Hệ tọa độ thiên văn – Wikipedia tiếng Việt

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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Đăng nhập</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Trang dành cho người dùng chưa đăng nhập <a href="/wiki/Tr%E1%BB%A3_gi%C3%BAp:Gi%E1%BB%9Bi_thi%E1%BB%87u" aria-label="Tìm hiểu thêm về sửa đổi"><span>tìm hiểu thêm</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:%C4%90%C3%B3ng_g%C3%B3p_c%E1%BB%A7a_t%C3%B4i" title="Danh sách các sửa đổi được thực hiện qua địa chỉ IP này [y]" accesskey="y"><span>Đóng góp</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Th%E1%BA%A3o_lu%E1%BA%ADn_t%C3%B4i" title="Thảo luận với địa chỉ IP này [n]" accesskey="n"><span>Thảo luận cho địa chỉ IP này</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Trang Web"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Nội dung" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Nội dung</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">chuyển sang thanh bên</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ẩn</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Đầu</div> </a> </li> <li id="toc-Các_hệ_tọa_độ_thiên_văn" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Các_hệ_tọa_độ_thiên_văn"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Các hệ tọa độ thiên văn</span> </div> </a> <ul id="toc-Các_hệ_tọa_độ_thiên_văn-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Chuyển_đổi_giữa_các_tọa_độ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Chuyển_đổi_giữa_các_tọa_độ"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Chuyển đổi giữa các tọa độ</span> </div> </a> <button aria-controls="toc-Chuyển_đổi_giữa_các_tọa_độ-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Hiện/ẩn mục Chuyển đổi giữa các tọa độ</span> </button> <ul id="toc-Chuyển_đổi_giữa_các_tọa_độ-sublist" class="vector-toc-list"> <li id="toc-Ký_hiệu" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ký_hiệu"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Ký hiệu</span> </div> </a> <ul id="toc-Ký_hiệu-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Góc_giờ_↔_xích_kinh" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Góc_giờ_↔_xích_kinh"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Góc giờ ↔ xích kinh</span> </div> </a> <ul id="toc-Góc_giờ_↔_xích_kinh-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Xích_đạo_↔_hoàng_đạo" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Xích_đạo_↔_hoàng_đạo"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Xích đạo ↔ hoàng đạo</span> </div> </a> <ul id="toc-Xích_đạo_↔_hoàng_đạo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Xích_đạo_↔_chân_trời" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Xích_đạo_↔_chân_trời"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Xích đạo ↔ chân trời</span> </div> </a> <ul id="toc-Xích_đạo_↔_chân_trời-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Xích_đạo_↔_thiên_hà" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Xích_đạo_↔_thiên_hà"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Xích đạo ↔ thiên hà</span> </div> </a> <ul id="toc-Xích_đạo_↔_thiên_hà-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Thiên_hà_↔_siêu_thiên_hà" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Thiên_hà_↔_siêu_thiên_hà"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Thiên hà ↔ siêu thiên hà</span> </div> </a> <ul id="toc-Thiên_hà_↔_siêu_thiên_hà-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lưu_ý_khi_chuyển_đổi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lưu_ý_khi_chuyển_đổi"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Lưu ý khi chuyển đổi</span> </div> </a> <ul id="toc-Lưu_ý_khi_chuyển_đổi-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Xem_thêm" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Xem_thêm"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Xem thêm</span> </div> </a> <ul id="toc-Xem_thêm-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Chú_thích" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Chú_thích"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Chú thích</span> </div> </a> <ul id="toc-Chú_thích-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tham_khảo" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tham_khảo"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Tham khảo</span> </div> </a> <button aria-controls="toc-Tham_khảo-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Hiện/ẩn mục Tham khảo</span> </button> <ul id="toc-Tham_khảo-sublist" class="vector-toc-list"> <li id="toc-Tham_khảo_sách" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tham_khảo_sách"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Tham khảo sách</span> </div> </a> <ul id="toc-Tham_khảo_sách-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Liên_kết_ngoài" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Liên_kết_ngoài"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Liên kết ngoài</span> </div> </a> <ul id="toc-Liên_kết_ngoài-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="Nội dung" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Mục lục" > <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="Đóng mở mục lục" > <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">Đóng mở mục lục</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">Hệ tọa độ thiên văn</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="Xem bài viết trong ngôn ngữ khác. Bài có sẵn trong 66 ngôn ngữ" > <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 ngôn ngữ</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 – Tiếng Hà Lan (Nam Phi)" lang="af" hreflang="af" data-title="Lugkoördinaatstelsel" data-language-autonym="Afrikaans" data-language-local-name="Tiếng Hà Lan (Nam Phi)" 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 – Tiếng Ả Rập" lang="ar" hreflang="ar" data-title="نظام إحداثيات فلكي" data-language-autonym="العربية" data-language-local-name="Tiếng Ả Rập" 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 – Tiếng Asturias" lang="ast" hreflang="ast" data-title="Coordenaes celestes" data-language-autonym="Asturianu" data-language-local-name="Tiếng Asturias" 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 – Tiếng Azerbaijan" lang="az" hreflang="az" data-title="Fəza koordinat sistemi" data-language-autonym="Azərbaycanca" data-language-local-name="Tiếng Azerbaijan" class="interlanguage-link-target"><span>Azərbaycanca</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 – Tiếng Indonesia" lang="id" hreflang="id" data-title="Tata koordinat langit" data-language-autonym="Bahasa Indonesia" data-language-local-name="Tiếng Indonesia" class="interlanguage-link-target"><span>Bahasa Indonesia</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 – Tiếng Mã Lai" lang="ms" hreflang="ms" data-title="Sistem koordinat cakerawala" data-language-autonym="Bahasa Melayu" data-language-local-name="Tiếng Mã Lai" class="interlanguage-link-target"><span>Bahasa Melayu</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 – Tiếng Belarus" lang="be" hreflang="be" data-title="Сістэма нябесных каардынат" data-language-autonym="Беларуская" data-language-local-name="Tiếng Belarus" 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-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Nebeski_koordinatni_sistem" title="Nebeski koordinatni sistem – Tiếng Bosnia" lang="bs" hreflang="bs" data-title="Nebeski