronomía)" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%B8%E0%A6%99%E0%A7%8D%E0%A6%97%E0%A6%A4%E0%A6%BF%E0%A6%A5%E0%A6%BF_(%E0%A6%9C%E0%A7%8D%E0%A6%AF%E0%A7%8B%E0%A6%A4%E0%A6%BF%E0%A6%B0%E0%A7%8D%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8)" title="প্রসঙ্গতিথি (জ্যোতির্বিজ্ঞান) – Bangla" lang="bn" hreflang="bn" data-title="প্রসঙ্গতিথি (জ্যোতির্বিজ্ঞান)" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D0%BF%D0%BE%D1%85%D0%B0_(%D0%B0%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%BE%D0%BC%D1%96%D1%8F)" title="Эпоха (астраномія) – Belarusian" lang="be" hreflang="be" data-title="Эпоха (астраномія)" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%AD%D0%BF%D0%BE%D1%85%D0%B0_(%D0%B0%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%BE%D0%BC%D1%96%D1%8F)" title="Эпоха (астраномія) – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Эпоха (астраномія)" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%BF%D0%BE%D1%85%D0%B0_(%D0%B0%D1%81%D1%82%D1%80%D0%BE%D0%BD%D0%BE%D0%BC%D0%B8%D1%8F)" title="Епоха (астрономия) – Bulgarian" lang="bg" hreflang="bg" data-title="Епоха (астрономия)" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Epoha_(astronomija)" title="Epoha (astronomija) – Bosnian" lang="bs" hreflang="bs" data-title="Epoha (astronomija)" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%88poca_(astronomia)" title="Època (astronomia) – Catalan" lang="ca" hreflang="ca" data-title="Època (astronomia)" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Ekvinokcium" title="Ekvinokcium – Czech" lang="cs" hreflang="cs" data-title="Ekvinokcium" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Epoche_(Astronomie)" title="Epoche (Astronomie) – German" lang="de" hreflang="de" data-title="Epoche (Astronomie)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CF%80%CE%BF%CF%87%CE%AE_(%CE%B1%CF%83%CF%84%CF%81%CE%BF%CE%BD%CE%BF%CE%BC%CE%AF%CE%B1)" title="Εποχή (αστρονομία) – Greek" lang="el" hreflang="el" data-title="Εποχή (αστρονομία)" 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/%C3%89poca_(astronom%C3%ADa)" title="Época (astronomía) – Spanish" lang="es" hreflang="es" data-title="Época (astronomía)" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Epoko_(astronomio)" title="Epoko (astronomio) – Esperanto" lang="eo" hreflang="eo" data-title="Epoko (astronomio)" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Garai_(astronomia)" title="Garai (astronomia) – Basque" lang="eu" hreflang="eu" data-title="Garai (astronomia)" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%A8%D8%AF%D8%A3_(%D8%A7%D8%AE%D8%AA%D8%B1%D8%B4%D9%86%D8%A7%D8%B3%DB%8C)" title="مبدأ (اخترشناسی) – Persian" lang="fa" hreflang="fa" data-title="مبدأ (اخترشناسی)" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%C3%89poque_(astronomie)" title="Époque (astronomie) – French" lang="fr" hreflang="fr" data-title="Époque (astronomie)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/%C3%89poca_(astronom%C3%ADa)" title="Época (astronomía) – Galician" lang="gl" hreflang="gl" data-title="Época (astronomía)" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%AD%EA%B8%B0%EC%A0%90" title="역기점 – Korean" lang="ko" hreflang="ko" data-title="역기점" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B7%D5%BA%D5%B8%D5%AD%D5%A1_(%D5%A1%D5%BD%D5%BF%D5%B2%D5%A1%D5%A3%D5%AB%D5%BF%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6)" title="Էպոխա (աստղագիտություն) – Armenian" lang="hy" hreflang="hy" data-title="Էպոխա (աստղագիտություն)" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AF%E0%A5%81%E0%A4%97%E0%A4%BE%E0%A4%B0%E0%A4%AE%E0%A5%8D%E0%A4%AD_(%E0%A4%96%E0%A4%97%E0%A5%8B%E0%A4%B2%E0%A4%B6%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0)" title="युगारम्भ (खगोलशास्त्र) – Hindi" lang="hi" hreflang="hi" data-title="युगारम्भ (खगोलशास्त्र)" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Epoha_(astronomija)" title="Epoha (astronomija) – Croatian" lang="hr" hreflang="hr" data-title="Epoha (astronomija)" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Epos_(astronomi)" title="Epos (astronomi) – Indonesian" lang="id" hreflang="id" data-title="Epos (astronomi)" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Epoca_(astronomia)" title="Epoca (astronomia) – Italian" lang="it" hreflang="it" data-title="Epoca (astronomia)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%A7%D7%95%D7%A4%D7%AA_%D7%99%D7%99%D7%97%D7%95%D7%A1_(%D7%90%D7%A1%D7%98%D7%A8%D7%95%D7%A0%D7%95%D7%9E%D7%99%D7%94)" title="תקופת ייחוס (אסטרונומיה) – Hebrew" lang="he" hreflang="he" data-title="תקופת ייחוס (אסטרונומיה)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%94%E1%83%9E%E1%83%9D%E1%83%A5%E1%83%90_(%E1%83%90%E1%83%A1%E1%83%A2%E1%83%A0%E1%83%9D%E1%83%9C%E1%83%9D%E1%83%9B%E1%83%98%E1%83%90)" title="ეპოქა (ასტრონომია) – Georgian" lang="ka" hreflang="ka" data-title="ეპოქა (ასტრონომია)" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Epocha_(astronomia)" title="Epocha (astronomia) – Latin" lang="la" hreflang="la" data-title="Epocha (astronomia)" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Epoch_(Astronomie)" title="Epoch (Astronomie) – Luxembourgish" lang="lb" hreflang="lb" data-title="Epoch (Astronomie)" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Epocha_(astronomija)" title="Epocha (astronomija) – Lithuanian" lang="lt" hreflang="lt" data-title="Epocha (astronomija)" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%95%D0%BF%D0%BE%D1%85%D0%B0_(%D0%B0%D1%81%D1%82%D1%80%D0%BE%D0%BD%D0%BE%D0%BC%D0%B8%D1%98%D0%B0)" title="Епоха (астрономија) – Macedonian" lang="mk" hreflang="mk" data-title="Епоха (астрономија)" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AF%E0%A5%81%E0%A4%97_(%E0%A4%96%E0%A4%97%E0%A5%8B%E0%A4%B2%E0%A4%B6%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0)" title="युग (खगोलशास्त्र) – Marathi" lang="mr" hreflang="mr" data-title="युग (खगोलशास्त्र)" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Epok_(astronomi)" title="Epok (astronomi) – Malay" lang="ms" hreflang="ms" data-title="Epok (astronomi)" 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-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Epoche_(astronomie)" title="Epoche (astronomie) – Dutch" lang="nl" hreflang="nl" data-title="Epoche (astronomie)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%85%83%E6%9C%9F" title="元期 – Japanese" lang="ja" hreflang="ja" data-title="元期" 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-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Epoke_(astronomi)" title="Epoke (astronomi) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Epoke (astronomi)" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Astronomisk_epoke" title="Astronomisk epoke – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Astronomisk epoke" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Davr_(astronomiya)" title="Davr (astronomiya) – Uzbek" lang="uz" hreflang="uz" data-title="Davr (astronomiya)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Epoka_(astronomia)" title="Epoka (astronomia) – Polish" lang="pl" hreflang="pl" data-title="Epoka (astronomia)" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%89poca_(astronomia)" title="Época (astronomia) – Portuguese" lang="pt" hreflang="pt" data-title="Época (astronomia)" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Epoc%C4%83_(astronomie)" title="Epocă (astronomie) – Romanian" lang="ro" hreflang="ro" data-title="Epocă (astronomie)" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BF%D0%BE%D1%85%D0%B0_(%D0%B0%D1%81%D1%82%D1%80%D0%BE%D0%BD%D0%BE%D0%BC%D0%B8%D1%8F)" title="Эпоха (астрономия) – Russian" lang="ru" hreflang="ru" data-title="Эпоха (астрономия)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Epoch_(astronomy)" title="Epoch (astronomy) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Epoch (astronomy)" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Epocha_(astron%C3%B3mia)" title="Epocha (astronómia) – Slovak" lang="sk" hreflang="sk" data-title="Epocha (astronómia)" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Epoha_(astronomija)" title="Epoha (astronomija) – Slovenian" lang="sl" hreflang="sl" data-title="Epoha (astronomija)" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Epoka_(astr%C5%8Dn%C5%8Dmij%C5%8F)" title="Epoka (astrōnōmijŏ) – Silesian" lang="szl" hreflang="szl" data-title="Epoka (astrōnōmijŏ)" data-language-autonym="Ślůnski" data-language-local-name="Silesian" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%95%D0%BF%D0%BE%D1%85%D0%B0_(%D0%B0%D1%81%D1%82%D1%80%D0%BE%D0%BD%D0%BE%D0%BC%D0%B8%D1%98%D0%B0)" title="Епоха (астрономија) – Serbian" lang="sr" hreflang="sr" data-title="Епоха (астрономија)" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Epoha_(astronomija)" title="Epoha (astronomija) – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Epoha (astronomija)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Epookki_(t%C3%A4htitiede)" title="Epookki (tähtitiede) – Finnish" lang="fi" hreflang="fi" data-title="Epookki (tähtitiede)" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Epok_(astronomi)" title="Epok (astronomi) – Swedish" lang="sv" hreflang="sv" data-title="Epok (astronomi)" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%95%E0%B9%89%E0%B8%99%E0%B8%A2%E0%B8%B8%E0%B8%84%E0%B8%AD%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%AD%E0%B8%B4%E0%B8%87_(%E0%B8%94%E0%B8%B2%E0%B8%A3%E0%B8%B2%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C)" title="ต้นยุคอ้างอิง (ดาราศาสตร์) – Thai" lang="th" hreflang="th" data-title="ต้นยุคอ้างอิง (ดาราศาสตร์)" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Devir_(astronomi)" title="Devir (astronomi) – Turkish" lang="tr" hreflang="tr" data-title="Devir (astronomi)" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D0%BF%D0%BE%D1%85%D0%B0_(%D0%B0%D1%81%D1%82%D1%80%D0%BE%D0%BD%D0%BE%D0%BC%D1%96%D1%8F)" title="Епоха (астрономія) – Ukrainian" lang="uk" hreflang="uk" data-title="Епоха (астрономія)" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/K%E1%BB%B7_nguy%C3%AAn_(thi%C3%AAn_v%C4%83n_h%E1%BB%8Dc)" title="Kỷ nguyên (thiên văn học) – Vietnamese" lang="vi" hreflang="vi" data-title="Kỷ nguyên (thiên văn học)" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%9B%86%E5%85%83" title="曆元 – Cantonese" lang="yue" hreflang="yue" data-title="曆元" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%9B%86%E5%85%83" title="曆元 – Chinese" lang="zh" hreflang="zh" data-title="曆元" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet 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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">Moment in time used as a reference point in astronomy</div> <p class="mw-empty-elt"> </p><p>In <a href="/wiki/Astronomy" title="Astronomy">astronomy</a>, an <b>epoch</b> or <b>reference epoch</b> is a <a href="/wiki/Instant" title="Instant">moment</a> in time used as a reference point for some time-varying astronomical quantity. It is useful for the <a href="/wiki/Celestial_coordinates" class="mw-redirect" title="Celestial coordinates">celestial coordinates</a> or <a href="/wiki/Orbital_elements" title="Orbital elements">orbital elements</a> of a <a href="/wiki/Astronomical_object" title="Astronomical object">celestial body</a>, as they are subject to <a href="/wiki/Perturbation_(astronomy)" title="Perturbation (astronomy)">perturbations</a> and vary with time.<sup id="cite_ref-FOOTNOTESoop1994_1-0" class="reference"><a href="#cite_note-FOOTNOTESoop1994-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> These time-varying astronomical quantities might include, for example, the <a href="/wiki/Mean_longitude" title="Mean longitude">mean longitude</a> or <a href="/wiki/Mean_anomaly" title="Mean anomaly">mean anomaly</a> of a body, the node of its orbit relative to a <a href="/wiki/Reference_plane" class="mw-redirect" title="Reference plane">reference plane</a>, the direction of the <a href="/wiki/Apogee" class="mw-redirect" title="Apogee">apogee</a> or <a href="/wiki/Perihelion_and_aphelion" class="mw-redirect" title="Perihelion and aphelion">aphelion</a> of its orbit, or the size of the <a href="/wiki/Major_axis" class="mw-redirect" title="Major axis">major axis</a> of its orbit. </p><p>The main use of astronomical quantities specified in this way is to calculate other relevant parameters of motion, in order to predict future positions and velocities. The applied tools of the disciplines of <a href="/wiki/Celestial_mechanics" title="Celestial mechanics">celestial mechanics</a> or its subfield <a href="/wiki/Orbital_mechanics" title="Orbital mechanics">orbital mechanics</a> (for predicting orbital paths and positions for bodies in motion under the gravitational effects of other bodies) can be used to generate an <a href="/wiki/Ephemeris" title="Ephemeris">ephemeris</a>, a table of values giving the positions and velocities of astronomical objects in the sky at a given time or times. </p><p>Astronomical quantities can be specified in any of several ways, for example, as a <a href="/wiki/Polynomial" title="Polynomial">polynomial</a> function of the time interval, with an epoch as a temporal point of origin (this is a common current way of using an epoch). Alternatively, the time-varying astronomical quantity can be expressed as a constant, equal to the measure that it had at the epoch, leaving its variation over time to be specified in some other way—for example, by a table, as was common during the 17th and 18th centuries. </p><p>The word <i>epoch</i> was often used in a different way in older astronomical literature, e.g. during the 18th century, in connection with astronomical tables. At that time, it was customary to denote as "epochs", not the standard date and time of origin for time-varying astronomical quantities, but rather the values at that date and time <i>of those time-varying quantities themselves</i>.<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> In accordance with that alternative historical usage, an expression such as "correcting the epochs" would refer to the adjustment, usually by a small amount, of the values of the tabulated astronomical quantities applicable to a fixed standard date and time of reference (and not, as might be expected from current usage, to a change from one date and time of reference to a different date and time). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Epoch_versus_equinox">Epoch versus equinox</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Epoch_(astronomy)&action=edit&section=1" title="Edit section: Epoch versus equinox"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Astronomical data are often specified not only in their relation to an epoch or date of reference but also in their relations to other conditions of reference, such as coordinate systems specified by "<a href="/wiki/Equinox_(celestial_coordinates)" title="Equinox (celestial coordinates)">equinox</a>", or "equinox and <a href="/wiki/Equator" title="Equator">equator</a>", or "equinox and <a href="/wiki/Ecliptic" title="Ecliptic">ecliptic</a>" – when these are needed for fully specifying astronomical data of the considered type. </p> <div class="mw-heading mw-heading3"><h3 id="Date-references_for_coordinate_systems">Date-references for coordinate systems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Epoch_(astronomy)&action=edit&section=2" title="Edit section: Date-references for coordinate systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When the data are dependent for their values on a particular coordinate system, the date of that coordinate system needs to be specified directly or indirectly. </p><p><a href="/wiki/Celestial_coordinate_system" class="mw-redirect" title="Celestial coordinate system">Celestial coordinate systems</a> most commonly used in astronomy are <a href="/wiki/Equatorial_coordinate_system" title="Equatorial coordinate system">equatorial coordinates</a> and <a href="/wiki/Ecliptic_coordinate_system" title="Ecliptic coordinate system">ecliptic coordinates</a>. These are defined relative to the (moving) <a href="/wiki/Equinox_(celestial_coordinates)" title="Equinox (celestial coordinates)">vernal equinox</a> position, which itself is determined by the orientations of the <a href="/wiki/Earth" title="Earth">Earth</a>'s rotation axis and orbit around the <a href="/wiki/Sun" title="Sun">Sun</a>. Their orientations vary (though slowly, e.g. due to <a href="/wiki/Precession" title="Precession">precession</a>), and there is an <a href="/wiki/Infinity" title="Infinity">infinity</a> of such coordinate