Système de coordonnées célestes

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mw-ui-icon-wikimedia-expand"></span> <span>Afficher / masquer la sous-section Conversions</span> </button> <ul id="toc-Conversions-sublist" class="vector-toc-list"> <li id="toc-Des_coordonnées_horizontales_aux_coordonnées_horaires" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Des_coordonnées_horizontales_aux_coordonnées_horaires"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Des coordonnées horizontales aux coordonnées horaires</span> </div> </a> <ul id="toc-Des_coordonnées_horizontales_aux_coordonnées_horaires-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Des_coordonnées_horaires_aux_coordonnées_horizontales" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Des_coordonnées_horaires_aux_coordonnées_horizontales"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Des coordonnées horaires aux coordonnées horizontales</span> </div> </a> <ul id="toc-Des_coordonnées_horaires_aux_coordonnées_horizontales-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Des_coordonnées_horaires_aux_coordonnées_équatoriales" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Des_coordonnées_horaires_aux_coordonnées_équatoriales"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Des coordonnées horaires aux coordonnées équatoriales</span> </div> </a> <ul id="toc-Des_coordonnées_horaires_aux_coordonnées_équatoriales-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Des_coordonnées_équatoriales_aux_coordonnées_horaires" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Des_coordonnées_équatoriales_aux_coordonnées_horaires"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Des coordonnées équatoriales aux coordonnées horaires</span> </div> </a> <ul id="toc-Des_coordonnées_équatoriales_aux_coordonnées_horaires-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Des_coordonnées_équatoriales_vers_les_coordonnées_écliptiques" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Des_coordonnées_équatoriales_vers_les_coordonnées_écliptiques"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Des coordonnées équatoriales vers les coordonnées écliptiques</span> </div> </a> <ul id="toc-Des_coordonnées_équatoriales_vers_les_coordonnées_écliptiques-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Des_coordonnées_écliptiques_vers_les_coordonnées_équatoriales" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Des_coordonnées_écliptiques_vers_les_coordonnées_équatoriales"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6</span> <span>Des coordonnées écliptiques vers les coordonnées équatoriales</span> </div> </a> <ul id="toc-Des_coordonnées_écliptiques_vers_les_coordonnées_équatoriales-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Voir_aussi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voir_aussi"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Voir aussi</span> </div> </a> <ul id="toc-Voir_aussi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liens_externes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Liens_externes"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Liens externes</span> </div> </a> <ul id="toc-Liens_externes-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="Sommaire" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table des matières" > <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="Basculer la table des matières" > <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">Basculer la table des matières</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">Système de coordonnées célestes</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="Aller à un article dans une autre langue. Disponible en 66 langues." > <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-66" 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">66 langues</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/Lugko%C3%B6rdinaatstelsel" title="Lugkoördinaatstelsel – afrikaans" lang="af" hreflang="af" data-title="Lugkoördinaatstelsel" 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/%D9%86%D8%B8%D8%A7%D9%85_%D8%A5%D8%AD%D8%AF%D8%A7%D8%AB%D9%8A%D8%A7%D8%AA_%D9%81%D9%84%D9%83%D9%8A" title="نظام إحداثيات فلكي – arabe" lang="ar" hreflang="ar" data-title="نظام إحداثيات فلكي" data-language-autonym="العربية" data-language-local-name="arabe" 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/Coordenaes_celestes" title="Coordenaes celestes – asturien" lang="ast" hreflang="ast" data-title="Coordenaes celestes" data-language-autonym="Asturianu" data-language-local-name="asturien" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/F%C9%99za_koordinat_sistemi" title="Fəza koordinat sistemi – azerbaïdjanais" lang="az" hreflang="az" data-title="Fəza koordinat sistemi" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaïdjanais" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%BD%D1%8F%D0%B1%D0%B5%D1%81%D0%BD%D1%8B%D1%85_%D0%BA%D0%B0%D0%B0%D1%80%D0%B4%D1%8B%D0%BD%D0%B0%D1%82" title="Сістэма нябесных каардынат – biélorusse" lang="be" hreflang="be" data-title="Сістэма нябесных каардынат" data-language-autonym="Беларуская" data-language-local-name="biélorusse" 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%A1%D1%8B%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%BD%D1%8F%D0%B1%D0%B5%D1%81%D0%BD%D1%8B%D1%85_%D0%BA%D0%B0%D0%B0%D1%80%D0%B4%D1%8B%D0%BD%D0%B0%D1%82" title="Сыстэма нябесных каардынат – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Сыстэма нябесных каардынат" 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%9D%D0%B5%D0%B1%D0%B5%D1%81%D0%BD%D0%B0_%D0%BA%D0%BE%D0%BE%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D1%82%D0%BD%D0%B0_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0" title="Небесна координатна система – bulgare" lang="bg" hreflang="bg" data-title="Небесна координатна система" data-language-autonym="Български" data-language-local-name="bulgare" 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/Nebeski_koordinatni_sistem" title="Nebeski koordinatni sistem – bosniaque" lang="bs" hreflang="bs" data-title="Nebeski koordinatni sistem" data-language-autonym="Bosanski" data-language-local-name="bosniaque" 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/Coordenades_astron%C3%B2miques" title="Coordenades astronòmiques – catalan" lang="ca" hreflang="ca" data-title="Coordenades astronòmiques" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%B3%DB%8C%D8%B3%D8%AA%DB%95%D9%85%DB%8C_%D9%BE%DB%86%D8%AA%D8%A7%D9%86%DB%8C_%D8%A6%D8%A7%D8%B3%D9%85%D8%A7%D9%86%DB%8C" title="سیستەمی پۆتانی ئاسمانی – sorani" lang="ckb" hreflang="ckb" data-title="سیستەمی پۆتانی ئاسمانی" data-language-autonym="کوردی" data-language-local-name="sorani" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Koordinatsystem_for_himmelrummet" title="Koordinatsystem for himmelrummet – danois" lang="da" hreflang="da" data-title="Koordinatsystem for himmelrummet" data-language-autonym="Dansk" data-language-local-name="danois" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Astronomische_Koordinatensysteme" title="Astronomische Koordinatensysteme – allemand" lang="de" hreflang="de" data-title="Astronomische Koordinatensysteme" data-language-autonym="Deutsch" data-language-local-name="allemand" 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%9F%CF%85%CF%81%CE%AC%CE%BD%CE%B9%CE%B5%CF%82_%CF%83%CF%85%CE%BD%CF%84%CE%B5%CF%84%CE%B1%CE%B3%CE%BC%CE%AD%CE%BD%CE%B5%CF%82" title="Ουράνιες συντεταγμένες – grec" lang="el" hreflang="el" data-title="Ουράνιες συντεταγμένες" data-language-autonym="Ελληνικά" data-language-local-name="grec" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Astronomical_coordinate_systems" title="Astronomical coordinate systems – anglais" lang="en" hreflang="en" data-title="Astronomical coordinate systems" data-language-autonym="English" data-language-local-name="anglais" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Coordenadas_celestes" title="Coordenadas celestes – espagnol" lang="es" hreflang="es" data-title="Coordenadas celestes" data-language-autonym="Español" data-language-local-name="espagnol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Taevakoordinaatide_s%C3%BCsteem" title="Taevakoordinaatide süsteem – estonien" lang="et" hreflang="et" data-title="Taevakoordinaatide süsteem" data-language-autonym="Eesti" data-language-local-name="estonien" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Koordenatu_sistema_astronomiko" title="Koordenatu sistema astronomiko – basque" lang="eu" hreflang="eu" data-title="Koordenatu sistema astronomiko" 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/%D8%AF%D8%B3%D8%AA%DA%AF%D8%A7%D9%87_%D9%85%D8%AE%D8%AA%D8%B5%D8%A7%D8%AA_%D8%B3%D9%85%D8%A7%D9%88%DB%8C" title="دستگاه مختصات سماوی – persan" lang="fa" hreflang="fa" data-title="دستگاه مختصات سماوی" data-language-autonym="فارسی" data-language-local-name="persan" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/T%C3%A4htitieteellinen_vertausj%C3%A4rjestelm%C3%A4" title="Tähtitieteellinen vertausjärjestelmä – finnois" lang="fi" hreflang="fi" data-title="Tähtitieteellinen vertausjärjestelmä" data-language-autonym="Suomi" data-language-local-name="finnois" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Coordenadas_celestes" title="Coordenadas