koordinatni sistem" data-language-autonym="Bosanski" data-language-local-name="Tiếng Bosnia" class="interlanguage-link-target"><span>Bosanski</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 – Tiếng Bulgaria" lang="bg" hreflang="bg" data-title="Небесна координатна система" data-language-autonym="Български" data-language-local-name="Tiếng Bulgaria" class="interlanguage-link-target"><span>Български</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 – Tiếng Catalan" lang="ca" hreflang="ca" data-title="Coordenades astronòmiques" data-language-autonym="Català" data-language-local-name="Tiếng Catalan" class="interlanguage-link-target"><span>Català</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 – Tiếng Đan Mạch" lang="da" hreflang="da" data-title="Koordinatsystem for himmelrummet" data-language-autonym="Dansk" data-language-local-name="Tiếng Đan Mạch" 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 – Tiếng Đức" lang="de" hreflang="de" data-title="Astronomische Koordinatensysteme" data-language-autonym="Deutsch" data-language-local-name="Tiếng Đức" class="interlanguage-link-target"><span>Deutsch</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 – Tiếng Estonia" lang="et" hreflang="et" data-title="Taevakoordinaatide süsteem" data-language-autonym="Eesti" data-language-local-name="Tiếng Estonia" class="interlanguage-link-target"><span>Eesti</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 – Tiếng Hy Lạp" lang="el" hreflang="el" data-title="Ουράνιες συντεταγμένες" data-language-autonym="Ελληνικά" data-language-local-name="Tiếng Hy Lạp" 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 – Tiếng Anh" lang="en" hreflang="en" data-title="Astronomical coordinate systems" data-language-autonym="English" data-language-local-name="Tiếng Anh" 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 – Tiếng Tây Ban Nha" lang="es" hreflang="es" data-title="Coordenadas celestes" data-language-autonym="Español" data-language-local-name="Tiếng Tây Ban Nha" class="interlanguage-link-target"><span>Español</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 – Tiếng Basque" lang="eu" hreflang="eu" data-title="Koordenatu sistema astronomiko" data-language-autonym="Euskara" data-language-local-name="Tiếng 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 – Tiếng Ba Tư" lang="fa" hreflang="fa" data-title="دستگاه مختصات سماوی" data-language-autonym="فارسی" data-language-local-name="Tiếng Ba Tư" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Syst%C3%A8me_de_coordonn%C3%A9es_c%C3%A9lestes" title="Système de coordonnées célestes – Tiếng Pháp" lang="fr" hreflang="fr" data-title="Système de coordonnées célestes" data-language-autonym="Français" data-language-local-name="Tiếng Pháp" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Coordenadas_celestes" title="Coordenadas celestes – Tiếng Galician" lang="gl" hreflang="gl" data-title="Coordenadas celestes" data-language-autonym="Galego" data-language-local-name="Tiếng Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%B2%9C%EA%B5%AC%EC%A2%8C%ED%91%9C%EA%B3%84" title="천구좌표계 – Tiếng Hàn" lang="ko" hreflang="ko" data-title="천구좌표계" data-language-autonym="한국어" data-language-local-name="Tiếng Hàn" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%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 – Tiếng Armenia" lang="hy" hreflang="hy" data-title="Երկնային կոորդինատների համակարգեր" data-language-autonym="Հայերեն" data-language-local-name="Tiếng Armenia" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%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 – Tiếng Hindi" lang="hi" hreflang="hi" data-title="खगोलीय निर्देशांक पद्धति" data-language-autonym="हिन्दी" data-language-local-name="Tiếng 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 – Tiếng Croatia" lang="hr" hreflang="hr" data-title="Nebeski koordinatni sustavi" data-language-autonym="Hrvatski" data-language-local-name="Tiếng Croatia" class="interlanguage-link-target"><span>Hrvatski</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 – Tiếng Igbo" lang="ig" hreflang="ig" data-title="Usoro nhazi mbara igwe" data-language-autonym="Igbo" data-language-local-name="Tiếng 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 – Tiếng Iloko" lang="ilo" hreflang="ilo" data-title="Sistema ti nainlangitan a nagsasabtan" data-language-autonym="Ilokano" data-language-local-name="Tiếng Iloko" 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 – Tiếng Iceland" lang="is" hreflang="is" data-title="Himinhvolfshnitakerfi" data-language-autonym="Íslenska" data-language-local-name="Tiếng Iceland" 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 – Tiếng Italy" lang="it" hreflang="it" data-title="Coordinate celesti" data-language-autonym="Italiano" data-language-local-name="Tiếng Italy" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%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 – Tiếng Do Thái" lang="he" hreflang="he" data-title="מערכת קואורדינטות שמימית" data-language-autonym="עברית" data-language-local-name="Tiếng Do Thái" class="interlanguage-link-target"><span>עברית</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 – Tiếng Kazakh" lang="kk" hreflang="kk" data-title="Аспан координаттар жүйесі" data-language-autonym="Қазақша" data-language-local-name="Tiếng Kazakh" class="interlanguage-link-target"><span>Қазақша</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 – Tiếng Swahili" lang="sw" hreflang="sw" data-title="Majiranukta ya anga" data-language-autonym="Kiswahili" data-language-local-name="Tiếng Swahili" class="interlanguage-link-target"><span>Kiswahili</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 – Tiếng La-tinh" lang="la" hreflang="la" data-title="Systema coordinatarum caelestium" data-language-autonym="Latina" data-language-local-name="Tiếng La-tinh" 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 – Tiếng Luxembourg" lang="lb" hreflang="lb" data-title="Himmelskoordinaten" data-language-autonym="Lëtzebuergesch" data-language-local-name="Tiếng Luxembourg" class="interlanguage-link-target"><span>Lëtzebuergesch</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 – Tiếng Hungary" lang="hu" hreflang="hu" data-title="Csillagászati koordináta-rendszer" data-language-autonym="Magyar" data-language-local-name="Tiếng Hungary" class="interlanguage-link-target"><span>Magyar</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 – Tiếng Macedonia" lang="mk" hreflang="mk" data-title="Небесен координатен систем" data-language-autonym="Македонски" data-language-local-name="Tiếng Macedonia" class="interlanguage-link-target"><span>Македонски</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 – Tiếng Minangkabau" lang="min" hreflang="min" data-title="Sistem koordinat astronomi" data-language-autonym="Minangkabau" data-language-local-name="Tiếng Minangkabau" class="interlanguage-link-target"><span>Minangkabau</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 – Tiếng Mông Cổ" lang="mn" hreflang="mn" data-title="Одон орны координатын систем" data-language-autonym="Монгол" data-language-local-name="Tiếng Mông Cổ" class="interlanguage-link-target"><span>Монгол</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 – Tiếng Miến Điện" lang="my" hreflang="my" data-title="နက္ခတ္တဗေဒဆိုင်ရာ ကိုဩဒိနိတ်စနစ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Tiếng Miến Điện" 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 – Tiếng Hà Lan" lang="nl" hreflang="nl" data-title="Astronomisch coördinatenstelsel" data-language-autonym="Nederlands" data-language-local-name="Tiếng Hà Lan" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%A4%A9%E7%90%83%E5%BA%A7%E6%A8%99%E7%B3%BB" title="天球座標系 – Tiếng Nhật" lang="ja" hreflang="ja" data-title="天球座標系" data-language-autonym="日本語" data-language-local-name="Tiếng Nhật" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Himmelkoordinat" title="Himmelkoordinat – Tiếng Na Uy (Bokmål)" lang="nb" hreflang="nb" data-title="Himmelkoordinat" data-language-autonym="Norsk bokmål" data-language-local-name="Tiếng Na Uy (Bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Himmelkoordinatar" title="Himmelkoordinatar – Tiếng Na Uy (Nynorsk)" lang="nn" hreflang="nn" data-title="Himmelkoordinatar" data-language-autonym="Norsk nynorsk" data-language-local-name="Tiếng Na Uy (Nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</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 – Tiếng Occitan" lang="oc" hreflang="oc" data-title="Sistèma de coordenadas celèstas" data-language-autonym="Occitan" data-language-local-name="Tiếng Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Astronomik_koordinatalar" title="Astronomik koordinatalar – Tiếng Uzbek" lang="uz" hreflang="uz" data-title="Astronomik koordinatalar" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Tiếng Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Uk%C5%82ad_wsp%C3%B3%C5%82rz%C4%99dnych_astronomicznych" title="Układ współrzędnych astronomicznych – Tiếng Ba Lan" lang="pl" hreflang="pl" data-title="Układ współrzędnych astronomicznych" data-language-autonym="Polski" data-language-local-name="Tiếng Ba Lan" 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 – Tiếng Bồ Đào Nha" lang="pt" hreflang="pt" data-title="Sistema de coordenadas celestes" data-language-autonym="Português" data-language-local-name="Tiếng Bồ Đào Nha" 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 – Tiếng Romania" lang="ro" hreflang="ro" data-title="Coordonate astronomice" data-language-autonym="Română" data-language-local-name="Tiếng Romania" 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 – Tiếng Nga" lang="ru" hreflang="ru" data-title="Система небесных координат" data-language-autonym="Русский" data-language-local-name="Tiếng Nga" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/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 – Tiếng Slovak" lang="sk" hreflang="sk" data-title="Astronomické súradnicové systémy" data-language-autonym="Slovenčina" data-language-local-name="Tiếng Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Nebesni_koordinatni_sistem" title="Nebesni koordinatni sistem – Tiếng Slovenia" lang="sl" hreflang="sl" data-title="Nebesni koordinatni sistem" data-language-autonym="Slovenščina" data-language-local-name="Tiếng Slovenia" class="interlanguage-link-target"><span>Slovenščina</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 – Tiếng Kurd Miền Trung" lang="ckb" hreflang="ckb" data-title="سیستەمی پۆتانی ئاسمانی" data-language-autonym="کوردی" data-language-local-name="Tiếng Kurd Miền Trung" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr badge-Q17437798 badge-goodarticle mw-list-item" title="bài viết tốt"><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 – Tiếng Serbia" lang="sr" hreflang="sr" data-title="Небески координатни системи" data-language-autonym="Српски / srpski" data-language-local-name="Tiếng Serbia" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Nebeski_koordinatni_sistemi" title="Nebeski koordinatni sistemi – Tiếng Serbo-Croatia" lang="sh" hreflang="sh" data-title="Nebeski koordinatni sistemi" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Tiếng Serbo-Croatia" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/T%C3%A4htitieteellinen_vertausj%C3%A4rjestelm%C3%A4" title="Tähtitieteellinen vertausjärjestelmä – Tiếng Phần Lan" lang="fi" hreflang="fi" data-title="Tähtitieteellinen vertausjärjestelmä" data-language-autonym="Suomi" data-language-local-name="Tiếng Phần Lan" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Astronomiska_koordinatsystem" title="Astronomiska koordinatsystem – Tiếng Thụy Điển" lang="sv" hreflang="sv" data-title="Astronomiska koordinatsystem" data-language-autonym="Svenska" data-language-local-name="Tiếng Thụy Điển" class="interlanguage-link-target"><span>Svenska</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 – Tiếng Tagalog" lang="tl" hreflang="tl" data-title="Sistemang panlangit ng mga koordinado" data-language-autonym="Tagalog" data-language-local-name="Tiếng Tagalog" class="interlanguage-link-target"><span>Tagalog</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 – Tiếng Thái" lang="th" hreflang="th" data-title="ระบบพิกัดทรงกลมท้องฟ้า" data-language-autonym="ไทย" data-language-local-name="Tiếng Thái" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/G%C3%B6ky%C3%BCz%C3%BC_koordinat_sistemi" title="Gökyüzü koordinat sistemi – Tiếng Thổ Nhĩ Kỳ" lang="tr" hreflang="tr" data-title="Gökyüzü koordinat sistemi" data-language-autonym="Türkçe" data-language-local-name="Tiếng Thổ Nhĩ Kỳ" 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 – Tiếng Ukraina" lang="uk" hreflang="uk" data-title="Системи небесних координат" data-language-autonym="Українська" data-language-local-name="Tiếng Ukraina" 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 – Tiếng Urdu" lang="ur" hreflang="ur" data-title="سماوی متناسق نظام" data-language-autonym="اردو" data-language-local-name="Tiếng Urdu" class="interlanguage-link-target"><span>اردو</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 – Tiếng Waray" lang="war" hreflang="war" data-title="Sistema pan-langit hin mga koordinato" data-language-autonym="Winaray" data-language-local-name="Tiếng 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 – Tiếng Ngô" lang="wuu" hreflang="wuu" data-title="天球坐标系统" data-language-autonym="吴语" data-language-local-name="Tiếng Ngô" class="interlanguage-link-target"><span>吴语</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 – Tiếng Quảng Đông" lang="yue" hreflang="yue" data-title="天球坐標系統" data-language-autonym="粵語" data-language-local-name="Tiếng Quảng Đông" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%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 – Tiếng Trung" lang="zh" hreflang="zh" data-title="天球坐标系统" data-language-autonym="中文" data-language-local-name="Tiếng Trung" class="interlanguage-link-target"><span>中文</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="Sửa liên kết giữa ngôn ngữ" class="wbc-editpage">Sửa liên kết</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="Không gian tên"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n" title="Xem bài viết [c]" accesskey="c"><span>Bài viết</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Th%E1%BA%A3o_lu%E1%BA%ADn:H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n" rel="discussion" title="Thảo luận về trang này [t]" accesskey="t"><span>Thảo luận</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Thay đổi biến thể ngôn ngữ" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tiếng Việt</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Giao diện"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n"><span>Đọc</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit" title="Sửa đổi trang này [v]" accesskey="v"><span>Sửa