systems possible. Thus the coordinate systems most used in astronomy need their own date-reference because the coordinate systems of that type are themselves in motion, e.g. by the <a href="/wiki/Precession_of_the_equinoxes" class="mw-redirect" title="Precession of the equinoxes">precession of the equinoxes</a>, nowadays often resolved into precessional components, separate precessions of the equator and of the ecliptic. </p><p>The epoch of the coordinate system need not be the same, and often in practice is not the same, as the epoch for the data themselves. </p><p>The difference between reference to an epoch alone, and a reference to a certain <a href="/wiki/Equinox_(celestial_coordinates)" title="Equinox (celestial coordinates)">equinox</a> with equator or ecliptic, is therefore that the reference to the epoch contributes to specifying the date of the values of astronomical variables themselves; while the reference to an equinox along with equator/ecliptic, of a certain date, addresses the identification of, or changes in, the coordinate system in terms of which those astronomical variables are expressed. (Sometimes the word 'equinox' may be used alone, e.g. where it is obvious from the context to users of the data in which form the considered astronomical variables are expressed, in equatorial form or ecliptic form.) </p><p>The equinox with equator/ecliptic of a given date defines which coordinate system is used. Most standard coordinates in use today refer to 2000 <b>TT</b> (i.e. to 12h (noon) on the <a href="/wiki/Terrestrial_Time" title="Terrestrial Time">Terrestrial Time</a> scale on January 1, 2000, see below), which occurred about 64 seconds sooner than noon <a href="/wiki/UT1" class="mw-redirect" title="UT1">UT1</a> on the same date (see <a href="/wiki/%CE%94T_(timekeeping)" title="ΔT (timekeeping)">ΔT</a>). Before about 1984, coordinate systems dated to 1950 or 1900 were commonly used. </p><p>There is a special meaning of the expression "equinox (and ecliptic/equator) <b>of date</b>". When coordinates are expressed as <a href="/wiki/Polynomial" title="Polynomial">polynomials</a> in time relative to a reference frame defined in this way, that means the values obtained for the coordinates in respect of any interval t after the stated epoch, are in terms of the coordinate system of the same date as the obtained values themselves, i.e. the date of the coordinate system is equal to (epoch + t).<sup id="cite_ref-NumExp_3-0" class="reference"><a href="#cite_note-NumExp-3"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> </p><p>It can be seen that the date of the coordinate system need not be the same as the epoch of the astronomical quantities themselves. But in that case (apart from the "equinox of date" case described above), two dates will be associated with the data: one date is the epoch for the time-dependent expressions giving the values, and the other date is that of the coordinate system in which the values are expressed. </p><p>For example, <a href="/wiki/Orbital_elements" title="Orbital elements">orbital elements</a>, especially <a href="/wiki/Osculating_elements" class="mw-redirect" title="Osculating elements">osculating elements</a> for minor planets, are routinely given with reference to two dates: first, relative to a recent epoch for all of the elements: but some of the data are dependent on a chosen coordinate system, and then it is usual to specify the coordinate system of a standard epoch which often is not the same as the epoch of the data. An example is as follows: For <a href="/wiki/Minor_planet" title="Minor planet">minor planet</a> (5145) <a href="/wiki/5145_Pholus" title="5145 Pholus">Pholus</a>, orbital elements have been given including the following data:<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <pre>Epoch 2010 Jan. 4.0 TT . . . = <a href="/wiki/Julian_day" title="Julian day">JDT</a> 2455200.5 M 72.00071 . . . . . . . .(2000.0) n. 0.01076162 .. . . . Peri . 354.75938 a 20.3181594 . . . . . Node . 119.42656 e. 0.5715321 . . . . . Incl .. 24.66109 </pre> <p>where the epoch is expressed in terms of Terrestrial Time, with an equivalent Julian date. Four of the elements are independent of any particular coordinate system: M is mean anomaly (deg), n: mean daily motion (deg/d), a: size of semi-major axis (AU), e: eccentricity (dimensionless). But the argument of perihelion, <a href="/wiki/Longitude_of_the_ascending_node" title="Longitude of the ascending node">longitude of the ascending node</a> and the inclination are all coordinate-dependent, and are specified relative to the reference frame of the equinox and ecliptic of another date "2000.0", otherwise known as J2000, i.e. January 1.5, 2000 (12h on January 1) or <a href="/wiki/Julian_day" title="Julian day">JD</a> 2451545.0.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Epochs_and_periods_of_validity">Epochs and periods of validity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Epoch_(astronomy)&action=edit&section=3" title="Edit section: Epochs and periods of validity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the particular set of coordinates exampled above, much of the elements has been omitted as unknown or undetermined; for example, the element n allows an approximate time-dependence of the element M to be calculated, but the other elements and n itself are treated as constant, which represents a temporary approximation (see <a href="/wiki/Osculating_elements" class="mw-redirect" title="Osculating elements">Osculating elements</a>). </p><p>Thus a particular coordinate system (equinox and equator/ecliptic of a particular date, such as J2000.0) could be used forever, but a set of osculating elements for a particular epoch may only be (approximately) valid for a rather limited time, because osculating elements such as those exampled above do not show the effect of future <a href="/wiki/Perturbation_(astronomy)" title="Perturbation (astronomy)">perturbations</a> which will change the values of the elements. </p><p>Nevertheless, the period of validity is a different matter in principle and not the result of the use of an epoch to express the data. In other cases, e.g. the case of a complete analytical theory of the motion of some astronomical body, all of the elements will usually be given in the form of polynomials in interval of time from the epoch, and they will also be accompanied by trigonometrical terms of periodical <a href="/wiki/Perturbation_(astronomy)" title="Perturbation (astronomy)">perturbations</a> specified appropriately. In that case, their period of validity may stretch over several centuries or even millennia on either side of the stated epoch. </p><p>Some data and some epochs have a long period of use for other reasons. For example, the boundaries of the <a href="/wiki/International_Astronomical_Union" title="International Astronomical Union">IAU</a> <a href="/wiki/Constellation" title="Constellation">constellations</a> are specified relative to an equinox from near the beginning of the year 1875. This is a matter of convention, but the convention is defined in terms of the equator and ecliptic as they were in 1875. To find out in which constellation a particular comet stands today, the current position of that comet must be expressed in the coordinate system of 1875 (equinox/equator of 1875). Thus that coordinate system can still be used today, even though most comet predictions made originally for 1875 (epoch = 1875) would no longer be useful today, because of the lack of information about their time-dependence and perturbations. </p> <div class="mw-heading mw-heading2"><h2 id="Changing_the_standard_equinox_and_epoch">Changing the standard equinox and epoch</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Epoch_(astronomy)&action=edit&section=4" title="Edit section: Changing the standard equinox and epoch"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>To calculate the visibility of a celestial object for an observer at a specific time and place on the Earth, the coordinates of the object are needed relative to a coordinate system of the current date. If coordinates relative to some other date are used, then that will cause errors in the results. The magnitude of those errors increases with the time difference