celestes – galicien" lang="gl" hreflang="gl" data-title="Coordenadas celestes" data-language-autonym="Galego" data-language-local-name="galicien" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A2%D7%A8%D7%9B%D7%AA_%D7%A7%D7%95%D7%90%D7%95%D7%A8%D7%93%D7%99%D7%A0%D7%98%D7%95%D7%AA_%D7%A9%D7%9E%D7%99%D7%9E%D7%99%D7%AA" title="מערכת קואורדינטות שמימית – hébreu" lang="he" hreflang="he" data-title="מערכת קואורדינטות שמימית" data-language-autonym="עברית" data-language-local-name="hébreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%96%E0%A4%97%E0%A5%8B%E0%A4%B2%E0%A5%80%E0%A4%AF_%E0%A4%A8%E0%A4%BF%E0%A4%B0%E0%A5%8D%E0%A4%A6%E0%A5%87%E0%A4%B6%E0%A4%BE%E0%A4%82%E0%A4%95_%E0%A4%AA%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%A4%E0%A4%BF" title="खगोलीय निर्देशांक पद्धति – hindi" lang="hi" hreflang="hi" data-title="खगोलीय निर्देशांक पद्धति" 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/Nebeski_koordinatni_sustavi" title="Nebeski koordinatni sustavi – croate" lang="hr" hreflang="hr" data-title="Nebeski koordinatni sustavi" data-language-autonym="Hrvatski" data-language-local-name="croate" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Csillag%C3%A1szati_koordin%C3%A1ta-rendszer" title="Csillagászati koordináta-rendszer – hongrois" lang="hu" hreflang="hu" data-title="Csillagászati koordináta-rendszer" data-language-autonym="Magyar" data-language-local-name="hongrois" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B5%D6%80%D5%AF%D5%B6%D5%A1%D5%B5%D5%AB%D5%B6_%D5%AF%D5%B8%D5%B8%D6%80%D5%A4%D5%AB%D5%B6%D5%A1%D5%BF%D5%B6%D5%A5%D6%80%D5%AB_%D5%B0%D5%A1%D5%B4%D5%A1%D5%AF%D5%A1%D6%80%D5%A3%D5%A5%D6%80" title="Երկնային կոորդինատների համակարգեր – arménien" lang="hy" hreflang="hy" data-title="Երկնային կոորդինատների համակարգեր" data-language-autonym="Հայերեն" data-language-local-name="arménien" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Tata_koordinat_langit" title="Tata koordinat langit – indonésien" lang="id" hreflang="id" data-title="Tata koordinat langit" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésien" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ig mw-list-item"><a href="https://ig.wikipedia.org/wiki/Usoro_nhazi_mbara_igwe" title="Usoro nhazi mbara igwe – igbo" lang="ig" hreflang="ig" data-title="Usoro nhazi mbara igwe" data-language-autonym="Igbo" data-language-local-name="igbo" class="interlanguage-link-target"><span>Igbo</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Sistema_ti_nainlangitan_a_nagsasabtan" title="Sistema ti nainlangitan a nagsasabtan – ilocano" lang="ilo" hreflang="ilo" data-title="Sistema ti nainlangitan a nagsasabtan" data-language-autonym="Ilokano" data-language-local-name="ilocano" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Himinhvolfshnitakerfi" title="Himinhvolfshnitakerfi – islandais" lang="is" hreflang="is" data-title="Himinhvolfshnitakerfi" data-language-autonym="Íslenska" data-language-local-name="islandais" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Coordinate_celesti" title="Coordinate celesti – italien" lang="it" hreflang="it" data-title="Coordinate celesti" data-language-autonym="Italiano" data-language-local-name="italien" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%A4%A9%E7%90%83%E5%BA%A7%E6%A8%99%E7%B3%BB" title="天球座標系 – japonais" lang="ja" hreflang="ja" data-title="天球座標系" data-language-autonym="日本語" data-language-local-name="japonais" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%81%D0%BF%D0%B0%D0%BD_%D0%BA%D0%BE%D0%BE%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D1%82%D1%82%D0%B0%D1%80_%D0%B6%D2%AF%D0%B9%D0%B5%D1%81%D1%96" title="Аспан координаттар жүйесі – kazakh" lang="kk" hreflang="kk" data-title="Аспан координаттар жүйесі" data-language-autonym="Қазақша" data-language-local-name="kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%B2%9C%EA%B5%AC%EC%A2%8C%ED%91%9C%EA%B3%84" title="천구좌표계 – coréen" lang="ko" hreflang="ko" data-title="천구좌표계" data-language-autonym="한국어" data-language-local-name="coréen" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Systema_coordinatarum_caelestium" title="Systema coordinatarum caelestium – latin" lang="la" hreflang="la" data-title="Systema coordinatarum caelestium" 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/Himmelskoordinaten" title="Himmelskoordinaten – luxembourgeois" lang="lb" hreflang="lb" data-title="Himmelskoordinaten" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxembourgeois" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Sistem_koordinat_astronomi" title="Sistem koordinat astronomi – minangkabau" lang="min" hreflang="min" data-title="Sistem koordinat astronomi" data-language-autonym="Minangkabau" data-language-local-name="minangkabau" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9D%D0%B5%D0%B1%D0%B5%D1%81%D0%B5%D0%BD_%D0%BA%D0%BE%D0%BE%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D1%82%D0%B5%D0%BD_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Небесен координатен систем – macédonien" lang="mk" hreflang="mk" data-title="Небесен координатен систем" data-language-autonym="Македонски" data-language-local-name="macédonien" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9E%D0%B4%D0%BE%D0%BD_%D0%BE%D1%80%D0%BD%D1%8B_%D0%BA%D0%BE%D0%BE%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D1%82%D1%8B%D0%BD_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Одон орны координатын систем – mongol" lang="mn" hreflang="mn" data-title="Одон орны координатын систем" data-language-autonym="Монгол" data-language-local-name="mongol" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sistem_koordinat_cakerawala" title="Sistem koordinat cakerawala – malais" lang="ms" hreflang="ms" data-title="Sistem koordinat cakerawala" data-language-autonym="Bahasa Melayu" data-language-local-name="malais" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%94%E1%80%80%E1%80%B9%E1%80%81%E1%80%90%E1%80%B9%E1%80%90%E1%80%97%E1%80%B1%E1%80%92%E1%80%86%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%9B%E1%80%AC_%E1%80%80%E1%80%AD%E1%80%AF%E1%80%A9%E1%80%92%E1%80%AD%E1%80%94%E1%80%AD%E1%80%90%E1%80%BA%E1%80%85%E1%80%94%E1%80%85%E1%80%BA" title="နက္ခတ္တဗေဒဆိုင်ရာ ကိုဩဒိနိတ်စနစ် – birman" lang="my" hreflang="my" data-title="နက္ခတ္တဗေဒဆိုင်ရာ ကိုဩဒိနိတ်စနစ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birman" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Astronomisch_co%C3%B6rdinatenstelsel" title="Astronomisch coördinatenstelsel – néerlandais" lang="nl" hreflang="nl" data-title="Astronomisch coördinatenstelsel" data-language-autonym="Nederlands" data-language-local-name="néerlandais" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Himmelkoordinatar" title="Himmelkoordinatar – norvégien nynorsk" lang="nn" hreflang="nn" data-title="Himmelkoordinatar" data-language-autonym="Norsk nynorsk" data-language-local-name="norvégien nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Himmelkoordinat" title="Himmelkoordinat – norvégien bokmål" lang="nb" hreflang="nb" data-title="Himmelkoordinat" data-language-autonym="Norsk bokmål" data-language-local-name="norvégien bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Sist%C3%A8ma_de_coordenadas_cel%C3%A8stas" title="Sistèma de coordenadas celèstas – occitan" lang="oc" hreflang="oc" data-title="Sistèma de coordenadas celèstas" data-language-autonym="Occitan" data-language-local-name="occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Uk%C5%82ad_wsp%C3%B3%C5%82rz%C4%99dnych_astronomicznych" title="Układ współrzędnych astronomicznych – polonais" lang="pl" hreflang="pl" data-title="Układ współrzędnych astronomicznych" data-language-autonym="Polski" data-language-local-name="polonais" 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/Sistema_de_coordenadas_celestes" title="Sistema de coordenadas celestes – portugais" lang="pt" hreflang="pt" data-title="Sistema de coordenadas celestes" data-language-autonym="Português" data-language-local-name="portugais" 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/Coordonate_astronomice" title="Coordonate astronomice – roumain" lang="ro" hreflang="ro" data-title="Coordonate astronomice" data-language-autonym="Română" data-language-local-name="roumain" 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%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D0%BD%D0%B5%D0%B1%D0%B5%D1%81%D0%BD%D1%8B%D1%85_%D0%BA%D0%BE%D0%BE%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D1%82" title="Система небесных координат – russe" lang="ru" hreflang="ru" data-title="Система небесных координат" data-language-autonym="Русский" data-language-local-name="russe" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Nebeski_koordinatni_sistemi" title="Nebeski koordinatni sistemi – serbo-croate" lang="sh" hreflang="sh" data-title="Nebeski koordinatni sistemi" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croate" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Celestial_coordinate_system" title="Celestial coordinate system – Simple English" lang="en-simple" hreflang="en-simple" data-title="Celestial coordinate system" 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/Astronomick%C3%A9_s%C3%BAradnicov%C3%A9_syst%C3%A9my" title="Astronomické súradnicové systémy – slovaque" lang="sk" hreflang="sk" data-title="Astronomické