đổi</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit" title="Sửa đổi mã nguồn của trang này [e]" accesskey="e"><span>Sửa mã nguồn</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=history" title="Các phiên bản cũ của trang này [h]" accesskey="h"><span>Xem lịch sử</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Công cụ trang"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Công cụ" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Công cụ</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Công cụ</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">chuyển sang thanh bên</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ẩn</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Thêm tùy chọn" > <div class="vector-menu-heading"> Tác vụ </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n"><span>Đọc</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit" title="Sửa đổi trang này [v]" accesskey="v"><span>Sửa đổi</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit" title="Sửa đổi mã nguồn của trang này [e]" accesskey="e"><span>Sửa mã nguồn</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=history"><span>Xem lịch sử</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Chung </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Li%C3%AAn_k%E1%BA%BFt_%C4%91%E1%BA%BFn_%C4%91%C3%A2y/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n" title="Các trang liên kết đến đây [j]" accesskey="j"><span>Các liên kết đến đây</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Thay_%C4%91%E1%BB%95i_li%C3%AAn_quan/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n" rel="nofollow" title="Thay đổi gần đây của các trang liên kết đến đây [k]" accesskey="k"><span>Thay đổi liên quan</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&oldid=70411833" title="Liên kết thường trực đến phiên bản này của trang"><span>Liên kết thường trực</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=info" title="Thêm chi tiết về trang này"><span>Thông tin trang</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:Tr%C3%ADch_d%E1%BA%ABn&page=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&id=70411833&wpFormIdentifier=titleform" title="Hướng dẫn cách trích dẫn trang này"><span>Trích dẫn trang này</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:UrlShortener&url=https%3A%2F%2Fvi.wikipedia.org%2Fwiki%2FH%25E1%25BB%2587_t%25E1%25BB%258Da_%25C4%2591%25E1%25BB%2599_thi%25C3%25AAn_v%25C4%2583n"><span>Lấy URL ngắn gọn</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:QrCode&url=https%3A%2F%2Fvi.wikipedia.org%2Fwiki%2FH%25E1%25BB%2587_t%25E1%25BB%258Da_%25C4%2591%25E1%25BB%2599_thi%25C3%25AAn_v%25C4%2583n"><span>Tải mã QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> In và xuất </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:S%C3%A1ch&bookcmd=book_creator&referer=H%E1%BB%87+t%E1%BB%8Da+%C4%91%E1%BB%99+thi%C3%AAn+v%C4%83n"><span>Tạo một quyển sách</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:DownloadAsPdf&page=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=show-download-screen"><span>Tải dưới dạng PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&printable=yes" title="Bản để in ra của trang [p]" accesskey="p"><span>Bản để in ra</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Tại dự án khác </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Celestial_coordinate_systems" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q86394" title="Liên kết đến khoản mục kết nối trong kho dữ liệu [g]" accesskey="g"><span>Khoản mục Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Công cụ trang"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Giao diện"> <div id="vector-appearance-pinned-container" 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<div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Bách khoa toàn thư mở Wikipedia</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="vi" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r72032465">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}.mw-parser-output .infobox--nowrap-label :not(.infobox-row--wrap-label)>.infobox-label{white-space:nowrap}</style><table class="infobox"><caption class="infobox-title">Định hướng tọa độ thiên văn</caption><tbody><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/T%E1%BA%ADp_tin:Ecliptic_equator_galactic_anim.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Ecliptic_equator_galactic_anim.gif/250px-Ecliptic_equator_galactic_anim.gif" decoding="async" width="250" height="254" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Ecliptic_equator_galactic_anim.gif/375px-Ecliptic_equator_galactic_anim.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Ecliptic_equator_galactic_anim.gif/500px-Ecliptic_equator_galactic_anim.gif 2x" data-file-width="1181" data-file-height="1200" /></a></span><div class="infobox-caption">Tọa độ <span style="background-color:yellow; color:black; border:1px solid #000000; text-align:center;">    </span><span class="nowrap"> </span><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_h%C3%A0" title="Hệ tọa độ thiên hà">thiên hà</a>, <span style="background-color:red; color:black; border:1px solid #000000; text-align:center;">    </span><span class="nowrap"> </span><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_ho%C3%A0ng_%C4%91%E1%BA%A1o" title="Hệ tọa độ hoàng đạo">hoàng đạo</a>, và <span style="background-color:blue; color:white; border:1px solid #000000; text-align:center;">    </span><span class="nowrap"> </span><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_x%C3%ADch_%C4%91%E1%BA%A1o" title="Hệ tọa độ xích đạo">xích đạo</a> của một ngôi <a href="/wiki/Sao" title="Sao">sao</a>, được chiếu trên <a href="/wiki/Thi%C3%AAn_c%E1%BA%A7u" title="Thiên cầu">thiên cầu</a>. Hệ tọa độ hoàng đạo và xích đạo đều lấy hướng cơ bản là hướng tới <span style="background-color:magenta; color:black; border:1px solid #000000; text-align:center;">    </span><span class="nowrap"> </span><a href="/wiki/Xu%C3%A2n_ph%C3%A2n_(t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n)" title="Xuân phân (tọa độ thiên văn)">điểm xuân phân</a> (vernal equinox), còn tọa độ thiên hà được <a href="/wiki/H%E1%BB%87_quy_chi%E1%BA%BFu" title="Hệ quy chiếu">tham chiếu</a> tới <span style="background-color:yellow; color:black; border:1px solid #000000; text-align:center;">    </span><span class="nowrap"> </span>trung tâm của <a href="/wiki/Ng%C3%A2n_H%C3%A0" title="Ngân Hà">Ngân Hà</a>. Gốc tọa độ của các hệ tọa độ trên ("tâm của <a href="/wiki/Thi%C3%AAn_c%E1%BA%A7u" title="Thiên cầu">thiên cầu</a>") có thể đặt tại tâm Trái Đất hoặc tại nơi người quan sát.