between the date and time of observation and the date of the coordinate system used, because of the precession of the equinoxes. If the time difference is small, then fairly easy and small corrections for the precession may well suffice. If the time difference gets large, then fuller and more accurate corrections must be applied. For this reason, a star position read from a star atlas or catalog based on a sufficiently old equinox and equator cannot be used without corrections if reasonable accuracy is required. </p><p>Additionally, stars move relative to each other through space. Apparent motion across the sky relative to other stars is called <a href="/wiki/Proper_motion" title="Proper motion">proper motion</a>. Most stars have very small proper motions, but a few have proper motions that accumulate to noticeable distances after a few tens of years. So, some stellar positions read from a star atlas or catalog for a sufficiently old epoch require proper motion corrections as well, for reasonable accuracy. </p><p>Due to precession and proper motion, star data become less useful as the age of the observations and their epoch, and the equinox and equator to which they are referred, get older. After a while, it is easier or better to switch to newer data, generally referred to as a newer epoch and equinox/equator, than to keep applying corrections to the older data. </p> <div class="mw-heading mw-heading2"><h2 id="Specifying_an_epoch_or_equinox">Specifying an epoch or equinox</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Epoch_(astronomy)&action=edit&section=5" title="Edit section: Specifying an epoch or equinox"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Epochs and equinoxes are moments in time, so they can be specified in the same way as moments that indicate things other than epochs and equinoxes. The following standard ways of specifying epochs and equinoxes seem the most popular: </p> <ul><li><a href="/wiki/Julian_day" title="Julian day">Julian days</a>, e.g., JD 2433282.4235 for January 0.9235, 1950 <a href="/wiki/Terrestrial_Time" title="Terrestrial Time">TT</a></li> <li><a href="/w/index.php?title=Besselian&action=edit&redlink=1" class="new" title="Besselian (page does not exist)">Besselian</a> years (see below), e.g., 1950.0 or B1950.0 for January 0.9235, 1950 TT</li> <li><a href="/wiki/Julian_year_(astronomy)" title="Julian year (astronomy)">Julian years</a>, e.g., J2000.0 for January 1.5, 2000 TT</li></ul> <p>All three of these are expressed in TT = <a href="/wiki/Terrestrial_Time" title="Terrestrial Time">Terrestrial Time</a>. </p><p>Besselian years, used mostly for star positions, can be encountered in older catalogs but are now becoming obsolete. The <a href="/wiki/Hipparcos" title="Hipparcos">Hipparcos</a> catalog summary,<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> for example, defines the "catalog epoch" as "J1991.25" (8.75 Julian years before January 1.5, 2000 TT, e.g., April 2.5625, 1991 TT). </p> <div class="mw-heading mw-heading2"><h2 id="Besselian_years">Besselian years</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Epoch_(astronomy)&action=edit&section=6" title="Edit section: Besselian years"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A Besselian year is named after the German mathematician and astronomer <a href="/wiki/Friedrich_Bessel" class="mw-redirect" title="Friedrich Bessel">Friedrich Bessel</a> (1784–1846). <a href="#CITEREFMeeus1991">Meeus 1991</a>, p. 125 defines the beginning of a Besselian year to be the moment at which the <a href="/wiki/Mean_longitude" title="Mean longitude">mean longitude</a> of the Sun, including the effect of <a href="/wiki/Aberration_of_light" class="mw-redirect" title="Aberration of light">aberration</a> and measured from the mean equinox of the date, is exactly 280 degrees. This moment falls near the beginning of the corresponding <a href="/wiki/Gregorian_year" class="mw-redirect" title="Gregorian year">Gregorian year</a>. The definition depended on a particular theory of the orbit of the Earth around the Sun, that of Newcomb (1895), which is now obsolete; for that reason among others, the use of Besselian years has also become or is becoming obsolete. </p><p><a href="#CITEREFLieske1979">Lieske 1979</a>, p. 282 says that a "Besselian epoch" can be calculated from the Julian date according to </p> <dl><dd>B = 1900.0 + (Julian date − 2415020.31352) / 365.242198781</dd></dl> <p>Lieske's definition is not exactly consistent with the earlier definition in terms of the mean longitude of the Sun. When using Besselian years, specify which definition is being used. </p><p>To distinguish between calendar years and Besselian years, it became customary to add ".0" to the Besselian years. Since the switch to Julian years in the mid-1980s, it has become customary to prefix "B" to Besselian years. So, "1950" is the calendar year 1950, and "1950.0" = "B1950.0" is the beginning of Besselian year 1950. </p> <ul><li>The IAU constellation boundaries are defined in the equatorial coordinate system relative to the equinox of B1875.0.</li> <li>The <a href="/wiki/Henry_Draper_Catalog" class="mw-redirect" title="Henry Draper Catalog">Henry Draper Catalog</a> uses the equinox B1900.0.</li> <li>The classical star atlas <a href="/w/index.php?title=Tabulae_Caelestes&action=edit&redlink=1" class="new" title="Tabulae Caelestes (page does not exist)">Tabulae Caelestes</a> used B1925.0 as its equinox.</li></ul> <p>According to Meeus, and also according to the formula given above, </p> <ul><li>B1900.0 = JDE 2415020.3135 = 1900 January 0.8135 TT</li> <li>B1950.0 = JDE 2433282.4235 = 1950 January 0.9235 TT</li></ul> <div class="mw-heading mw-heading2"><h2 id="Julian_years_and_J2000">Julian years and J2000<span class="anchor" id="J2000"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Epoch_(astronomy)&action=edit&section=7" title="Edit section: Julian years and J2000"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A Julian year is an interval with the length of a mean year in the <a href="/wiki/Julian_calendar" title="Julian calendar">Julian calendar</a>, i.e. 365.25 days. This interval measure does not itself define any epoch: the <a href="/wiki/Gregorian_calendar" title="Gregorian calendar">Gregorian calendar</a> is in general use for dating. But, standard conventional epochs which are not Besselian epochs have been often designated nowadays with a prefix "J", and the calendar date to which they refer is widely known, although not always the same date in the year: thus "J2000" refers to the instant of 12 noon (midday) on January 1, 2000, and J1900 refers to the instant of 12 noon on <a href="/wiki/January_0" class="mw-redirect" title="January 0">January 0</a>, 1900, equal to December 31, 1899.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> It is also usual now to specify on what time scale the time of day is expressed in that epoch-designation, e.g. often <a href="/wiki/Terrestrial_Time" title="Terrestrial Time">Terrestrial Time</a>. </p><p>In addition, an epoch optionally prefixed by "J" and designated as a year with decimals (<span class="texhtml">2000 + <var style="padding-right: 1px;">x</var></span>), where <var style="padding-right: 1px;">x</var> is either positive or negative and is quoted to 1 or 2 decimal places, has come to mean a date that is an interval of <var style="padding-right: 1px;">x</var> Julian years of 365.25 days away from the epoch J2000 = JD 2451545.0 (TT), still corresponding (in spite of the use of the prefix "J" or word "Julian") to the <a href="/wiki/Gregorian_calendar" title="Gregorian calendar">Gregorian calendar</a> date of January 1, 2000, at 12h TT (about 64 seconds before noon UTC on the same calendar day).<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> (See also <a href="/wiki/Julian_year_(astronomy)" title="Julian year (astronomy)">Julian year (astronomy)</a>.) Like the Besselian epoch, an arbitrary Julian epoch is therefore related to the Julian date by </p> <dl><dd><span class="texhtml">J = 2000 + (Julian date − 2451545.0) ÷ 365.25</span></dd></dl> <p>The IAU decided at their General Assembly of 1976<sup id="cite_ref-FOOTNOTEAokiSomaKinoshitaInoue1983263–267_9-0" class="reference"><a href="#cite_note-FOOTNOTEAokiSomaKinoshitaInoue1983263–267-9"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> that the new standard equinox of J2000.0 should be used starting in 1984. Before that, the equinox of B1950.0 seems to have been the standard.