súradnicové systémy" data-language-autonym="Slovenčina" data-language-local-name="slovaque" 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/Nebesni_koordinatni_sistem" title="Nebesni koordinatni sistem – slovène" lang="sl" hreflang="sl" data-title="Nebesni koordinatni sistem" data-language-autonym="Slovenščina" data-language-local-name="slovène" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr badge-Q17437798 badge-goodarticle mw-list-item" title="bon article"><a href="https://sr.wikipedia.org/wiki/%D0%9D%D0%B5%D0%B1%D0%B5%D1%81%D0%BA%D0%B8_%D0%BA%D0%BE%D0%BE%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D1%82%D0%BD%D0%B8_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B8" title="Небески координатни системи – serbe" lang="sr" hreflang="sr" data-title="Небески координатни системи" data-language-autonym="Српски / srpski" data-language-local-name="serbe" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Astronomiska_koordinatsystem" title="Astronomiska koordinatsystem – suédois" lang="sv" hreflang="sv" data-title="Astronomiska koordinatsystem" data-language-autonym="Svenska" data-language-local-name="suédois" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Majiranukta_ya_anga" title="Majiranukta ya anga – swahili" lang="sw" hreflang="sw" data-title="Majiranukta ya anga" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A3%E0%B8%B0%E0%B8%9A%E0%B8%9A%E0%B8%9E%E0%B8%B4%E0%B8%81%E0%B8%B1%E0%B8%94%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%81%E0%B8%A5%E0%B8%A1%E0%B8%97%E0%B9%89%E0%B8%AD%E0%B8%87%E0%B8%9F%E0%B9%89%E0%B8%B2" title="ระบบพิกัดทรงกลมท้องฟ้า – thaï" lang="th" hreflang="th" data-title="ระบบพิกัดทรงกลมท้องฟ้า" data-language-autonym="ไทย" data-language-local-name="thaï" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Sistemang_panlangit_ng_mga_koordinado" title="Sistemang panlangit ng mga koordinado – tagalog" lang="tl" hreflang="tl" data-title="Sistemang panlangit ng mga koordinado" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/G%C3%B6ky%C3%BCz%C3%BC_koordinat_sistemi" title="Gökyüzü koordinat sistemi – turc" lang="tr" hreflang="tr" data-title="Gökyüzü koordinat sistemi" data-language-autonym="Türkçe" data-language-local-name="turc" 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%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B8_%D0%BD%D0%B5%D0%B1%D0%B5%D1%81%D0%BD%D0%B8%D1%85_%D0%BA%D0%BE%D0%BE%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D1%82" title="Системи небесних координат – ukrainien" lang="uk" hreflang="uk" data-title="Системи небесних координат" data-language-autonym="Українська" data-language-local-name="ukrainien" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B3%D9%85%D8%A7%D9%88%DB%8C_%D9%85%D8%AA%D9%86%D8%A7%D8%B3%D9%82_%D9%86%D8%B8%D8%A7%D9%85" title="سماوی متناسق نظام – ourdou" lang="ur" hreflang="ur" data-title="سماوی متناسق نظام" data-language-autonym="اردو" data-language-local-name="ourdou" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Astronomik_koordinatalar" title="Astronomik koordinatalar – ouzbek" lang="uz" hreflang="uz" data-title="Astronomik koordinatalar" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ouzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n" title="Hệ tọa độ thiên văn – vietnamien" lang="vi" hreflang="vi" data-title="Hệ tọa độ thiên văn" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamien" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Sistema_pan-langit_hin_mga_koordinato" title="Sistema pan-langit hin mga koordinato – waray" lang="war" hreflang="war" data-title="Sistema pan-langit hin mga koordinato" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%A4%A9%E7%90%83%E5%9D%90%E6%A0%87%E7%B3%BB%E7%BB%9F" title="天球坐标系统 – wu" lang="wuu" hreflang="wuu" data-title="天球坐标系统" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A4%A9%E7%90%83%E5%9D%90%E6%A0%87%E7%B3%BB%E7%BB%9F" title="天球坐标系统 – chinois" lang="zh" hreflang="zh" data-title="天球坐标系统" data-language-autonym="中文" data-language-local-name="chinois" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%A4%A9%E7%90%83%E5%9D%90%E6%A8%99%E7%B3%BB%E7%B5%B1" title="天球坐標系統 – cantonais" lang="yue" hreflang="yue" data-title="天球坐標系統" data-language-autonym="粵語" data-language-local-name="cantonais" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q86394#sitelinks-wikipedia" title="Modifier les liens interlangues" class="wbc-editpage">Modifier les liens</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Espaces de noms"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div 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data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Apparence</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">déplacer vers la barre latérale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">masquer</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Un article de Wikipédia, l'encyclopédie libre.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="fr" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r194021218">.mw-parser-output .autres-projets>.titre{text-align:center;margin:0.2em 0}.mw-parser-output .autres-projets>ul{margin:0;padding:0}.mw-parser-output .autres-projets>ul>li{list-style:none;margin:0.2em 0;text-indent:0;padding-left:24px;min-height:20px;text-align:left;display:block}.mw-parser-output .autres-projets>ul>li>a{font-style:italic}@media(max-width:720px){.mw-parser-output .autres-projets{float:none}}</style><div class="autres-projets boite-grise boite-a-droite noprint js-interprojets"> <p class="titre">Sur les autres projets Wikimedia :</p> <ul class="noarchive plainlinks"> <li class="wiktionary"><a href="https://fr.wiktionary.org/wiki/coordonn%C3%A9e" class="extiw" title="wikt:coordonnée">coordonnée</a>, <span class="nowrap">sur le <span class="project">Wiktionnaire</span></span></li> </ul> </div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier:Celestial.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Celestial.png/220px-Celestial.png" decoding="async" width="220" height="197" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Celestial.png/330px-Celestial.png 1.5x, //upload.wikimedia.org/wikipedia/commons/f/fc/Celestial.png 2x" data-file-width="416" data-file-height="373" /></a><figcaption></figcaption></figure> <p>En <a href="/wiki/Astronomie" title="Astronomie">astronomie</a>, un <b>système de coordonnées céleste</b> est un <a href="/wiki/Syst%C3%A8me_de_coordonn%C3%A9es" title="Système de coordonnées">système de coordonnées</a> permettant de déterminer une position dans le ciel, généralement exprimée en notation <a href="/wiki/D%C3%A9cimal" class="mw-redirect" title="Décimal">décimale</a> ou pseudo-<a href="/wiki/Sexag%C3%A9simal" class="mw-redirect" title="Sexagésimal">sexagésimale</a> (l'unité de base de l'<a href="/wiki/Ascension_droite" title="Ascension droite">ascension droite</a> étant cependant l'<a href="/wiki/Temps_sid%C3%A9ral" title="Temps sidéral">heure sidérale</a>, équivalente à 15°). </p><p>Il existe plusieurs systèmes, utilisant une <a href="/w/index.php?title=Grille_de_coordonn%C3%A9es&action=edit&redlink=1" class="new" title="Grille de coordonnées (page inexistante)">grille de coordonnées</a> projetée sur la <a href="/wiki/Sph%C3%A8re_c%C3%A9leste" title="Sphère céleste">sphère céleste</a>, de manière analogue aux <a href="/wiki/Syst%C3%A8me_de_coordonn%C3%A9es_(cartographie)" title="Système de coordonnées (cartographie)">systèmes de coordonnées géographiques</a> utilisés à la surface de la <a href="/wiki/Terre" title="Terre">Terre</a>. Les systèmes de coordonnées célestes différent seulement dans le choix du <a href="/w/index.php?title=Plan_de_r%C3%A9f%C3%A9rence&action=edit&redlink=1" class="new" title="Plan de référence (page inexistante)">plan de référence</a>, qui divise le ciel en deux <a href="/wiki/H%C3%A9misph%C3%A8re_(g%C3%A9ographie)" title="Hémisphère (géographie)">hémisphères</a> le long d'un <a href="/wiki/Grand_cercle" title="Grand cercle">grand cercle</a> (le plan de référence du système de coordonnées géographiques est l'<a href="/wiki/%C3%89quateur_(ligne_%C3%A9quinoxiale)" class="mw-redirect" title="Équateur (ligne équinoxiale)">équateur</a> terrestre). Chaque système est nommé d'après son plan de référence : </p> <ul><li><a href="/wiki/Syst%C3%A8me_de_coordonn%C3%A9es_horizontales" title="Système de coordonnées horizontales">système de coordonnées horizontales</a> ;</li> <li><a href="/wiki/Syst%C3%A8me_de_coordonn%C3%A9es_horaires" title="Système de coordonnées horaires">système de coordonnées horaires</a> ;</li> <li><a href="/wiki/Syst%C3%A8me_de_coordonn%C3%A9es_%C3%A9quatoriales" title="Système de coordonnées équatoriales">système de coordonnées équatoriales</a> ;</li> <li><a href="/wiki/Syst%C3%A8me_de_coordonn%C3%A9es_%C3%A9cliptiques" title="Système de coordonnées écliptiques">système de coordonnées écliptiques</a> ;</li> <li><a href="/wiki/Syst%C3%A8me_de_coordonn%C3%A9es_galactiques" title="Système de coordonnées galactiques">système de coordonnées galactiques</a>.</li></ul> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Conversions">Conversions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&veaction=edit&section=1" title="Modifier la section : Conversions" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&action=edit&section=1" title="Modifier le code source de la section : Conversions"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier:EARTHandSUN.