</div></td></tr></tbody></table> <p>Trong <a href="/wiki/Thi%C3%AAn_v%C4%83n_h%E1%BB%8Dc" title="Thiên văn học">thiên văn học</a>, <b>hệ tọa độ thiên văn</b> là một <a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_c%E1%BA%A7u" title="Hệ tọa độ cầu">hệ tọa độ mặt cầu</a> dùng để xác định vị trí biểu kiến của <a href="/wiki/Thi%C3%AAn_th%E1%BB%83" title="Thiên thể">thiên thể</a> trên <a href="/wiki/Thi%C3%AAn_c%E1%BA%A7u" title="Thiên cầu">thiên cầu</a>. </p><p>Trong <a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_Descartes" title="Hệ tọa độ Descartes">tọa độ Descartes</a>, một vật thể có ba tọa độ trong không gian ba chiều được xác định trên ba trục <i>x</i>, <i>y</i> và <i>z</i>. Ngược lại hệ tọa độ thiên văn của thiên thể không xác định khoảng cách đến người quan sát mà chỉ xác định các hướng quan sát của nó trên thiên cầu. </p><p>Có nhiều loại hệ tọa độ thiên văn khác nhau, được phân biệt và được đặt tên theo <a href="/wiki/M%E1%BA%B7t_ph%E1%BA%B3ng_tham_chi%E1%BA%BFu" title="Mặt phẳng tham chiếu">mặt phẳng tham chiếu</a> (mặt phẳng cơ bản), hay các trục chính của hệ tọa độ. Mặt phẳng tham chiếu cắt thiên cầu tại <a href="/wiki/%C4%90%C6%B0%E1%BB%9Dng_tr%C3%B2n_l%E1%BB%9Bn" title="Đường tròn lớn">đường tròn lớn</a> nhất, chia thiên cầu thành hai nửa bằng nhau. </p><p>Định nghĩa các trục và mặt phẳng trong các hệ tọa độ có thể dùng hệ thống <a href="/w/index.php?title=B1950&action=edit&redlink=1" class="new" title="B1950 (trang không tồn tại)">B1950</a> hay hệ thống <a href="/wiki/K%E1%BB%B7_nguy%C3%AAn_(thi%C3%AAn_v%C4%83n_h%E1%BB%8Dc)#Năm_Julius_và_J2000" title="Kỷ nguyên (thiên văn học)">J2000</a> hiện đại hơn. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Các_hệ_tọa_độ_thiên_văn"><span id="C.C3.A1c_h.E1.BB.87_t.E1.BB.8Da_.C4.91.E1.BB.99_thi.C3.AAn_v.C4.83n"></span>Các hệ tọa độ thiên văn</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=1" title="Sửa đổi phần “Các hệ tọa độ thiên văn”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=1" title="Sửa mã nguồn tại đề mục: Các hệ tọa độ thiên văn"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Có nhiều hệ tọa độ được dùng trong thiên văn, trong đó các hệ tọa độ phổ biến là: </p> <ul><li><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_ch%C3%A2n_tr%E1%BB%9Di" title="Hệ tọa độ chân trời">Hệ tọa độ chân trời</a> có mặt phẳng tham chiếu là mặt phẳng <a href="/wiki/Ch%C3%A2n_tr%E1%BB%9Di" title="Chân trời">chân trời</a>, tại vị trí người quan sát.</li> <li><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_x%C3%ADch_%C4%91%E1%BA%A1o" title="Hệ tọa độ xích đạo">Hệ tọa độ xích đạo</a> với mặt phẳng tham chiếu là mặt phẳng <a href="/wiki/X%C3%ADch_%C4%91%E1%BA%A1o_thi%C3%AAn_c%E1%BA%A7u" title="Xích đạo thiên cầu">xích đạo</a> của <a href="/wiki/Tr%C3%A1i_%C4%90%E1%BA%A5t" title="Trái Đất">Trái Đất</a>. Đây là hệ tọa độ thiên văn được sử dụng phổ biến nhất.</li> <li><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_ho%C3%A0ng_%C4%91%E1%BA%A1o" title="Hệ tọa độ hoàng đạo">Hệ tọa độ hoàng đạo</a> dùng mặt phẳng <a href="/wiki/Ho%C3%A0ng_%C4%91%E1%BA%A1o" title="Hoàng đạo">hoàng đạo</a> làm mặt phẳng tham chiếu.</li> <li><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_h%C3%A0" title="Hệ tọa độ thiên hà">Hệ tọa độ thiên hà</a> dùng mặt phẳng <a href="/wiki/Ng%C3%A2n_H%C3%A0" title="Ngân Hà">Ngân Hà</a> làm mặt phẳng tham chiếu.</li> <li><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_si%C3%AAu_thi%C3%AAn_h%C3%A0" title="Hệ tọa độ siêu thiên hà">Hệ tọa độ siêu thiên hà</a> có mặt phẳng tham chiếu chứa số lượng <a href="/wiki/Nh%C3%B3m_%C4%90%E1%BB%8Ba_ph%C6%B0%C6%A1ng" title="Nhóm Địa phương">thiên hà địa phương</a> nhiều hơn trung bình khi quan sát từ Trái Đất.</li></ul> <table class="wikitable" style="text-align:center;"> <tbody><tr> <th rowspan="2">Hệ tọa độ<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </th> <th rowspan="2">Tâm của thiên cầu (điểm gốc tọa độ) </th> <th rowspan="2">Mặt phẳng cơ bản <p>(vĩ độ 0°) </p> </th> <th rowspan="2">Điểm cực <p>(vĩ độ ±90°) </p> </th> <th colspan="2">Tọa độ </th> <th rowspan="2">Hướng cơ bản <p>(kinh độ 0°) </p> </th></tr> <tr> <th>Vĩ độ </th> <th>Kinh độ </th></tr> <tr> <td><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_ch%C3%A2n_tr%E1%BB%9Di" title="Hệ tọa độ chân trời">Chân trời</a> (còn gọi là hệ <abbr title="altitude (độ cao)">alt</abbr>-<abbr title="azimuth (phương vị)">az</abbr> hay <abbr title="elevation (độ cao)">el</abbr>-az) </td> <td>Người quan sát </td> <td><a href="/wiki/Ch%C3%A2n_tr%E1%BB%9Di" title="Chân trời">Chân trời</a> </td> <td><a href="/wiki/Thi%C3%AAn_%C4%91%E1%BB%89nh" title="Thiên đỉnh">Thiên đỉnh</a>, <a href="/wiki/Thi%C3%AAn_%C4%91%E1%BB%83" title="Thiên để">thiên để</a> </td> <td>Góc cao hay độ cao (<span class="texhtml"><i>a</i></span>) </td> <td><a href="/wiki/G%C3%B3c_ph%C6%B0%C6%A1ng_v%E1%BB%8B" title="Góc phương vị">Góc phương vị</a> (<span class="texhtml"><i>A</i></span>) </td> <td>Điểm hướng <a href="/wiki/H%C6%B0%E1%BB%9Bng_Nam" class="mw-redirect" title="Hướng Nam">nam</a> hoặc <a href="/wiki/H%C6%B0%E1%BB%9Bng_B%E1%BA%AFc" class="mw-redirect" title="Hướng Bắc">bắc</a> trên chân trời </td></tr> <tr> <td><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_x%C3%ADch_%C4%91%E1%BA%A1o" title="Hệ tọa độ xích đạo">Xích đạo</a> </td> <td rowspan="2">Tâm của <a href="/wiki/Tr%C3%A1i_%C4%90%E1%BA%A5t" title="Trái Đất">Trái Đất</a><span class="nowrap"> </span>(địa<span class="nowrap"> </span>tâm) hoặc <a href="/wiki/M%E1%BA%B7t_Tr%E1%BB%9Di" title="Mặt Trời">Mặt Trời</a><span class="nowrap"> </span>(nhật<span class="nowrap"> </span>tâm) </td> <td><a href="/wiki/X%C3%ADch_%C4%91%E1%BA%A1o_thi%C3%AAn_c%E1%BA%A7u" title="Xích đạo thiên cầu">Xích đạo thiên cầu</a> </td> <td><a href="/wiki/Thi%C3%AAn_c%E1%BB%B1c" title="Thiên cực">Thiên cực</a> </td> <td><a href="/wiki/X%C3%ADch_v%C4%A9" title="Xích vĩ">Xích vĩ</a> (<span class="texhtml"><i>δ</i></span>) </td> <td><a href="/wiki/X%C3%ADch_kinh" title="Xích kinh">Xích kinh</a> (<span class="texhtml"><i>α</i></span>) <p>hay <a href="/wiki/G%C3%B3c_gi%E1%BB%9D" title="Góc giờ">góc giờ</a> (<span class="texhtml"><i>h</i></span>) </p> </td> <td rowspan="2"><a href="/wiki/Xu%C3%A2n_ph%C3%A2n_(t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n)" title="Xuân phân (tọa độ thiên văn)">Điểm xuân phân</a> </td></tr> <tr> <td><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_ho%C3%A0ng_%C4%91%E1%BA%A1o" title="Hệ tọa độ hoàng đạo">Hoàng đạo</a> </td> <td><a href="/wiki/Ho%C3%A0ng_%C4%91%E1%BA%A1o" title="Hoàng đạo">Hoàng đạo</a> </td> <td><a href="/wiki/%C4%90i%E1%BB%83m_c%E1%BB%B1c_qu%E1%BB%B9_%C4%91%E1%BA%A1o#Hoàng_cực" title="Điểm cực quỹ đạo">Hoàng cực</a> </td> <td><a href="/wiki/Ho%C3%A0ng_v%C4%A9" title="Hoàng vĩ">Hoàng vĩ</a> (<span class="texhtml"><i>β</i></span>) </td> <td><a href="/wiki/Ho%C3%A0ng_kinh" title="Hoàng kinh">Hoàng kinh</a> (<span class="texhtml"><i>λ</i></span>) </td></tr> <tr> <td><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_h%C3%A0" title="Hệ tọa độ thiên hà">Thiên hà</a> </td> <td>Tâm của <a href="/wiki/M%E1%BA%B7t_Tr%E1%BB%9Di" title="Mặt Trời">Mặt Trời</a> </td> <td><a href="/wiki/M%E1%BA%B7t_ph%E1%BA%B3ng_thi%C3%AAn_h%C3%A0" title="Mặt phẳng thiên hà">Mặt phẳng Ngân Hà</a> </td> <td><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_h%C3%A0" title="Hệ tọa độ thiên hà">Cực thiên hà</a> </td> <td>Vĩ độ thiên hà (<span class="texhtml"><i>b</i></span>) </td> <td>Kinh độ thiên hà (<span class="texhtml"><i>l</i></span>) </td> <td><a href="/wiki/Trung_t%C3%A2m_Ng%C3%A2n_H%C3%A0" title="Trung tâm Ngân Hà">Trung tâm Ngân Hà</a> </td></tr> <tr> <td><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_si%C3%AAu_thi%C3%AAn_h%C3%A0" title="Hệ tọa độ siêu thiên hà">Siêu thiên hà</a> </td> <td> </td> <td><a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_si%C3%AAu_thi%C3%AAn_h%C3%A0" title="Hệ tọa độ siêu thiên hà">Mặt phẳng siêu thiên hà</a> </td> <td>Cực siêu thiên hà </td> <td>Vĩ độ siêu thiên hà (<span class="texhtml"><i>SGB</i></span>) </td> <td>Kinh độ siêu thiên hà (<span class="texhtml"><i>SGL</i></span>) </td> <td>Giao điểm của mặt phẳng siêu thiên hà và mặt phẳng Ngân Hà </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Chuyển_đổi_giữa_các_tọa_độ"><span id="Chuy.E1.BB.83n_.C4.91.E1.BB.95i_gi.E1.BB.AFa_c.C3.A1c_t.E1.BB.8Da_.C4.91.E1.BB.99"></span>Chuyển đổi giữa các tọa độ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=2" title="Sửa đổi phần “Chuyển đổi giữa các tọa độ”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=2" title="Sửa mã nguồn tại đề mục: Chuyển đổi giữa các tọa độ"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r72019635">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Xem thêm: <a href="/wiki/Tham_s%E1%BB%91_qu%E1%BB%B9_%C4%91%E1%BA%A1o" title="Tham số quỹ đạo">Tham số quỹ đạo</a>, <a href="/wiki/G%C3%B3c_Euler" title="Góc Euler">Góc Euler</a>, và <a href="/w/index.php?title=Ma_tr%E1%BA%ADn_quay&action=edit&redlink=1" class="new" title="Ma trận quay (trang không tồn tại)">Ma trận quay</a></div><p>Dưới đây đưa ra các phép chuyển đổi giữa các hệ tọa độ thiên văn.