<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. (April 2012)">citation needed</span></a></i>]</sup> </p><p>Different astronomers or groups of astronomers used to define individually, but today standard epochs are generally defined by international agreements through the <a href="/wiki/IAU" class="mw-redirect" title="IAU">IAU</a>, so astronomers worldwide can collaborate more effectively. It is inefficient and error-prone if data or observations of one group have to be translated in non-standard ways so that other groups could compare the data with information from other sources. An example of how this works: if a star's position is measured by someone today, they then use a standard transformation to obtain the position expressed in terms of the standard reference frame of J2000, and it is often then this J2000 position which is shared with others. </p><p>On the other hand, there has also been an astronomical tradition of retaining observations in just the form in which they were made, so that others can later correct the reductions to standard if that proves desirable, as has sometimes occurred. </p><p>The currently used standard epoch "J2000" is defined by international agreement to be equivalent to: </p> <ol><li>The <a href="/wiki/Gregorian_date" class="mw-redirect" title="Gregorian date">Gregorian date</a> January 1, 2000, at 12:00 TT (<a href="/wiki/Terrestrial_Time" title="Terrestrial Time">Terrestrial Time</a>).</li> <li>The <a href="/wiki/Julian_date" class="mw-redirect" title="Julian date">Julian date</a> 2451545.0 TT (<a href="/wiki/Terrestrial_Time" title="Terrestrial Time">Terrestrial Time</a>).<sup id="cite_ref-FOOTNOTESeidelmann20068_10-0" class="reference"><a href="#cite_note-FOOTNOTESeidelmann20068-10"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li> <li>January 1, 2000, 11:59:27.816 TAI (<a href="/wiki/International_Atomic_Time" title="International Atomic Time">International Atomic Time</a>).<sup id="cite_ref-FOOTNOTESeidelmann2006Glossary,_s.v._Terrestrial_Dynamical_Time._11-0" class="reference"><a href="#cite_note-FOOTNOTESeidelmann2006Glossary,_s.v._Terrestrial_Dynamical_Time.-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></li> <li>January 1, 2000, 11:58:55.816 UTC (<a href="/wiki/Coordinated_Universal_Time" title="Coordinated Universal Time">Coordinated Universal Time</a>).<sup id="cite_ref-clock24_12-0" class="reference"><a href="#cite_note-clock24-12"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup></li></ol> <div class="mw-heading mw-heading2"><h2 id="Epoch_of_the_day">Epoch of the day</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Epoch_(astronomy)&action=edit&section=8" title="Edit section: Epoch of the day"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Over shorter timescales, there are a variety of practices for defining when each day begins. In ordinary usage, the <a href="/wiki/Civil_time" title="Civil time">civil day</a> is reckoned by the <a href="/wiki/Midnight" title="Midnight">midnight</a> epoch, that is, the civil day begins at midnight. But in older astronomical usage, it was usual, until January 1, 1925, to reckon by a <a href="/wiki/Noon" title="Noon">noon</a> epoch, 12 hours after the start of the civil day of the same denomination, so that the day began when the mean sun crossed the <a href="/wiki/Meridian_(astronomy)" title="Meridian (astronomy)">meridian</a> at noon.<sup id="cite_ref-FOOTNOTEWilson19251–2_13-0" class="reference"><a href="#cite_note-FOOTNOTEWilson19251–2-13"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> This is still reflected in the definition of J2000, which started at noon, Terrestrial Time. </p><p>In traditional cultures and in antiquity other epochs were used. In <a href="/wiki/Ancient_Egypt" title="Ancient Egypt">ancient Egypt</a>, days were reckoned from sunrise to sunrise, following a morning epoch. This may be related to the fact that the Egyptians regulated their year by the <a href="/wiki/Heliacal_rising" title="Heliacal rising">heliacal rising</a> of the star <a href="/wiki/Sirius" title="Sirius">Sirius</a>, a phenomenon which occurs in the morning just before dawn.<sup id="cite_ref-FOOTNOTENeugebauer20041067_14-0" class="reference"><a href="#cite_note-FOOTNOTENeugebauer20041067-14"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>In some cultures following a <a href="/wiki/Lunar_calendar" title="Lunar calendar">lunar</a> or <a href="/wiki/Lunisolar_calendar" title="Lunisolar calendar">lunisolar calendar</a>, in which the beginning of the month is determined by the appearance of the New Moon in the evening, the beginning of the day was reckoned from sunset to sunset, following an evening epoch, e.g. the <a href="/wiki/Hebrew_calendar" title="Hebrew calendar">Jewish</a> and <a href="/wiki/Islamic_calendar" title="Islamic calendar">Islamic calendars</a><sup id="cite_ref-FOOTNOTENeugebauer20041067–1069_15-0" class="reference"><a href="#cite_note-FOOTNOTENeugebauer20041067–1069-15"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> and in Medieval Western Europe in reckoning the dates of religious festivals,<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> while in others a morning epoch was followed, e.g. the <a href="/wiki/Hindu_calendar" title="Hindu calendar">Hindu</a> and <a href="/wiki/Buddhist_calendar" title="Buddhist calendar">Buddhist calendars</a>. </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=Epoch_(astronomy)&action=edit&section=9" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Astrometry" title="Astrometry">Astrometry</a></li> <li><a href="/wiki/Ephemeris_time" title="Ephemeris time">Ephemeris time</a></li> <li><a href="/wiki/Epoch" title="Epoch">Epoch</a></li> <li><a href="/wiki/International_Celestial_Reference_System_and_its_realizations" title="International Celestial Reference System and its realizations">International Celestial Reference System and its realizations</a></li> <li><a href="/wiki/Time_in_astronomy" class="mw-redirect" title="Time in astronomy">Time in astronomy</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=Epoch_(astronomy)&action=edit&section=10" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Notes">Notes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Epoch_(astronomy)&action=edit&section=11" 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 reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-NumExp-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-NumExp_3-0">^</a></b></span> <span class="reference-text">Examples of this usage are seen in: <a href="#CITEREFSimonBretagnonChaprontChapront-Touze1994">Simon et al. 1994</a>, pp. 663–683 </span> </li> <li id="cite_note-clock24-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-clock24_12-0">^</a></b></span> <span class="reference-text">This article uses a 24-hour clock, so 11:59:27.816 is equivalent to 11:59:27.816 a.m.</span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Citations">Citations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Epoch_(astronomy)&action=edit&section=12" title="Edit section: Citations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-FOOTNOTESoop1994-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESoop1994_1-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSoop1994">Soop 1994</a>.</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">M. Chapront-Touzé (ed.), <i>Jean le Rond d'Alembert, Oeuvres Complètes: Ser. 1, Vol. 6</i>, Paris (CNRS) (2002), p. xxx, n. 50.</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"><a rel="nofollow" class="external text" href="http://scully.cfa.harvard.edu/~cgi/ReturnPrepEph?d=d&o=05145">Harvard Minor Planet Center, data for <i>Pholus</i></a><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged January 2018">permanent dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup></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">See <a rel="nofollow" class="external text" href="http://www.cfa.harvard.edu/iau/info/OrbElsExplanation.html">Explanation of Orbital Elements</a>.