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/EARTHandSUN.png/220px-EARTHandSUN.png" decoding="async" width="220" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/EARTHandSUN.png/330px-EARTHandSUN.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b6/EARTHandSUN.png/440px-EARTHandSUN.png 2x" data-file-width="1235" data-file-height="1146" /></a><figcaption>Le système du soleil est en bleu, celui de la terre en rouge. Le soleil est orienté selon OL. P est la position sur terre. a est l'angle horaire. az est l’azimut. z est le zénith. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }" /></span> est la latitude. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5321cfa797202b3e1f8620663ff43c4660ea03a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:2.343ex;" alt="{\displaystyle \delta }" /></span> est la déclinaison. Remarque: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h+z={\frac {\pi }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo>+</mo> <mi>z</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h+z={\frac {\pi }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62d99353fc6dc099c0bc66499d27946ad7676ab8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.534ex; height:4.676ex;" alt="{\displaystyle h+z={\frac {\pi }{2}}}" /></span></figcaption></figure> <p>Il existe des formules permettant de passer, de proche en proche, d'un système de coordonnées célestes à un autre système de coordonnées célestes. </p><p>Dans le formulaire qui suit, les groupes formés de trois formules doivent être entièrement pris en compte (on ne peut se contenter de respecter 2 formules sur 3), car les fonctions inverses des sinus et des cosinus ne donnent pas nécessairement la bonne solution. <br /><br /><br /> Grâce à la <a href="/wiki/Trigonom%C3%A9trie_sph%C3%A9rique" title="Trigonométrie sphérique">trigonométrie sphérique</a> (formule des cosinus), le triangle sphérique <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle PNL}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>N</mi> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle PNL}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b0110c4328cb5ad8c0ac36b1fd3c6a9396d9ac2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.392ex; height:2.176ex;" alt="{\displaystyle PNL}" /></span> du graphique livre les relations suivantes :<br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos(z)=\cos \left({\frac {\pi }{2}}-\varphi \right)\cdot \cos \left({\frac {\pi }{2}}-\delta \right)+\cos(a)\cdot \sin \left({\frac {\pi }{2}}-\varphi \right)\cdot \sin \left({\frac {\pi }{2}}-\delta \right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mi>δ</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mi>δ</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos(z)=\cos \left({\frac {\pi }{2}}-\varphi \right)\cdot \cos \left({\frac {\pi }{2}}-\delta \right)+\cos(a)\cdot \sin \left({\frac {\pi }{2}}-\varphi \right)\cdot \sin \left({\frac {\pi }{2}}-\delta \right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba99c3136e209a50b133e58ff2327bb8ddbfbfed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:71.342ex; height:4.843ex;" alt="{\displaystyle \cos(z)=\cos \left({\frac {\pi }{2}}-\varphi \right)\cdot \cos \left({\frac {\pi }{2}}-\delta \right)+\cos(a)\cdot \sin \left({\frac {\pi }{2}}-\varphi \right)\cdot \sin \left({\frac {\pi }{2}}-\delta \right)}" /></span> mais aussi<br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos \left({\frac {\pi }{2}}-\delta \right)=\cos \left({\frac {\pi }{2}}-\varphi \right)\cdot \cos(z)+\cos(\pi -az)\cdot \sin \left({\frac {\pi }{2}}-\varphi \right)\cdot \sin(z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mi>δ</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>π</mi> <mo>−</mo> <mi>a</mi> <mi>z</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \left({\frac {\pi }{2}}-\delta \right)=\cos \left({\frac {\pi }{2}}-\varphi \right)\cdot \cos(z)+\cos(\pi -az)\cdot \sin \left({\frac {\pi }{2}}-\varphi \right)\cdot \sin(z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4cd38bcbfa0ea195ef61b5694addee1be2bc353f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:70.667ex; height:4.843ex;" alt="{\displaystyle \cos \left({\frac {\pi }{2}}-\delta \right)=\cos \left({\frac {\pi }{2}}-\varphi \right)\cdot \cos(z)+\cos(\pi -az)\cdot \sin \left({\frac {\pi }{2}}-\varphi \right)\cdot \sin(z)}" /></span><br /> Le triangle sphérique <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle PQL}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mi>Q</mi> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle PQL}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e572153c8fa7e07dc14b39f7c9d1021429c55c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.167ex; height:2.509ex;" alt="{\displaystyle PQL}" /></span> du graphique livre la relation suivante pour le cosinus de l'angle en pointillé :<br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos(z)\cdot \cos(\varphi )+\cos(az)\cdot \sin(z)\cdot \sin(\varphi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>z</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos(z)\cdot \cos(\varphi )+\cos(az)\cdot \sin(z)\cdot \sin(\varphi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/743df3bd1784f194e63618b137ca011acf455e50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.503ex; height:2.843ex;" alt="{\displaystyle \cos(z)\cdot \cos(\varphi )+\cos(az)\cdot \sin(z)\cdot \sin(\varphi )}" /></span>, qui vaut également <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos(a)\cdot \cos(\delta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos(a)\cdot \cos(\delta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2305743a62d3dcbf9a360369fe42cae7e4611e2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.798ex; height:2.843ex;" alt="{\displaystyle \cos(a)\cdot \cos(\delta )}" /></span><br /> Ainsi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos(z)\cdot \cos(\varphi )+\cos(az)\cdot \sin(z)\cdot \sin(\varphi )=\cos(a)\cdot \cos(\delta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>z</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos(z)\cdot \cos(\varphi )+\cos(az)\cdot \sin(z)\cdot \sin(\varphi )=\cos(a)\cdot \cos(\delta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9d467d171512c0299463257fbf7e274b20c7c43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:56.4ex; height:2.843ex;" alt="{\displaystyle \cos(z)\cdot \cos(\varphi )+\cos(az)\cdot \sin(z)\cdot \sin(\varphi )=\cos(a)\cdot \cos(\delta )}" /></span><br /> </p><p>En résumé, nous obtenons, grâce à la trigonométrie sphérique :<br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin(h)=\sin(\varphi )\cdot \sin(\delta )+\cos(a)\cdot \cos(\varphi )\cdot \cos(\delta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(h)=\sin(\varphi )\cdot \sin(\delta )+\cos(a)\cdot \cos(\varphi )\cdot \cos(\delta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b9e80b085b12edf0cae1b6ae449d39711c087131" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:47.438ex; height:2.843ex;" alt="{\displaystyle \sin(h)=\sin(\varphi )\cdot \sin(\delta )+\cos(a)\cdot \cos(\varphi )\cdot \cos(\delta )}" /></span><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin(\delta )=\sin(\varphi )\cdot \sin(h)-\cos(az)\cdot \cos(\varphi )\cdot \cos(h)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>z</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(\delta )=\sin(\varphi )\cdot \sin(h)-\cos(az)\cdot \cos(\varphi )\cdot \cos(h)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d50abde2945f517fdba93e0654c6d668296b55c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:48.817ex; height:2.843ex;" alt="{\displaystyle \sin(\delta )=\sin(\varphi )\cdot \sin(h)-\cos(az)\cdot \cos(\varphi )\cdot \cos(h)}" /></span><br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin(h)\cdot \cos(\varphi )+\cos(az)\cdot \cos(h)\cdot \sin(\varphi )=\cos(a)\cdot \cos(\delta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>z</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(h)\cdot \cos(\varphi )+\cos(az)\cdot \cos(h)\cdot \sin(\varphi )=\cos(a)\cdot \cos(\delta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7596676fa99e7dbcce01220d36bbb80fe6efb7b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:56.902ex; height:2.843ex;" alt="{\displaystyle \sin(h)\cdot \cos(\varphi )+\cos(az)\cdot \cos(h)\cdot \sin(\varphi )=\cos(a)\cdot \cos(\delta )}" /></span><br /> formules en tout point identiques à celles indiquées en dessous (il faut juste remplacer <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}" /></span> par <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{H}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{H}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b078c29db5aad1f260f44bec7f8c766bf950df1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.435ex; height:2.509ex;" alt="{\displaystyle A_{H}}" /></span> et <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle az}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle az}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7906599a638e61b162bc3e05d49faa7cd2046ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.318ex; height:1.676ex;" alt="{\displaystyle az}" /></span> par <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}" /></span>). </p><p>Remarquons enfin que :<br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin(\varphi )\cdot \cos(\delta )\cdot \cos(a)-\cos(\varphi )\cdot \sin(\delta )=\sin(\varphi )\cdot (\sin(h)\cdot \cos(\varphi )+\cos(az)\cdot \cos(h)\cdot \sin(\varphi ))-\cos(\varphi )\cdot (\sin(\varphi )\cdot \sin(h)-\cos(az)\cdot \cos(\varphi )\cdot \cos(h))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>z</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>z</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(\varphi )\cdot \cos(\delta )\cdot \cos(a)-\cos(\varphi )\cdot \sin(\delta )=\sin(\varphi )\cdot (\sin(h)\cdot \cos(\varphi )+\cos(az)\cdot \cos(h)\cdot \sin(\varphi ))-\cos(\varphi )\cdot (\sin(\varphi )\cdot \sin(h)-\cos(az)\cdot \cos(\varphi )\cdot \cos(h))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1aac4209627860706a12103878d486d8c6af6eff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:143.887ex; height:2.843ex;" alt="{\displaystyle \sin(\varphi )\cdot \cos(\delta )\cdot \cos(a)-\cos(\varphi )\cdot \sin(\delta )=\sin(\varphi )\cdot (\sin(h)\cdot \cos(\varphi )+\cos(az)\cdot \cos(h)\cdot \sin(\varphi ))-\cos(\varphi )\cdot (\sin(\varphi )\cdot \sin(h)-\cos(az)\cdot \cos(\varphi )\cdot \cos(h))}" /></span> et donc <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin(\varphi )\cdot \cos(\delta )\cdot \cos(a)-\cos(\varphi )\cdot \sin(\delta )=\cos(h)\cdot \cos(az)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(\varphi )\cdot \cos(\delta )\cdot \cos(a)-\cos(\varphi )\cdot \sin(\delta )=\cos(h)\cdot \cos(az)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/610286b9501f4a25c3b641dca9985d228b96ff80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:56.611ex; height:2.843ex;" alt="{\displaystyle \sin(\varphi )\cdot \cos(\delta )\cdot \cos(a)-\cos(\varphi )\cdot \sin(\delta )=\cos(h)\cdot \cos(az)}" /></span> </p> <div class="mw-heading mw-heading3"><h3 id="Des_coordonnées_horizontales_aux_coordonnées_horaires"><span id="Des_coordonn.C3.A9es_horizontales_aux_coordonn.C3.A9es_horaires"></span>Des coordonnées horizontales aux coordonnées horaires</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&veaction=edit&section=2" title="Modifier la section : Des coordonnées horizontales aux coordonnées horaires" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&action=edit&section=2" title="Modifier le code source de la section : Des coordonnées horizontales aux coordonnées horaires"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Connaissant les valeurs respectives Z et h de l'<a href="/wiki/Azimut" title="Azimut">azimut</a> et de la <a href="/wiki/Hauteur_(angle)" title="Hauteur (angle)">hauteur</a>, la <a href="/wiki/D%C3%A9clinaison_(astronomie)" title="Déclinaison (astronomie)">déclinaison</a> δ et l'<a href="/wiki/Angle_horaire" title="Angle horaire">angle horaire</a> A<sub>H</sub> peuvent être obtenus grâce aux trois formules suivantes : </p> <center> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{matrix}\sin \delta &=&\sin \varphi \sin h-\cos \varphi \cos h\cos Z\\\cos \delta \sin A_{H}&=&\cos h\sin Z\\\cos \delta \cos A_{H}&=&\cos \varphi \sin h+\sin \varphi \cos h\cos Z\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mi>δ</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> <mi>sin</mi> <mo>⁡</mo> <mi>h</mi> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>h</mi> <mi>cos</mi> <mo>⁡</mo> <mi>Z</mi> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mi>δ</mi> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>cos</mi> <mo>⁡</mo> <mi>h</mi> <mi>sin</mi> <mo>⁡</mo> <mi>Z</mi> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mi>δ</mi> <mi>cos</mi> <mo>⁡</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mi>sin</mi> <mo>⁡</mo> <mi>h</mi> <mo>+</mo> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>h</mi> <mi>cos</mi> <mo>⁡</mo> <mi>Z</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}\sin \delta &=&\sin \varphi \sin h-\cos \varphi \cos h\cos Z\\\cos \delta \sin A_{H}&=&\cos h\sin Z\\\cos \delta \cos A_{H}&=&\cos \varphi \sin h+\sin \varphi \cos h\cos Z\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2204b1b7a0cd0dc53b05ddf270745af55bf66e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:47.452ex; height:9.509ex;" alt="{\displaystyle {\begin{matrix}\sin \delta &=&\sin \varphi \sin h-\cos \varphi \cos h\cos Z\\\cos \delta \sin A_{H}&=&\cos h\sin Z\\\cos \delta \cos A_{H}&=&\cos \varphi \sin h+\sin \varphi \cos h\cos Z\end{matrix}}}" /></span></center> <p>où l'angle <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }" /></span> représente la <a href="/wiki/Latitude" title="Latitude">latitude</a> astronomique du lieu d'observation. L'azimut Z est compté à partir du sud géographique, croissant vers l'ouest. </p> <div class="mw-heading mw-heading3"><h3 id="Des_coordonnées_horaires_aux_coordonnées_horizontales"><span id="Des_coordonn.C3.A9es_horaires_aux_coordonn.C3.A9es_horizontales"></span>Des coordonnées horaires aux coordonnées horizontales</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&veaction=edit&section=3" title="Modifier la section : Des coordonnées horaires aux coordonnées horizontales" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&action=edit&section=3" title="Modifier le code source de la section : Des coordonnées horaires aux coordonnées horizontales"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Connaissant les valeurs respectives A<sub>H</sub> et δ de l'<a href="/wiki/Angle_horaire" title="Angle horaire">angle horaire</a> et de la <a href="/wiki/D%C3%A9clinaison_(astronomie)" title="Déclinaison (astronomie)">déclinaison</a>, la <a href="/wiki/Hauteur_(angle)" title="Hauteur (angle)">hauteur</a> h et l'<a href="/wiki/Azimut" title="Azimut">azimut</a> Z peuvent être obtenus grâce aux trois formules suivantes : </p> <center> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{matrix}\sin h&=&\cos \varphi \cos \delta \cos A_{H}+\sin \varphi \sin \delta \\\cos h\sin Z&=&cos\,\delta \sin A_{H}\\\cos h\cos Z&=&\sin \varphi \cos \delta \cos A_{H}-\cos \varphi \sin \delta \end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mi>h</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>δ</mi> <mi>cos</mi> <mo>⁡</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mo>+</mo> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> <mi>sin</mi> <mo>⁡</mo> <mi>δ</mi> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mi>h</mi> <mi>sin</mi> <mo>⁡</mo> <mi>Z</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mspace width="thinmathspace"></mspace> <mi>δ</mi> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mi>h</mi> <mi>cos</mi> <mo>⁡</mo> <mi>Z</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>δ</mi> <mi>cos</mi> <mo>⁡</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mi>sin</mi> <mo>⁡</mo> <mi>δ</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}\sin h&=&\cos \varphi \cos \delta \cos A_{H}+\sin \varphi \sin \delta \\\cos h\sin Z&=&cos\,\delta \sin A_{H}\\\cos h\cos Z&=&\sin \varphi \cos \delta \cos A_{H}-\cos \varphi \sin \delta \end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d3e3fa5e66de0e9edd9bb9985e0ed735b739443" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:47.162ex; height:9.509ex;" alt="{\displaystyle {\begin{matrix}\sin h&=&\cos \varphi \cos \delta \cos A_{H}+\sin \varphi \sin \delta \\\cos h\sin Z&=&cos\,\delta \sin A_{H}\\\cos h\cos Z&=&\sin \varphi \cos \delta \cos A_{H}-\cos \varphi \sin \delta \end{matrix}}}" /></span></center> <p>où l'angle <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }" /></span> représente la <a href="/wiki/Latitude" title="Latitude">latitude</a> astronomique du lieu d'observation. </p> <div class="mw-heading mw-heading3"><h3 id="Des_coordonnées_horaires_aux_coordonnées_équatoriales"><span id="Des_coordonn.C3.A9es_horaires_aux_coordonn.C3.A9es_.C3.A9quatoriales"></span>Des coordonnées horaires aux coordonnées équatoriales</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&veaction=edit&section=4" title="Modifier la section : Des coordonnées horaires aux coordonnées équatoriales" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&action=edit&section=4" title="Modifier le code source de la section : Des coordonnées horaires aux coordonnées équatoriales"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Connaissant les valeurs respectives A<sub>H</sub> et δ de l'<a href="/wiki/Angle_horaire" title="Angle horaire">angle horaire</a> et de la <a href="/wiki/D%C3%A9clinaison_(astronomie)" title="Déclinaison (astronomie)">déclinaison</a>, l'<a href="/wiki/Ascension_droite" title="Ascension droite">ascension droite</a> α peut être obtenue très simplement grâce à l'unique formule suivante (la déclinaison reste la même) : </p> <center> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha =S_{l}-A_{H}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha =S_{l}-A_{H}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6678f6156f9a5415a3e53ce5a23ea7f5a3e3eed4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.396ex; height:2.509ex;" alt="{\displaystyle \alpha =S_{l}-A_{H}\,}" /></span></center> <p>où <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{l}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{l}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56251c7a3e64915190abff835828a2e0e82d993c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.147ex; height:2.509ex;" alt="{\displaystyle S_{l}}" /></span> représente le <a href="/wiki/Temps_sid%C3%A9ral" title="Temps sidéral">temps sidéral</a> au moment de l'observation. </p> <div class="mw-heading mw-heading3"><h3 id="Des_coordonnées_équatoriales_aux_coordonnées_horaires"><span id="Des_coordonn.C3.A9es_.C3.A9quatoriales_aux_coordonn.C3.A9es_horaires"></span>Des coordonnées équatoriales aux coordonnées horaires</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&veaction=edit&section=5" title="Modifier la section : Des coordonnées équatoriales aux coordonnées horaires" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&action=edit&section=5" title="Modifier le code source de la section : Des coordonnées équatoriales aux coordonnées horaires"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Connaissant les valeurs respectives α et δ de l'ascension droite et de la <a href="/wiki/D%C3%A9clinaison_(astronomie)" title="Déclinaison (astronomie)">déclinaison</a>, l'<a href="/wiki/Angle_horaire" title="Angle horaire">angle horaire</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{H}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{H}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b078c29db5aad1f260f44bec7f8c766bf950df1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.435ex; height:2.509ex;" alt="{\displaystyle A_{H}}" /></span> peut être obtenu très simplement grâce à l'unique formule suivante (la déclinaison reste la même) : </p> <center> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{H}=S_{l}-\alpha \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> <mo>−</mo> <mi>α</mi> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{H}=S_{l}-\alpha \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e99dfeceea9050c867b37369417921e609630559" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.396ex; height:2.509ex;" alt="{\displaystyle A_{H}=S_{l}-\alpha \,}" /></span></center> <p>où <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{l}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{l}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56251c7a3e64915190abff835828a2e0e82d993c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.147ex; height:2.509ex;" alt="{\displaystyle S_{l}}" /></span> représente le <a href="/wiki/Temps_sid%C3%A9ral" title="Temps sidéral">temps sidéral</a> au moment de l'observation. </p> <div class="mw-heading mw-heading3"><h3 id="Des_coordonnées_équatoriales_vers_les_coordonnées_écliptiques"><span id="Des_coordonn.C3.A9es_.C3.A9quatoriales_vers_les_coordonn.C3.A9es_.C3.A9cliptiques"></span>Des coordonnées équatoriales vers les coordonnées écliptiques</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&veaction=edit&section=6" title="Modifier la section : Des coordonnées équatoriales vers les coordonnées écliptiques" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&action=edit&section=6" title="Modifier le code source de la section : Des coordonnées équatoriales vers les coordonnées écliptiques"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Connaissant les valeurs respectives α et δ de l'<a href="/wiki/Ascension_droite" title="Ascension droite">ascension droite</a> et de la <a href="/wiki/D%C3%A9clinaison_(astronomie)" title="Déclinaison (astronomie)">déclinaison</a>, les coordonnées écliptiques β (latitude) et λ (longitude) peuvent être obtenues grâce aux trois formules suivantes : </p> <center> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{matrix}\sin \beta &=&\cos \varepsilon \sin \delta -\sin \varepsilon \sin \alpha \cos \delta \\\cos \lambda \cos \beta &=&\cos \alpha \cos \delta \\\sin \lambda \cos \beta &=&\sin \varepsilon \sin \delta +\cos \varepsilon \sin \alpha \cos \delta \end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>cos</mi> <mo>⁡</mo> <mi>ε</mi> <mi>sin</mi> <mo>⁡</mo> <mi>δ</mi> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mi>ε</mi> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>δ</mi> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mi>λ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>δ</mi> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mi>λ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>sin</mi> <mo>⁡</mo> <mi>ε</mi> <mi>sin</mi> <mo>⁡</mo> <mi>δ</mi> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mi>ε</mi> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>δ</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}\sin \beta &=&\cos \varepsilon \sin \delta -\sin \varepsilon \sin \alpha \cos \delta \\\cos \lambda \cos \beta &=&\cos \alpha \cos \delta \\\sin \lambda \cos \beta &=&\sin \varepsilon \sin \delta +\cos \varepsilon \sin \alpha \cos \delta \end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff3c84ba02cdaea130cf050225f6ed8e9d46e7eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:43.754ex; height:9.176ex;" alt="{\displaystyle {\begin{matrix}\sin \beta &=&\cos \varepsilon \sin \delta -\sin \varepsilon \sin \alpha \cos \delta \\\cos \lambda \cos \beta &=&\cos \alpha \cos \delta \\\sin \lambda \cos \beta &=&\sin \varepsilon \sin \delta +\cos \varepsilon \sin \alpha \cos \delta \end{matrix}}}" /></span></center> <p>où ε = 23.439281° représente l'<a href="/wiki/%C3%89cliptique#Inclinaison" title="Écliptique">obliquité de l'écliptique</a>, c'est-à-dire l'angle que forme le plan de l'équateur terrestre avec le plan de l'orbite terrestre autour du soleil. </p><p>On peut, alors, calculer l'<a href="/wiki/Arc_tangente" title="Arc tangente">arc tangente</a> suivant la formule suivante puis placer l'angle dans le bon <a href="/wiki/Quadrant_(math%C3%A9matiques)" title="Quadrant (mathématiques)">quadrant</a> (car tangente a une période de 180° alors que cosinus et sinus ont des périodes de 360°). La fonction <a href="/wiki/Atan2" title="Atan2">atan2</a> facilite ce calcul. </p> <center> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{matrix}\tan \lambda &=&{\sin \varepsilon \tan \delta +\cos \varepsilon \sin \alpha \over \cos \alpha }\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>tan</mi> <mo>⁡</mo> <mi>λ</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>ε</mi> <mi>tan</mi> <mo>⁡</mo> <mi>δ</mi> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mi>ε</mi> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mrow> <mrow> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}\tan \lambda &=&{\sin \varepsilon \tan \delta +\cos \varepsilon \sin \alpha \over \cos \alpha }\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d4f54e4d5087c3391fb3bdd7c969eabe0aa77f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:28.684ex; height:3.676ex;" alt="{\displaystyle {\begin{matrix}\tan \lambda &=&{\sin \varepsilon \tan \delta +\cos \varepsilon \sin \alpha \over \cos \alpha }\end{matrix}}}" /></span></center> <div class="mw-heading mw-heading3"><h3 id="Des_coordonnées_écliptiques_vers_les_coordonnées_équatoriales"><span id="Des_coordonn.C3.A9es_.C3.A9cliptiques_vers_les_coordonn.C3.A9es_.C3.A9quatoriales"></span>Des coordonnées écliptiques vers les coordonnées équatoriales</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&veaction=edit&section=7" title="Modifier la section : Des coordonnées écliptiques vers les coordonnées équatoriales" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&action=edit&section=7" title="Modifier le code source de la section : Des coordonnées écliptiques vers les coordonnées équatoriales"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Connaissant les valeurs respectives λ et ß de la longitude et de la latitude écliptiques, la <a href="/wiki/D%C3%A9clinaison_(astronomie)" title="Déclinaison (astronomie)">déclinaison</a> δ et l'<a href="/wiki/Ascension_droite" title="Ascension droite">ascension droite</a> α peuvent être obtenues grâce aux trois formules suivantes : </p> <center> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{matrix}\sin \delta &=&\sin \varepsilon \sin \lambda \cos \beta +\cos \varepsilon \sin \beta \\\cos \alpha \cos \delta &=&\cos \lambda \cos \beta \\\sin \alpha \cos \delta &=&\cos \varepsilon \sin \lambda \cos \beta -\sin \varepsilon \sin \beta \end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mi>δ</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>sin</mi> <mo>⁡</mo> <mi>ε</mi> <mi>sin</mi> <mo>⁡</mo> <mi>λ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mi>ε</mi> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>δ</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>cos</mi> <mo>⁡</mo> <mi>λ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> <mi>cos</mi> <mo>⁡</mo> <mi>δ</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mi>cos</mi> <mo>⁡</mo> <mi>ε</mi> <mi>sin</mi> <mo>⁡</mo> <mi>λ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>β</mi> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mi>ε</mi> <mi>sin</mi> <mo>⁡</mo> <mi>β</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}\sin \delta &=&\sin \varepsilon \sin \lambda \cos \beta +\cos \varepsilon \sin \beta \\\cos \alpha \cos \delta &=&\cos \lambda \cos \beta \\\sin \alpha \cos \delta &=&\cos \varepsilon \sin \lambda \cos \beta -\sin \varepsilon \sin \beta \end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ffa24d1f3f58aa66a4874b1b2d12b271da49ab6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:44.037ex; height:9.176ex;" alt="{\displaystyle {\begin{matrix}\sin \delta &=&\sin \varepsilon \sin \lambda \cos \beta +\cos \varepsilon \sin \beta \\\cos \alpha \cos \delta &=&\cos \lambda \cos \beta \\\sin \alpha \cos \delta &=&\cos \varepsilon \sin \lambda \cos \beta -\sin \varepsilon \sin \beta \end{matrix}}}" /></span></center> <p>où ε = 23.439281° représente l'<a href="/wiki/%C3%89cliptique#Inclinaison" title="Écliptique">obliquité de l'écliptique</a>, c'est-à-dire l'angle que forme le plan de l'équateur terrestre avec le plan de l'orbite terrestre autour du soleil. </p><p>On peut, alors, calculer l'<a href="/wiki/Arc_tangente" title="Arc tangente">arc tangente</a> suivant la formule suivante puis placer l'angle dans le bon <a href="/wiki/Quadrant_(math%C3%A9matiques)" title="Quadrant (mathématiques)">quadrant</a> (car tangente a une période de 180° alors que cosinus et sinus ont des périodes de 360°). La fonction <a href="/wiki/Atan2" title="Atan2">atan2</a> facilite ce calcul. </p> <center> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{matrix}\tan \alpha &=&{\cos \varepsilon \sin \lambda -\sin \varepsilon \tan \beta \over \cos \lambda }\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> </mtd> <mtd> <mo>=</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>cos</mi> <mo>⁡</mo> <mi>ε</mi> <mi>sin</mi> <mo>⁡</mo> <mi>λ</mi> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mi>ε</mi> <mi>tan</mi> <mo>⁡</mo> <mi>β</mi> </mrow> <mrow> <mi>cos</mi> <mo>⁡</mo> <mi>λ</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}\tan \alpha &=&{\cos \varepsilon \sin \lambda -\sin \varepsilon \tan \beta \over \cos \lambda }\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e49ddd88fc72c859905ed920f18a417a690d5182" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.192ex; margin-bottom: -0.312ex; width:28.923ex; height:4.176ex;" alt="{\displaystyle {\begin{matrix}\tan \alpha &=&{\cos \varepsilon \sin \lambda -\sin \varepsilon \tan \beta \over \cos \lambda }\end{matrix}}}" /></span></center> <div class="mw-heading mw-heading2"><h2 id="Voir_aussi">Voir aussi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&veaction=edit&section=8" title="Modifier la section : Voir aussi" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&action=edit&section=8" title="Modifier le code source de la section : Voir aussi"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Coordonn%C3%A9es_sph%C3%A9riques" title="Coordonnées sphériques">Coordonnées sphériques</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Liens_externes">Liens externes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&veaction=edit&section=9" title="Modifier la section : Liens externes" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes&action=edit&section=9" title="Modifier le code source de la section : Liens externes"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p class="mw-empty-elt"> </p> <ul><li class="mw-empty-elt"></li> <li class="mw-empty-elt"></li> <li><div class="liste-horizontale"><span class="wd_identifiers">Notices dans des dictionnaires ou encyclopédies généralistes<span class="noprint wikidata-linkback skin-invert"><span class="mw-valign-baseline noviewer" typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q86394?uselang=fr#identifiers" title="Voir et modifier les données sur Wikidata"><img alt="Voir et modifier les données sur Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></span></span> : <ul><li><a rel="nofollow" class="external text" href="https://www.enciclopedia.cat/EC-GEC-0093835.xml"><i>Gran Enciclopèdia Catalana</i></a></li> <li><a rel="nofollow" class="external text" href="https://snl.no/astronomiske_koordinater"><i>Store norske leksikon</i></a></li> </ul></div></li> <li class="mw-empty-elt"></li></ul> <div class="navbox-container" style="clear:both;"> <table class="navbox collapsible noprint autocollapse" style=""> <tbody><tr><th class="navbox-title" colspan="2" style=""><div style="float:left; width:6em; text-align:left"><div class="noprint plainlinks nowrap tnavbar" style="padding:0; font-size:xx-small; color:var(--color-emphasized, #000000);"><a href="/wiki/Mod%C3%A8le:Palette_Orbites" title="Modèle:Palette Orbites"><abbr class="abbr" title="Voir ce modèle.">v</abbr></a> · <a class="external text" href="https://fr.wikipedia.org/w/index.php?title=Mod%C3%A8le:Palette_Orbites&action=edit"><abbr class="abbr" title="Modifier ce modèle. Merci de prévisualiser avant de sauvegarder.">m</abbr></a></div></div><div style="font-size:110%"><a href="/wiki/Orbite" title="Orbite">Orbites</a></div></th> </tr> <tr> <th class="navbox-group" style="">Général</th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Orbite_en_bo%C3%AEte" title="Orbite en boîte">Orbite en boîte</a></li> <li><a href="/wiki/Orbite_circulaire" title="Orbite circulaire">Circulaire</a></li> <li><a href="/wiki/Orbite_d%27attente" title="Orbite d'attente">Orbite d'attente</a></li> <li><a href="/wiki/Trajectoire_parabolique" title="Trajectoire parabolique">Orbite d'évasion</a></li> <li><a href="/wiki/Orbite_de_rebut" title="Orbite de rebut">Orbite de rebut</a></li> <li><a href="/wiki/Orbite_elliptique" title="Orbite elliptique">Elliptique</a> <ul><li><a href="/wiki/Orbite_elliptique_%C3%A9lev%C3%A9e" title="Orbite elliptique élevée">Elliptique élevée</a></li></ul></li> <li><a href="/wiki/Orbite_inclin%C3%A9e" title="Orbite inclinée">Orbite inclinée</a></li> <li><a href="/wiki/Orbite_non_inclin%C3%A9e" title="Orbite non inclinée">Orbite non inclinée</a></li> <li><a href="/wiki/Orbite_osculatrice" title="Orbite osculatrice">Osculatrice</a></li> <li><a href="/wiki/Orbite_synchrone" title="Orbite synchrone">Synchrone</a> <ul><li><a href="/wiki/Orbite_semi-synchrone" title="Orbite semi-synchrone">Semi-synchrone</a></li> <li><a href="/wiki/Orbite_sous-synchrone" title="Orbite sous-synchrone">Sous-synchrone</a></li> <li><a href="/wiki/Orbite_super-synchrone" title="Orbite super-synchrone">Super-synchrone</a></li></ul></li> <li><a href="/wiki/Trajectoire_hyperbolique" title="Trajectoire hyperbolique">Trajectoire hyperbolique</a></li> <li><a href="/wiki/Trajectoire_parabolique" title="Trajectoire parabolique">Trajectoire parabolique</a> (capture)</li></ul> </div></td> </tr> <tr> <th class="navbox-group" style=""><a href="/wiki/Orbite_terrestre" title="Orbite terrestre">Géocentrique</a></th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Orbite_h%C3%A9liosynchrone" title="Orbite héliosynchrone">Orbite héliosynchrone</a></li> <li><a href="/wiki/Orbite_g%C3%A9ostationnaire" title="Orbite géostationnaire">Géostationnaire</a></li> <li><a href="/wiki/Orbite_g%C3%A9osynchrone" title="Orbite géosynchrone">Géosynchrone</a></li> <li><a href="/wiki/Orbite_de_Molnia" title="Orbite de Molnia">Orbite de Molnia</a></li> <li><a href="/wiki/Orbite_polaire" title="Orbite polaire">Polaire</a></li> <li><a href="/wiki/Orbite_quasi_%C3%A9quatoriale" title="Orbite quasi équatoriale">Quasi équatoriale</a></li> <li><a href="/wiki/Orbite_terrestre_basse" title="Orbite terrestre basse">Terrestre basse</a></li> <li><a href="/wiki/Orbite_terrestre_moyenne" title="Orbite terrestre moyenne">Terrestre moyenne</a></li> <li><a href="/wiki/Orbite_terrestre_haute" title="Orbite terrestre haute">Terrestre haute</a></li> <li><a href="/wiki/Orbite_toundra" title="Orbite toundra">Toundra</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Non géocentrique</th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Orbite_ar%C3%A9ocentrique" title="Orbite aréocentrique">Aréocentrique</a> <ul><li><a href="/wiki/Orbite_ar%C3%A9osynchrone" title="Orbite aréosynchrone">Aréosynchrone</a></li> <li><a href="/wiki/Orbite_ar%C3%A9ostationnaire" title="Orbite aréostationnaire">Aréostationnaire</a></li></ul></li> <li><a href="/wiki/Orbite_de_halo" title="Orbite de halo">Halo</a></li> <li><a href="/wiki/Orbite_h%C3%A9liocentrique" title="Orbite héliocentrique">Héliocentrique</a> <ul><li><a href="/wiki/Orbite_h%C3%A9liostationnaire" title="Orbite héliostationnaire">Héliostationnaire</a></li></ul></li> <li><a href="/wiki/Orbite_de_Lissajous" title="Orbite de Lissajous">Lissajous</a></li> <li><a href="/wiki/Orbite_s%C3%A9l%C3%A9nocentrique" title="Orbite sélénocentrique">Sélénocentrique</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Paramètres</th> <td class="navbox-list navbox-even" style=""><table class="navbox-subgroup" style=""> <tbody><tr> <th class="navbox-group" style="width:50px;">Classiques</th> <td class="navbox-list" style="text-align:left;;"><div class="liste-horizontale"> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M_{0}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M_{0}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2fab040de06acd9b92a729c3623819333d6f3503" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:3.695ex; height:2.509ex;" alt="{\displaystyle M_{0}\,\!