<sup id="cite_ref-Meeus_2-0" class="reference"><a href="#cite_note-Meeus-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Xem <a class="mw-selflink-fragment" href="#Lưu_ý_khi_chuyển_đổi">lưu ý</a> trước khi sử dụng các phương trình. </p><div class="mw-heading mw-heading3"><h3 id="Ký_hiệu"><span id="K.C3.BD_hi.E1.BB.87u"></span>Ký hiệu</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=3" title="Sửa đổi phần “Ký hiệu”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=3" title="Sửa mã nguồn tại đề mục: Ký hiệu"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Hệ tọa độ chân trời <ul><li><span class="texhtml mvar" style="font-style:italic;">A</span>, <a href="/wiki/G%C3%B3c_ph%C6%B0%C6%A1ng_v%E1%BB%8B" title="Góc phương vị">góc phương vị</a></li> <li><span class="texhtml mvar" style="font-style:italic;">a</span>, <a href="/wiki/G%C3%B3c_cao" class="mw-redirect" title="Góc cao">góc cao</a></li></ul></li> <li>Hệ tọa độ xích đạo <ul><li><span class="texhtml mvar" style="font-style:italic;">α</span>, <a href="/wiki/X%C3%ADch_kinh" title="Xích kinh">xích kinh</a></li> <li><span class="texhtml mvar" style="font-style:italic;">δ</span>, <a href="/wiki/X%C3%ADch_v%C4%A9" title="Xích vĩ">xích vĩ</a></li> <li><span class="texhtml mvar" style="font-style:italic;">h</span>, <a href="/wiki/G%C3%B3c_gi%E1%BB%9D" title="Góc giờ">góc giờ</a></li></ul></li> <li>Hệ tọa độ hoàng đạo <ul><li><span class="texhtml mvar" style="font-style:italic;">λ</span>, <a href="/wiki/Ho%C3%A0ng_kinh" title="Hoàng kinh">hoàng kinh</a></li> <li><span class="texhtml mvar" style="font-style:italic;">β</span>, <a href="/wiki/Ho%C3%A0ng_v%C4%A9" title="Hoàng vĩ">hoàng vĩ</a></li></ul></li> <li>Hệ tọa độ thiên hà <ul><li><span class="texhtml mvar" style="font-style:italic;">l</span>, <a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_h%C3%A0" title="Hệ tọa độ thiên hà">kinh độ thiên hà</a></li> <li><span class="texhtml mvar" style="font-style:italic;">b</span>, <a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_h%C3%A0" title="Hệ tọa độ thiên hà">vĩ độ thiên hà</a></li></ul></li> <li>Các ký hiệu khác <ul><li><span class="texhtml"><i>λ</i><sub>o</sub></span>, <a href="/wiki/Kinh_%C4%91%E1%BB%99" title="Kinh độ">kinh độ của người quan sát</a></li> <li><span class="texhtml"><i>ϕ</i><sub>o</sub></span>, <a href="/wiki/V%C4%A9_%C4%91%E1%BB%99" title="Vĩ độ">vĩ độ của người quan sát</a></li> <li><span class="texhtml mvar" style="font-style:italic;">ε</span>, <a href="/wiki/%C4%90%E1%BB%99_nghi%C3%AAng_tr%E1%BB%A5c_quay" title="Độ nghiêng trục quay">độ nghiêng trục quay</a> Trái Đất (khoảng 23.4°)</li> <li><span class="texhtml"><i>θ</i><sub>L</sub></span>, <a href="/wiki/Th%E1%BB%9Di_gian_thi%C3%AAn_v%C4%83n" title="Thời gian thiên văn">thời gian sao địa phương</a></li> <li><span class="texhtml"><i>θ</i><sub>G</sub></span>, <a href="/wiki/Th%E1%BB%9Di_gian_thi%C3%AAn_v%C4%83n" title="Thời gian thiên văn">thời gian sao Greenwich</a></li></ul></li></ul> <div class="mw-heading mw-heading3"><h3 id="Góc_giờ_↔_xích_kinh"><span id="G.C3.B3c_gi.E1.BB.9D_.E2.86.94_x.C3.ADch_kinh"></span>Góc giờ ↔ xích kinh</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=4" title="Sửa đổi phần “Góc giờ ↔ xích kinh”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=4" title="Sửa mã nguồn tại đề mục: Góc giờ ↔ xích kinh"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><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{aligned}h&=\theta _{\text{L}}-\alpha &&{\mbox{or}}&h&=\theta _{\text{G}}+\lambda _{\text{o}}-\alpha \\\alpha &=\theta _{\text{L}}-h&&{\mbox{or}}&\alpha &=\theta _{\text{G}}+\lambda _{\text{o}}-h\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>h</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> </msub> <mo>−</mo> <mi>α</mi> </mtd> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>or</mtext> </mstyle> </mrow> </mtd> <mtd> <mi>h</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>−</mo> <mi>α</mi> </mtd> </mtr> <mtr> <mtd> <mi>α</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> </msub> <mo>−</mo> <mi>h</mi> </mtd> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>or</mtext> </mstyle> </mrow> </mtd> <mtd> <mi>α</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>−</mo> <mi>h</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}h&=\theta _{\text{L}}-\alpha &&{\mbox{or}}&h&=\theta _{\text{G}}+\lambda _{\text{o}}-\alpha \\\alpha &=\theta _{\text{L}}-h&&{\mbox{or}}&\alpha &=\theta _{\text{G}}+\lambda _{\text{o}}-h\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3dabf3cb4acc8de2573ce32fb10ceaa423719cef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:40.157ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}h&=\theta _{\text{L}}-\alpha &&{\mbox{or}}&h&=\theta _{\text{G}}+\lambda _{\text{o}}-\alpha \\\alpha &=\theta _{\text{L}}-h&&{\mbox{or}}&\alpha &=\theta _{\text{G}}+\lambda _{\text{o}}-h\end{aligned}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Xích_đạo_↔_hoàng_đạo"><span id="X.C3.ADch_.C4.91.E1.BA.A1o_.E2.86.94_ho.C3.A0ng_.C4.91.E1.BA.A1o"></span>Xích đạo ↔ hoàng đạo</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=5" title="Sửa đổi phần “Xích đạo ↔ hoàng đạo”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=5" title="Sửa mã nguồn tại đề mục: Xích đạo ↔ hoàng đạo"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Các phương trình cổ điển sau, được suy ra từ tính toán <a href="/w/index.php?title=L%C6%B0%E1%BB%A3ng_gi%C3%A1c_c%E1%BA%A7u&action=edit&redlink=1" class="new" title="Lượng giác cầu (trang không tồn tại)">lượng giác cầu</a>, đối với các phương trình cho tọa độ kinh độ được viết bên phải dấu ngoặc nhọn; chỉ cần chia phương trình thứ nhất cho phương trình thứ hai để có được phương trình với hàm tan thuận tiện hơn bên trái (phép chia này là không rõ ràng vì tan có chu kỳ 180° (<span class="texhtml">π</span>) trong khi cos và sin có chu kỳ 360° (2<span class="texhtml">π</span>)).<sup id="cite_ref-ExplSupp_3-0" class="reference"><a href="#cite_note-ExplSupp-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Công thức tương đương với ma trận quay được cho bên dưới mỗi trường hợp.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><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{aligned}\tan \left(\lambda \right)&={\sin \left(\alpha \right)\cos \left(\varepsilon \right)+\tan \left(\delta \right)\sin \left(\varepsilon \right) \over \cos \left(\alpha \right)};\qquad {\begin{cases}\cos \left(\beta \right)\sin \left(\lambda \right)=\cos \left(\delta \right)\sin \left(\alpha \right)\cos \left(\varepsilon \right)+\sin \left(\delta \right)\sin \left(\varepsilon \right);\\\cos \left(\beta \right)\cos \left(\lambda \right)=\cos \left(\delta \right)\cos \left(\alpha \right).