</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">"The Hipparcos and Tycho Catalogues", ESA SP-1200, Vol. 1, page XV. ESA, 1997</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">See <a rel="nofollow" class="external text" href="https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/FORTRAN/spicelib/j1900.html">NASA Jet Propulsion Laboratory 'spice' toolkit documentation, function J1900</a>.</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"><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 report cs1"><a rel="nofollow" class="external text" href="http://www.iausofa.org/sofa_ts_c.pdf">SOFA Time Scale and Calendar Tools</a> <span class="cs1-format">(PDF)</span> (Report). C programming language. International Astronomical Union. October 9, 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=SOFA+Time+Scale+and+Calendar+Tools&rft.series=C+programming+language&rft.pub=International+Astronomical+Union&rft.date=2017-10-09&rft_id=http%3A%2F%2Fwww.iausofa.org%2Fsofa_ts_c.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEpoch+%28astronomy%29" class="Z3988"></span> (Document revision 1.5.)</span> </li> <li id="cite_note-FOOTNOTEAokiSomaKinoshitaInoue1983263–267-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEAokiSomaKinoshitaInoue1983263–267_9-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFAokiSomaKinoshitaInoue1983">Aoki et al. 1983</a>, pp. 263–267.</span> </li> <li id="cite_note-FOOTNOTESeidelmann20068-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESeidelmann20068_10-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSeidelmann2006">Seidelmann 2006</a>, p. 8.</span> </li> <li id="cite_note-FOOTNOTESeidelmann2006Glossary,_s.v._Terrestrial_Dynamical_Time.-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESeidelmann2006Glossary,_s.v._Terrestrial_Dynamical_Time._11-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSeidelmann2006">Seidelmann 2006</a>, Glossary, s.v. Terrestrial Dynamical Time..</span> </li> <li id="cite_note-FOOTNOTEWilson19251–2-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWilson19251–2_13-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWilson1925">Wilson 1925</a>, pp. 1–2.</span> </li> <li id="cite_note-FOOTNOTENeugebauer20041067-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTENeugebauer20041067_14-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFNeugebauer2004">Neugebauer 2004</a>, p. 1067.</span> </li> <li id="cite_note-FOOTNOTENeugebauer20041067–1069-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTENeugebauer20041067–1069_15-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFNeugebauer2004">Neugebauer 2004</a>, pp. 1067–1069.</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"><a href="/wiki/Bede" title="Bede">Bede</a>, <i>The Reckoning of Time</i>, 5, trans. Faith Wallis, (Liverpool: Liverpool University Press, 2004), pp. 22–24. <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/0-85323-693-3" title="Special:BookSources/0-85323-693-3">0-85323-693-3</a></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Epoch_(astronomy)&action=edit&section=13" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAokiSomaKinoshitaInoue1983" class="citation journal cs1">Aoki, S.; Soma, M.; Kinoshita, H.; Inoue, K. (December 1983). "Conversion matrix of epoch B 1950.0 FK 4-based positions of stars to epoch J 2000.0 positions in accordance with the new IAU resolutions". <i>Astronomy and Astrophysics</i>. <b>128</b> (3): <span class="nowrap">263–</span>267. <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/1983A&A...128..263A">1983A&A...128..263A</a>. <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/0004-6361">0004-6361</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astronomy+and+Astrophysics&rft.atitle=Conversion+matrix+of+epoch+B+1950.0+FK+4-based+positions+of+stars+to+epoch+J+2000.0+positions+in+accordance+with+the+new+IAU+resolutions&rft.volume=128&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E263-%3C%2Fspan%3E267&rft.date=1983-12&rft.issn=0004-6361&rft_id=info%3Abibcode%2F1983A%26A...128..263A&rft.aulast=Aoki&rft.aufirst=S.&rft.au=Soma%2C+M.&rft.au=Kinoshita%2C+H.&rft.au=Inoue%2C+K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEpoch+%28astronomy%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLieske1979" class="citation journal cs1">Lieske, J.H. (1979). "Precession Matrix Based on IAU (1976) System of Astronomical Constants". <i>Astronomy & Astrophysics</i>. <b>73</b> (3): <span class="nowrap">282–</span>284. <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/1979A&A....73..282L">1979A&A....73..282L</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astronomy+%26+Astrophysics&rft.atitle=Precession+Matrix+Based+on+IAU+%281976%29+System+of+Astronomical+Constants&rft.volume=73&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E282-%3C%2Fspan%3E284&rft.date=1979&rft_id=info%3Abibcode%2F1979A%26A....73..282L&rft.aulast=Lieske&rft.aufirst=J.H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEpoch+%28astronomy%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMeeus1991" class="citation book cs1"><a href="/wiki/Jean_Meeus" title="Jean Meeus">Meeus, Jean</a> (1991). <a rel="nofollow" class="external text" href="https://archive.org/details/astronomicalalgorithmsjeanmeeus1991"><i>Astronomical Algorithms</i></a>. Willmann-Bell. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-943396-35-4" title="Special:BookSources/978-0-943396-35-4"><bdi>978-0-943396-35-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Astronomical+Algorithms&rft.pub=Willmann-Bell&rft.date=1991&rft.isbn=978-0-943396-35-4&rft.aulast=Meeus&rft.aufirst=Jean&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fastronomicalalgorithmsjeanmeeus1991&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEpoch+%28astronomy%29" class="Z3988"></span></li></ul> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNeugebauer2004" class="citation book cs1">Neugebauer, O. (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=vO5FCVIxz2YC&pg=PA1067"><i>A History of Ancient Mathematical Astronomy</i></a>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-06995-9" title="Special:BookSources/978-3-540-06995-9"><bdi>978-3-540-06995-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Ancient+Mathematical+Astronomy&rft.pub=Springer&rft.date=2004&rft.isbn=978-3-540-06995-9&rft.aulast=Neugebauer&rft.aufirst=O.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DvO5FCVIxz2YC%26pg%3DPA1067&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEpoch+%28astronomy%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSeidelmann2006" class="citation book cs1">Seidelmann, P. Kenneth, ed. (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=uJ4JhGJANb4C"><i>Explanatory Supplement to the Astronomical Almanac</i></a>. Sausalito, CA: University Science Books. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-891389-45-0" title="Special:BookSources/978-1-891389-45-0"><bdi>978-1-891389-45-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Explanatory+Supplement+to+the+Astronomical+Almanac&rft.place=Sausalito%2C+CA&rft.pub=University+Science+Books&rft.date=2006&rft.isbn=978-1-891389-45-0&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DuJ4JhGJANb4C&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEpoch+%28astronomy%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSimonBretagnonChaprontChapront-Touze1994" class="citation journal cs1">Simon, J. L.; Bretagnon, P.; Chapront, J.; Chapront-Touze, M.; Francou, G.; Laskar, J (1994). "Numerical expressions for precession formulae and mean elements for the Moon and the planets". <i>Astronomy and Astrophysics</i>. <b>282</b>: <span class="nowrap">663–</span>683. <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/1994A&A...282..663S">1994A&A...282..663S</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astronomy+and+Astrophysics&rft.atitle=Numerical+expressions+for+precession+formulae+and+mean+elements+for+the+Moon+and+the+planets.&rft.volume=282&rft.pages=%3Cspan+class%3D%22nowrap%22%3E663-%3C%2Fspan%3E683&rft.date=1994&rft_id=info%3Abibcode%2F1994A%26A...282..663S&rft.aulast=Simon&rft.aufirst=J.+L.&rft.au=Bretagnon%2C+P.&rft.au=Chapront%2C+J.&rft.au=Chapront-Touze%2C+M.&rft.au=Francou%2C+G.