}" /></span> <a href="/wiki/Anomalie_moyenne" title="Anomalie moyenne">Anomalie moyenne</a> à l'<a href="/wiki/%C3%89poque_(astronomie)" title="Époque (astronomie)">époque</a></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92658a4da1783d12cb53c1fffc24b29b4963f20f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.833ex; height:1.676ex;" alt="{\displaystyle \omega \,\!}" /></span> <a href="/wiki/Argument_du_p%C3%A9riastre" title="Argument du périastre">Argument du périastre</a></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99a94f96d2455b9d7faf3cec3eb02ab3c455aec1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.617ex; height:1.676ex;" alt="{\displaystyle a\,\!}" /></span> <a href="/wiki/Grand_axe" title="Grand axe">Demi-grand axe</a></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32308a9beabe5e8a2c683aa285cfd6e8abafb02c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.471ex; height:1.676ex;" alt="{\displaystyle e\,\!}" /></span> <a href="/wiki/Excentricit%C3%A9_orbitale" title="Excentricité orbitale">Excentricité</a></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea0042f70417500ed06b77bf2b87ef913cd3127b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.19ex; height:2.176ex;" alt="{\displaystyle i\,\!}" /></span> <a href="/wiki/Inclinaison_orbitale" title="Inclinaison orbitale">Inclinaison</a></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Omega \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω</mi> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93847015f621d7ad9940329db05ee4cfa7ee0689" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.065ex; height:2.176ex;" alt="{\displaystyle \Omega \,\!}" /></span> <a href="/wiki/Longitude_du_n%C5%93ud_ascendant" title="Longitude du nœud ascendant">Longitude du nœud ascendant</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="width:50px;">Autres</th> <td class="navbox-list navbox-even" style="text-align:left;;"><div class="liste-horizontale"> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1592db19e68e9789c5ed320d611f7c9a328341cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.163ex; height:2.176ex;" alt="{\displaystyle E\,\!}" /></span> <a href="/wiki/Anomalie_excentrique" title="Anomalie excentrique">Anomalie excentrique</a></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nu \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/817715b4ce1e4f00fa003b902c5d71ad172df22e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.619ex; height:1.676ex;" alt="{\displaystyle \nu \,\!}" /></span> <a href="/wiki/Anomalie_vraie" title="Anomalie vraie">Anomalie vraie</a></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb1dfcc2fcd791aacf48286147257b507b009e78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.385ex; height:2.176ex;" alt="{\displaystyle b\,\!}" /></span> <a href="/wiki/Petit_axe" title="Petit axe">Demi-petit axe</a></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϵ</mi> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0908a81825c617639f3401ee1f29c4aae45b5c78" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.331ex; height:1.676ex;" alt="{\displaystyle \epsilon \,\!}" /></span> <a href="/wiki/Excentricit%C3%A9_(math%C3%A9matiques)" title="Excentricité (mathématiques)">Excentricité</a></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09a0c8422640181668bbefa6f5d5481dbc1f03df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.97ex; height:2.176ex;" alt="{\displaystyle L\,\!}" /></span> <a href="/wiki/Longitude_moyenne" title="Longitude moyenne">Longitude moyenne</a></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b29435a849761c988f6c160c9e8bd9dda302c319" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.08ex; height:2.176ex;" alt="{\displaystyle l\,\!}" /></span> <a href="/wiki/Longitude_vraie" title="Longitude vraie">Longitude vraie</a></li> <li><a href="/wiki/Param%C3%A8tres_orbitaux_%C3%A0_deux_lignes" title="Paramètres orbitaux à deux lignes">Paramètres orbitaux à deux lignes</a></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e6be5af8259cedf1aac5ae3f6a5fad65ec2ef87" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:2.023ex; height:2.176ex;" alt="{\displaystyle T\,\!}" /></span> <a href="/wiki/P%C3%A9riode_de_r%C3%A9volution" title="Période de révolution">Période orbitale</a></li></ul> </div></td> </tr> </tbody></table></td> </tr> <tr> <th class="navbox-group" style=""><a href="/wiki/Man%C5%93uvre_orbitale" title="Manœuvre orbitale">Manœuvres</a></th> <td class="navbox-list" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/A%C3%A9rofreinage" title="Aérofreinage">Aérofreinage</a></li> <li><a href="/wiki/Assistance_gravitationnelle" title="Assistance gravitationnelle">Assistance gravitationnelle</a></li> <li><a href="/wiki/Capture_balistique" title="Capture balistique">Capture balistique</a></li> <li><a href="/wiki/Bilan_des_modifications_du_vecteur_vitesse" title="Bilan des modifications du vecteur vitesse">Bilan des modifications du vecteur vitesse</a></li> <li><a href="/wiki/Correction_d%27inclinaison" title="Correction d'inclinaison">Correction d'inclinaison</a></li> <li><a href="/wiki/Correction_du_phasage" title="Correction du phasage">Correction du phasage</a></li> <li><a href="/wiki/Effet_Oberth" title="Effet Oberth">Effet Oberth</a></li> <li><a href="/wiki/%C3%89vitement_de_collision" title="Évitement de collision">Évitement de collision</a></li> <li><a href="/wiki/Orbite_de_transfert_g%C3%A9ostationnaire" title="Orbite de transfert géostationnaire">Orbite de transfert géostationnaire</a></li> <li><a href="/wiki/Rendez-vous_spatial" title="Rendez-vous spatial">Rendez-vous</a></li> <li><a href="/wiki/Rotation_gravitationnelle" title="Rotation gravitationnelle">Rotation gravitationnelle</a> (Trajectoire à incidence nulle)</li> <li><a href="/wiki/Transfert_%C3%A0_faible_%C3%A9nergie" title="Transfert à faible énergie">Transfert à faible énergie</a></li> <li><a href="/wiki/Transfert_bi-elliptique" title="Transfert bi-elliptique">Transfert bi-elliptique</a></li> <li><a href="/wiki/Orbite_de_transfert#Orbite_de_transfert_de_Hohmann" title="Orbite de transfert">Transfert de Hohmann</a></li> <li><a href="/wiki/Transposition,_amarrage_et_extraction" title="Transposition, amarrage et extraction">Transposition, amarrage et extraction</a></li></ul> </div></td> </tr> <tr> <th class="navbox-group" style="">Mécanique<br />orbitale</th> <td class="navbox-list navbox-even" style=""><div class="liste-horizontale"> <ul><li><a href="/wiki/Apside" title="Apside">Apsides</a> <ul><li><a href="/wiki/P%C3%A9riapside" title="Périapside">Périapside</a></li> <li><a href="/wiki/Apoapside" title="Apoapside">Apoapside</a></li></ul></li> <li><a href="/wiki/%C3%89nergie_orbitale_sp%C3%A9cifique" title="Énergie orbitale spécifique">Énergie orbitale spécifique</a></li> <li><a href="/wiki/%C3%89poque_(astronomie)" title="Époque (astronomie)">Époque</a></li> <li><a href="/wiki/%C3%89ph%C3%A9m%C3%A9ride_(astronomie)" title="Éphéméride (astronomie)">Éphéméride</a></li> <li><a href="/wiki/%C3%89quation_de_Kepler" title="Équation de Kepler">Équation de Kepler</a></li> <li><a href="/wiki/%C3%89quation_d%27orbite" title="Équation d'orbite">Équation d'orbite</a></li> <li><a href="/wiki/Lois_de_Kepler" title="Lois de Kepler">Lois de Kepler</a></li> <li><a href="/wiki/Moment_cin%C3%A9tique_sp%C3%A9cifique" title="Moment cinétique spécifique">Moment cinétique spécifique</a></li> <li><a href="/wiki/Mouvement_k%C3%A9pl%C3%A9rien" title="Mouvement képlérien">Mouvement képlérien</a></li> <li><a href="/wiki/Mouvement_prograde_ou_r%C3%A9trograde" title="Mouvement prograde ou rétrograde">Rétrograde</a></li> <li><a href="/wiki/Perturbation_(astronomie)" title="Perturbation (astronomie)">Perturbation</a></li> <li><a href="/wiki/Point_de_Lagrange" title="Point de Lagrange">Point de Lagrange</a></li> <li><a href="/wiki/Probl%C3%A8me_%C3%A0_N_corps" title="Problème à N corps">Problème à N corps</a></li> <li><a href="/wiki/Probl%C3%A8me_%C3%A0_deux_corps" title="Problème à deux corps">Problème à deux corps</a></li> <li><a href="/wiki/R%C3%A9seau_de_transport_interplan%C3%A9taire" title="Réseau de transport interplanétaire">Réseau de transport interplanétaire</a></li> <li><a href="/wiki/Syst%C3%A8me_de_coordonn%C3%A9es_%C3%A9quatoriales" title="Système de coordonnées équatoriales">Système de coordonnées équatoriales</a></li> <li><a class="mw-selflink selflink">Système de coordonnées célestes</a></li> <li><a href="/wiki/Trace_au_sol" title="Trace au sol">Trace au sol</a></li> <li><a href="/wiki/Trou_de_serrure_gravitationnel" title="Trou de serrure gravitationnel">Trou de serrure gravitationnel</a></li> <li><a href="/wiki/Vecteur_d%27%C3%A9tat_orbital" title="Vecteur d'état orbital">Vecteur d'état orbital</a></li> <li><a href="/wiki/Vitesse_de_lib%C3%A9ration" title="Vitesse de libération">Vitesse de libération</a></li> <li><a href="/wiki/Vitesse_orbitale" title="Vitesse orbitale">Vitesse orbitale</a></li></ul> </div></td> </tr> <tr> <td class="navbox-banner" style="" colspan="2"><a href="/wiki/Liste_d%27orbites" title="Liste d'orbites">Liste d'orbites</a></td></tr></tbody></table> </div> <ul id="bandeau-portail" class="bandeau-portail"><li><span 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Système de coordonnées célestes — Wikipédia