\end{cases}}\\\sin \left(\beta \right)&=\sin \left(\delta \right)\cos \left(\varepsilon \right)-\cos \left(\delta \right)\sin \left(\varepsilon \right)\sin \left(\alpha \right)\\[3pt]{\begin{bmatrix}\cos \left(\beta \right)\cos \left(\lambda \right)\\\cos \left(\beta \right)\sin \left(\lambda \right)\\\sin \left(\beta \right)\end{bmatrix}}&={\begin{bmatrix}1&0&0\\0&\cos \left(\varepsilon \right)&\sin \left(\varepsilon \right)\\0&-\sin \left(\varepsilon \right)&\cos \left(\varepsilon \right)\end{bmatrix}}{\begin{bmatrix}\cos \left(\delta \right)\cos \left(\alpha \right)\\\cos \left(\delta \right)\sin \left(\alpha \right)\\\sin \left(\delta \right)\end{bmatrix}}\\[6pt]\tan \left(\alpha \right)&={\sin \left(\lambda \right)\cos \left(\varepsilon \right)-\tan \left(\beta \right)\sin \left(\varepsilon \right) \over \cos \left(\lambda \right)};\qquad {\begin{cases}\cos \left(\delta \right)\sin \left(\alpha \right)=\cos \left(\beta \right)\sin \left(\lambda \right)\cos \left(\varepsilon \right)-\sin \left(\beta \right)\sin \left(\varepsilon \right);\\\cos \left(\delta \right)\cos \left(\alpha \right)=\cos \left(\beta \right)\cos \left(\lambda \right).\end{cases}}\\[3pt]\sin \left(\delta \right)&=\sin \left(\beta \right)\cos \left(\varepsilon \right)+\cos \left(\beta \right)\sin \left(\varepsilon \right)\sin \left(\lambda \right).\\[6pt]{\begin{bmatrix}\cos \left(\delta \right)\cos \left(\alpha \right)\\\cos \left(\delta \right)\sin \left(\alpha \right)\\\sin \left(\delta \right)\end{bmatrix}}&={\begin{bmatrix}1&0&0\\0&\cos \left(\varepsilon \right)&-\sin \left(\varepsilon \right)\\0&\sin \left(\varepsilon \right)&\cos \left(\varepsilon \right)\end{bmatrix}}{\begin{bmatrix}\cos \left(\beta \right)\cos \left(\lambda \right)\\\cos \left(\beta \right)\sin \left(\lambda \right)\\\sin \left(\beta \right)\end{bmatrix}}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt 0.6em 0.9em 0.6em 0.9em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>tan</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>tan</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> <mo>;</mo> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> <mo>;</mo> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>tan</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> <mo>−</mo> <mi>tan</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> <mo>;</mo> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> <mo>;</mo> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>β</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\tan \left(\lambda \right)&={\sin \left(\alpha \right)\cos \left(\varepsilon \right)+\tan \left(\delta \right)\sin \left(\varepsilon \right) \over \cos \left(\alpha \right)};\qquad {\begin{cases}\cos \left(\beta \right)\sin \left(\lambda \right)=\cos \left(\delta \right)\sin \left(\alpha \right)\cos \left(\varepsilon \right)+\sin \left(\delta \right)\sin \left(\varepsilon \right);\\\cos \left(\beta \right)\cos \left(\lambda \right)=\cos \left(\delta \right)\cos \left(\alpha \right).\end{cases}}\\\sin \left(\beta \right)&=\sin \left(\delta \right)\cos \left(\varepsilon \right)-\cos \left(\delta \right)\sin \left(\varepsilon \right)\sin \left(\alpha \right)\\[3pt]{\begin{bmatrix}\cos \left(\beta \right)\cos \left(\lambda \right)\\\cos \left(\beta \right)\sin \left(\lambda \right)\\\sin \left(\beta \right)\end{bmatrix}}&={\begin{bmatrix}1&0&0\\0&\cos \left(\varepsilon \right)&\sin \left(\varepsilon \right)\\0&-\sin \left(\varepsilon \right)&\cos \left(\varepsilon \right)\end{bmatrix}}{\begin{bmatrix}\cos \left(\delta \right)\cos \left(\alpha \right)\\\cos \left(\delta \right)\sin \left(\alpha \right)\\\sin \left(\delta \right)\end{bmatrix}}\\[6pt]\tan \left(\alpha \right)&={\sin \left(\lambda \right)\cos \left(\varepsilon \right)-\tan \left(\beta \right)\sin \left(\varepsilon \right) \over \cos \left(\lambda \right)};\qquad {\begin{cases}\cos \left(\delta \right)\sin \left(\alpha \right)=\cos \left(\beta \right)\sin \left(\lambda \right)\cos \left(\varepsilon \right)-\sin \left(\beta \right)\sin \left(\varepsilon \right);\\\cos \left(\delta \right)\cos \left(\alpha \right)=\cos \left(\beta \right)\cos \left(\lambda \right).\end{cases}}\\[3pt]\sin \left(\delta \right)&=\sin \left(\beta \right)\cos \left(\varepsilon \right)+\cos \left(\beta \right)\sin \left(\varepsilon \right)\sin \left(\lambda \right).\\[6pt]{\begin{bmatrix}\cos \left(\delta \right)\cos \left(\alpha \right)\\\cos \left(\delta \right)\sin \left(\alpha \right)\\\sin \left(\delta \right)\end{bmatrix}}&={\begin{bmatrix}1&0&0\\0&\cos \left(\varepsilon \right)&-\sin \left(\varepsilon \right)\\0&\sin \left(\varepsilon \right)&\cos \left(\varepsilon \right)\end{bmatrix}}{\begin{bmatrix}\cos \left(\beta \right)\cos \left(\lambda \right)\\\cos \left(\beta \right)\sin \left(\lambda \right)\\\sin \left(\beta \right)\end{bmatrix}}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32e64f7f6ef1f8a0eda9cf775fa41f0023c54d4d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -21.005ex; width:107.792ex; height:43.176ex;" alt="{\displaystyle {\begin{aligned}\tan \left(\lambda \right)&={\sin \left(\alpha \right)\cos \left(\varepsilon \right)+\tan \left(\delta \right)\sin \left(\varepsilon \right) \over \cos \left(\alpha \right)};\qquad {\begin{cases}\cos \left(\beta \right)\sin \left(\lambda \right)=\cos \left(\delta \right)\sin \left(\alpha \right)\cos \left(\varepsilon \right)+\sin \left(\delta \right)\sin \left(\varepsilon \right);\\\cos \left(\beta \right)\cos \left(\lambda \right)=\cos \left(\delta \right)\cos \left(\alpha \right).\end{cases}}\\\sin \left(\beta \right)&=\sin \left(\delta \right)\cos \left(\varepsilon \right)-\cos \left(\delta \right)\sin \left(\varepsilon \right)\sin \left(\alpha \right)\\[3pt]{\begin{bmatrix}\cos \left(\beta \right)\cos \left(\lambda \right)\\\cos \left(\beta \right)\sin \left(\lambda \right)\\\sin \left(\beta \right)\end{bmatrix}}&={\begin{bmatrix}1&0&0\\0&\cos \left(\varepsilon \right)&\sin \left(\varepsilon \right)\\0&-\sin \left(\varepsilon \right)&\cos \left(\varepsilon \right)\end{bmatrix}}{\begin{bmatrix}\cos \left(\delta \right)\cos \left(\alpha \right)\\\cos \left(\delta \right)\sin \left(\alpha \right)\\\sin \left(\delta \right)\end{bmatrix}}\\[6pt]\tan \left(\alpha \right)&={\sin \left(\lambda \right)\cos \left(\varepsilon \right)-\tan \left(\beta \right)\sin \left(\varepsilon \right) \over \cos \left(\lambda \right)};\qquad {\begin{cases}\cos \left(\delta \right)\sin \left(\alpha \right)=\cos \left(\beta \right)\sin \left(\lambda \right)\cos \left(\varepsilon \right)-\sin \left(\beta \right)\sin \left(\varepsilon \right);\\\cos \left(\delta \right)\cos \left(\alpha \right)=\cos \left(\beta \right)\cos \left(\lambda \right).\end{cases}}\\[3pt]\sin \left(\delta \right)&=\sin \left(\beta \right)\cos \left(\varepsilon \right)+\cos \left(\beta \right)\sin \left(\varepsilon \right)\sin \left(\lambda \right).\\[6pt]{\begin{bmatrix}\cos \left(\delta \right)\cos \left(\alpha \right)\\\cos \left(\delta \right)\sin \left(\alpha \right)\\\sin \left(\delta \right)\end{bmatrix}}&={\begin{bmatrix}1&0&0\\0&\cos \left(\varepsilon \right)&-\sin \left(\varepsilon \right)\\0&\sin \left(\varepsilon \right)&\cos \left(\varepsilon \right)\end{bmatrix}}{\begin{bmatrix}\cos \left(\beta \right)\cos \left(\lambda \right)\\\cos \left(\beta \right)\sin \left(\lambda \right)\\\sin \left(\beta \right)\end{bmatrix}}.