&rft.au=Laskar%2C+J&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEpoch+%28astronomy%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSoop1994" class="citation book cs1">Soop, E.M. (1994). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=hqhZKjLaYZUC"><i>Handbook of Geostationary Orbits</i></a>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7923-3054-7" title="Special:BookSources/978-0-7923-3054-7"><bdi>978-0-7923-3054-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Handbook+of+Geostationary+Orbits&rft.pub=Springer&rft.date=1994&rft.isbn=978-0-7923-3054-7&rft.aulast=Soop&rft.aufirst=E.M.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DhqhZKjLaYZUC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEpoch+%28astronomy%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilson1925" class="citation journal cs1">Wilson, H. C. (1925). "Change of astronomical time". <i>Popular Astronomy</i>. <b>33</b>: <span class="nowrap">1–</span>2. <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/1925PA.....33....1W">1925PA.....33....1W</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Popular+Astronomy&rft.atitle=Change+of+astronomical+time&rft.volume=33&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1-%3C%2Fspan%3E2&rft.date=1925&rft_id=info%3Abibcode%2F1925PA.....33....1W&rft.aulast=Wilson&rft.aufirst=H.+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEpoch+%28astronomy%29" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Further_reading">Further reading</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Epoch_(astronomy)&action=edit&section=14" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239549316"><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStandish1982" class="citation journal cs1">Standish, E. M. Jr. (November 1982). "Conversion of positions and proper motions from B1950.0 to the IAU system at J2000.0". <i>Astronomy and Astrophysics</i>. <b>115</b> (1): <span class="nowrap">20–</span>22. <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/1982A&A...115...20S">1982A&A...115...20S</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Astronomy+and+Astrophysics&rft.atitle=Conversion+of+positions+and+proper+motions+from+B1950.0+to+the+IAU+system+at+J2000.0&rft.volume=115&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E20-%3C%2Fspan%3E22&rft.date=1982-11&rft_id=info%3Abibcode%2F1982A%26A...115...20S&rft.aulast=Standish&rft.aufirst=E.+M.+Jr.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEpoch+%28astronomy%29" class="Z3988"></span></li></ul> </div> <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=Epoch_(astronomy)&action=edit&section=15" 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="http://aa.usno.navy.mil/faq/docs/TT.html">What is Terrestrial Time?</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060806040555/http://aa.usno.navy.mil/faq/docs/TT.html">Archived</a> August 6, 2006, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> – U.S. Naval Observatory</li> <li><a rel="nofollow" class="external text" href="http://aa.usno.navy.mil/faq/docs/ICRS_doc.html">International Celestial Reference System, or ICRS</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060805073908/http://aa.usno.navy.mil/faq/docs/ICRS_doc.html">Archived</a> August 5, 2006, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> – U.S. Naval Observatory</li> <li><a rel="nofollow" class="external text" href="http://www.iers.org/MainDisp.csl?pid=46-25776">IERS Conventions 2003 (defines ICRS and other related standards)</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131213022556/http://www.iers.org/MainDisp.csl?pid=46-25776">Archived</a> December 13, 2013, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></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 ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline 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.navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Gravitational_orbits256" style="padding:3px"><table class="nowraplinks hlist mw-collapsible expanded navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Orbits" title="Template:Orbits"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Orbits" title="Template talk:Orbits"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Orbits" title="Special:EditPage/Template:Orbits"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Gravitational_orbits256" style="font-size:114%;margin:0 4em">Gravitational <a href="/wiki/Orbit" title="Orbit">orbits</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_orbits" title="List of orbits">Types</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Box_orbit" title="Box orbit">Box</a></li> <li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Capture</a></li> <li><a href="/wiki/Circular_orbit" title="Circular orbit">Circular</a></li> <li><a href="/wiki/Elliptic_orbit" title="Elliptic orbit">Elliptical</a> / <a href="/wiki/Highly_elliptical_orbit" title="Highly elliptical orbit">Highly elliptical</a></li> <li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Escape</a></li> <li><a href="/wiki/Horseshoe_orbit" title="Horseshoe orbit">Horseshoe</a></li> <li><a href="/wiki/Hyperbolic_trajectory" title="Hyperbolic trajectory">Hyperbolic trajectory</a></li> <li><a href="/wiki/Inclined_orbit" title="Inclined orbit">Inclined</a> / <a href="/wiki/Non-inclined_orbit" class="mw-redirect" title="Non-inclined orbit">Non-inclined</a></li> <li><a href="/wiki/Kepler_orbit" title="Kepler orbit">Kepler</a></li> <li><a href="/wiki/Lagrange_point" title="Lagrange point">Lagrange point</a></li> <li><a href="/wiki/Osculating_orbit" title="Osculating orbit">Osculating</a></li> <li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Parabolic trajectory</a></li> <li><a href="/wiki/Parking_orbit" title="Parking orbit">Parking</a></li> <li><a href="/wiki/Retrograde_and_prograde_motion" title="Retrograde and prograde motion">Prograde / Retrograde</a></li> <li><a href="/wiki/Synchronous_orbit" title="Synchronous orbit">Synchronous</a> <ul><li><a href="/wiki/Semi-synchronous_orbit" title="Semi-synchronous orbit">semi</a></li> <li><a href="/wiki/Subsynchronous_orbit" title="Subsynchronous orbit">sub</a></li></ul></li> <li><a href="/wiki/Hohmann_transfer_orbit" title="Hohmann transfer orbit">Transfer orbit</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em"><a href="/wiki/Geocentric_orbit" title="Geocentric orbit">Geocentric</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Geosynchronous_orbit" title="Geosynchronous orbit">Geosynchronous</a> <ul><li><a href="/wiki/Geostationary_orbit" title="Geostationary orbit">Geostationary</a></li> <li><a href="/wiki/Geostationary_transfer_orbit" title="Geostationary transfer orbit">Geostationary transfer</a></li></ul></li> <li><a href="/wiki/Graveyard_orbit" title="Graveyard orbit">Graveyard</a></li> <li><a href="/wiki/High_Earth_orbit" title="High Earth orbit">High Earth</a></li> <li><a href="/wiki/Low_Earth_orbit" title="Low Earth orbit">Low Earth</a></li> <li><a href="/wiki/Medium_Earth_orbit" title="Medium Earth orbit">Medium Earth</a></li> <li><a href="/wiki/Molniya_orbit" title="Molniya orbit">Molniya</a></li> <li><a href="/wiki/Near-equatorial_orbit" title="Near-equatorial orbit">Near-equatorial</a></li> <li><a href="/wiki/Orbit_of_the_Moon" title="Orbit of the Moon">Orbit of the Moon</a></li> <li><a href="/wiki/Polar_orbit" title="Polar orbit">Polar</a></li> <li><a href="/wiki/Sun-synchronous_orbit" title="Sun-synchronous orbit">Sun-synchronous</a></li> <li><a href="/wiki/Transatmospheric_orbit" title="Transatmospheric orbit">Transatmospheric</a></li> <li><a href="/wiki/Tundra_orbit" title="Tundra orbit">Tundra</a></li> <li><a href="/wiki/Very_low_Earth_orbit" title="Very low Earth orbit">Very low Earth</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">About<br />other points</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li>Mars <ul><li><a href="/wiki/Areocentric_orbit" title="Areocentric orbit">Areocentric</a></li> <li><a href="/wiki/Areosynchronous_orbit" title="Areosynchronous orbit">Areosynchronous</a></li> <li><a href="/wiki/Areostationary_orbit" title="Areostationary orbit">Areostationary</a></li></ul></li> <li>Lagrange points <ul><li><a href="/wiki/Distant_retrograde_orbit" title="Distant retrograde orbit">Distant retrograde</a></li> <li><a href="/wiki/Halo_orbit" title="Halo orbit">Halo</a></li> <li><a href="/wiki/Lissajous_orbit" title="Lissajous orbit">Lissajous</a></li> <li><a href="/wiki/Libration_point_orbit" title="Libration point orbit">Libration</a></li></ul></li> <li><a href="/wiki/Lunar_orbit" title="Lunar orbit">Lunar</a></li> <li>Sun <ul><li><a href="/wiki/Heliocentric_orbit" title="Heliocentric orbit">Heliocentric</a> <ul><li><a href="/wiki/Earth%27s_orbit" title="Earth's orbit">Earth's orbit</a></li></ul></li> <li><a href="/wiki/Mars_cycler" title="Mars cycler">Mars cycler</a></li> <li><a href="/wiki/Sun-synchronous_orbit" title="Sun-synchronous orbit">Heliosynchronous</a></li></ul></li> <li>Other <ul><li><a href="/wiki/Lunar_cycler" title="Lunar cycler">Lunar cycler</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Orbital_elements" title="Orbital elements">Parameters</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em"><div class="hlist"><ul><li>Shape</li><li>Size</li></ul></div></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">e</span>  <a href="/wiki/Orbital_eccentricity" title="Orbital eccentricity">Eccentricity</a></li> <li><span class="texhtml mvar" style="font-style:italic;">a</span>  <a href="/wiki/Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">Semi-major axis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">b</span>  <a href="/wiki/Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">Semi-minor axis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">Q</span>, <span class="texhtml mvar" style="font-style:italic;">q</span>  <a href="/wiki/Apsis" title="Apsis">Apsides</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">Orientation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">i</span>  <a href="/wiki/Orbital_inclination" title="Orbital inclination">Inclination</a></li> <li><span class="texhtml mvar" style="font-style:italic;">Ω</span>  <a href="/wiki/Longitude_of_the_ascending_node" title="Longitude of the ascending node">Longitude of the ascending node</a></li> <li><span class="texhtml mvar" style="font-style:italic;">ω</span>  <a href="/wiki/Argument_of_periapsis" title="Argument of periapsis">Argument of periapsis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">ϖ</span>  <a href="/wiki/Longitude_of_the_periapsis" class="mw-redirect" title="Longitude of the periapsis">Longitude of the periapsis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">Position</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">M</span>  <a href="/wiki/Mean_anomaly" title="Mean anomaly">Mean anomaly</a></li> <li><span class="texhtml mvar" style="font-style:italic;">ν</span>, <span class="texhtml mvar" style="font-style:italic;">θ</span>, <span class="texhtml mvar" style="font-style:italic;">f</span>  <a href="/wiki/True_anomaly" title="True anomaly">True anomaly</a></li> <li><span class="texhtml mvar" style="font-style:italic;">E</span>  <a href="/wiki/Eccentric_anomaly" title="Eccentric anomaly">Eccentric anomaly</a></li> <li><span class="texhtml mvar" style="font-style:italic;">L</span>  <a href="/wiki/Mean_longitude" title="Mean longitude">Mean longitude</a></li> <li><span class="texhtml mvar" style="font-style:italic;">l</span>  <a href="/wiki/True_longitude" title="True longitude">True longitude</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">Variation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">T</span>  <a href="/wiki/Orbital_period" title="Orbital period">Orbital period</a></li> <li><span class="texhtml mvar" style="font-style:italic;">n</span>  <a href="/wiki/Mean_motion" title="Mean motion">Mean motion</a></li> <li><span class="texhtml mvar" style="font-style:italic;">v</span>  <a href="/wiki/Orbital_speed" title="Orbital speed">Orbital speed</a></li> <li><span class="texhtml"><i>t</i><sub>0</sub></span>  <a class="mw-selflink selflink">Epoch</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Orbital_maneuver" title="Orbital maneuver">Maneuvers</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/Bi-elliptic_transfer" title="Bi-elliptic transfer">Bi-elliptic transfer</a></li> <li><a href="/wiki/Collision_avoidance_(spacecraft)" title="Collision avoidance (spacecraft)">Collision avoidance (spacecraft)</a></li> <li><a href="/wiki/Delta-v" title="Delta-v">Delta-v</a></li> <li><a href="/wiki/Delta-v_budget" title="Delta-v budget">Delta-v budget</a></li> <li><a href="/wiki/Gravity_assist" title="Gravity assist">Gravity assist</a></li> <li><a href="/wiki/Gravity_turn" title="Gravity turn">Gravity turn</a></li> <li><a href="/wiki/Hohmann_transfer_orbit" title="Hohmann transfer orbit">Hohmann transfer</a></li> <li><a href="/wiki/Orbital_inclination_change" title="Orbital inclination change">Inclination change</a></li> <li><a href="/wiki/Low-energy_transfer" title="Low-energy transfer">Low-energy transfer</a></li> <li><a href="/wiki/Oberth_effect" title="Oberth effect">Oberth effect</a></li> <li><a href="/wiki/Orbit_phasing" title="Orbit phasing">Phasing</a></li> <li><a href="/wiki/Tsiolkovsky_rocket_equation" title="Tsiolkovsky rocket equation">Rocket equation</a></li> <li><a href="/wiki/Space_rendezvous" title="Space rendezvous">Rendezvous</a></li> <li><a href="/wiki/Trans-lunar_injection" title="Trans-lunar injection">Trans-lunar injection</a></li> <li><a href="/wiki/Transposition,_docking,_and_extraction" title="Transposition, docking, and extraction">Transposition, docking, and extraction</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Orbital_mechanics" title="Orbital mechanics">Orbital<br />mechanics</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/Astronomical_coordinate_systems" title="Astronomical coordinate systems">Astronomical coordinate systems</a></li> <li><a href="/wiki/Characteristic_energy" title="Characteristic energy">Characteristic energy</a></li> <li><a href="/wiki/Escape_velocity" title="Escape velocity">Escape velocity</a></li> <li><a href="/wiki/Ephemeris" title="Ephemeris">Ephemeris</a></li> <li><a href="/wiki/Equatorial_coordinate_system" title="Equatorial coordinate system">Equatorial coordinate system</a></li> <li><a href="/wiki/Ground_track" class="mw-redirect" title="Ground track">Ground track</a></li> <li><a href="/wiki/Hill_sphere" title="Hill sphere">Hill sphere</a></li> <li><a href="/wiki/Interplanetary_Transport_Network" title="Interplanetary Transport Network">Interplanetary Transport Network</a></li> <li><a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws of planetary motion</a></li> <li><a href="/wiki/Kozai_mechanism" title="Kozai mechanism">Kozai mechanism</a></li> <li><a href="/wiki/Lagrange_point" title="Lagrange point">Lagrangian point</a></li> <li><a href="/wiki/N-body_problem" title="N-body problem"><i>n</i>-body problem</a></li> <li><a href="/wiki/Orbit_equation" title="Orbit equation">Orbit equation</a></li> <li><a href="/wiki/Orbital_state_vectors" title="Orbital state vectors">Orbital state vectors</a></li> <li><a href="/wiki/Perturbation_(astronomy)" title="Perturbation (astronomy)">Perturbation</a></li> <li><a href="/wiki/Retrograde_and_prograde_motion" title="Retrograde and prograde motion">Retrograde and prograde motion</a></li> <li><a href="/wiki/Specific_orbital_energy" title="Specific orbital energy">Specific orbital energy</a></li> <li><a href="/wiki/Specific_angular_momentum" title="Specific angular momentum">Specific angular momentum</a></li> <li><a href="/wiki/Two-line_element_set" title="Two-line element set">Two-line elements</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="List-Class article"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/16px-Symbol_list_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/23px-Symbol_list_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/31px-Symbol_list_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/List_of_orbits" title="List of orbits">List of orbits</a></li></ul> </div></td></tr></tbody></table></div> <style data-mw-deduplicate="TemplateStyles:r1130092004">.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;justify-content:center;align-items:baseline}.mw-parser-output .portal-bar-bordered{padding:0 2em;background-color:#fdfdfd;border:1px solid #a2a9b1;clear:both;margin:1em auto 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