\end{aligned}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Xích_đạo_↔_chân_trời"><span id="X.C3.ADch_.C4.91.E1.BA.A1o_.E2.86.94_ch.C3.A2n_tr.E1.BB.9Di"></span>Xích đạo ↔ chân trời</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=6" title="Sửa đổi phần “Xích đạo ↔ chân trời”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=6" title="Sửa mã nguồn tại đề mục: Xích đạo ↔ chân trời"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lưu ý rằng góc phương vị (<span class="texhtml mvar" style="font-style:italic;">A</span>) được đo từ điểm hướng nam, chiều dương hướng theo phía tây.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <a href="/wiki/G%C3%B3c_thi%C3%AAn_%C4%91%E1%BB%89nh" class="mw-redirect" title="Góc thiên đỉnh">Góc thiên đỉnh</a>, tức là khoảng cách góc dọc theo đường tròn lớn từ <a href="/wiki/Thi%C3%AAn_%C4%91%E1%BB%89nh" title="Thiên đỉnh">thiên đỉnh</a> tới vị trí thiên thể, đơn giản là <a href="/wiki/G%C3%B3c_ph%E1%BB%A5_nhau" class="mw-redirect" title="Góc phụ nhau">góc phụ</a> với góc cao: <span class="texhtml">90° − <i>a</i></span>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><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{aligned}\tan \left(A\right)&={\sin \left(h\right) \over \cos \left(h\right)\sin \left(\phi _{\text{o}}\right)-\tan \left(\delta \right)\cos \left(\phi _{\text{o}}\right)};\qquad {\begin{cases}\cos \left(a\right)\sin \left(A\right)=\cos \left(\delta \right)\sin \left(h\right);\\\cos \left(a\right)\cos \left(A\right)=\cos \left(\delta \right)\cos \left(h\right)\sin \left(\phi _{\text{o}}\right)-\sin \left(\delta \right)\cos \left(\phi _{\text{o}}\right)\end{cases}}\\[3pt]\sin \left(a\right)&=\sin \left(\phi _{\text{o}}\right)\sin \left(\delta \right)+\cos \left(\phi _{\text{o}}\right)\cos \left(\delta \right)\cos \left(h\right);\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.6em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>tan</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mo>−</mo> <mi>tan</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> <mo>;</mo> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>;</mo> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>;</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\tan \left(A\right)&={\sin \left(h\right) \over \cos \left(h\right)\sin \left(\phi _{\text{o}}\right)-\tan \left(\delta \right)\cos \left(\phi _{\text{o}}\right)};\qquad {\begin{cases}\cos \left(a\right)\sin \left(A\right)=\cos \left(\delta \right)\sin \left(h\right);\\\cos \left(a\right)\cos \left(A\right)=\cos \left(\delta \right)\cos \left(h\right)\sin \left(\phi _{\text{o}}\right)-\sin \left(\delta \right)\cos \left(\phi _{\text{o}}\right)\end{cases}}\\[3pt]\sin \left(a\right)&=\sin \left(\phi _{\text{o}}\right)\sin \left(\delta \right)+\cos \left(\phi _{\text{o}}\right)\cos \left(\delta \right)\cos \left(h\right);\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24591754e1a4d05bbcb52fd2b752ad2fa281ad42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:103.036ex; height:10.176ex;" alt="{\displaystyle {\begin{aligned}\tan \left(A\right)&={\sin \left(h\right) \over \cos \left(h\right)\sin \left(\phi _{\text{o}}\right)-\tan \left(\delta \right)\cos \left(\phi _{\text{o}}\right)};\qquad {\begin{cases}\cos \left(a\right)\sin \left(A\right)=\cos \left(\delta \right)\sin \left(h\right);\\\cos \left(a\right)\cos \left(A\right)=\cos \left(\delta \right)\cos \left(h\right)\sin \left(\phi _{\text{o}}\right)-\sin \left(\delta \right)\cos \left(\phi _{\text{o}}\right)\end{cases}}\\[3pt]\sin \left(a\right)&=\sin \left(\phi _{\text{o}}\right)\sin \left(\delta \right)+\cos \left(\phi _{\text{o}}\right)\cos \left(\delta \right)\cos \left(h\right);\end{aligned}}}"></span></dd></dl> <p>Khi giải phương trình <span class="texhtml">tan(<i>A</i>)</span> để tìm phương vị <span class="texhtml"><i>A</i></span>, nên sử dụng hàm <a href="/wiki/H%C3%A0m_l%C6%B0%E1%BB%A3ng_gi%C3%A1c_ng%C6%B0%E1%BB%A3c" class="mw-redirect" title="Hàm lượng giác ngược">arctan</a> <a href="/w/index.php?title=Atan2&action=edit&redlink=1" class="new" title="Atan2 (trang không tồn tại)">hai đối số</a>, ký hiệu là <span class="texhtml">arctan(<i>x</i>,<i>y</i>)</span> để tránh nhầm lẫn về giá trị góc. Hàm arctan hai đối số tính toán arctan của <span class="texhtml"><style data-mw-deduplicate="TemplateStyles:r68144636">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num,.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0 0.1em}.mw-parser-output .sfrac .den{border-top:1px solid}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac"><span class="tion"><span class="num"><i>y</i></span><span class="sr-only">/</span><span class="den"><i>x</i></span></span></span></span>, với giá trị được xác định tùy theo <a href="/wiki/G%C3%B3c_ph%E1%BA%A7n_t%C6%B0" title="Góc phần tư">góc phần tư</a> chứa cặp <span class="texhtml">(<i>x</i>,<i>y</i>)</span>. Do đó, giá trị phương vị là phù hợp với quy ước góc phương vị được đo từ phía nam và chiều dương tới phía tây, </p> <dl><dd><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=-\arctan(x,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mo>−</mo> <mi>arctan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=-\arctan(x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d320d9f2cf97eb81179dceedded00d18b41db8e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.831ex; height:2.843ex;" alt="{\displaystyle A=-\arctan(x,y)}"></span>,</dd></dl> <p>trong đó </p> <dl><dd><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{aligned}x&=-\sin \left(\phi _{\text{o}}\right)\cos \left(\delta \right)\cos \left(h\right)+\cos \left(\phi _{\text{o}}\right)\sin \left(\delta \right)\\y&=\cos \left(\delta \right)\sin \left(h\right)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>x</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}x&=-\sin \left(\phi _{\text{o}}\right)\cos \left(\delta \right)\cos \left(h\right)+\cos \left(\phi _{\text{o}}\right)\sin \left(\delta \right)\\y&=\cos \left(\delta \right)\sin \left(h\right)\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5acc5f844c748270660fdb347d9bb1d38fcdcf2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:43.783ex; height:6.176ex;" alt="{\displaystyle {\begin{aligned}x&=-\sin \left(\phi _{\text{o}}\right)\cos \left(\delta \right)\cos \left(h\right)+\cos \left(\phi _{\text{o}}\right)\sin \left(\delta \right)\\y&=\cos \left(\delta \right)\sin \left(h\right)\end{aligned}}}"></span>.</dd></dl> <p>Nếu công thức trên cho một giá trị <span class="texhtml"><i>A</i></span> âm, nó có thể được đổi thành dương bằng cách chỉ cần cộng thêm 360°. </p> <dl><dd><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{aligned}{\begin{bmatrix}\cos \left(a\right)\cos \left(A\right)\\\cos \left(a\right)\sin \left(A\right)\\\sin \left(a\right)\end{bmatrix}}&={\begin{bmatrix}\sin \left(\phi _{\text{o}}\right)&0&-\cos \left(\phi _{\text{o}}\right)\\0&1&0\\\cos \left(\phi _{\text{o}}\right)&0&\sin \left(\phi _{\text{o}}\right)\end{bmatrix}}{\begin{bmatrix}\cos \left(\delta \right)\cos \left(h\right)\\\cos \left(\delta \right)\sin \left(h\right)\\\sin \left(\delta \right)\end{bmatrix}}\\&={\begin{bmatrix}\sin \left(\phi _{\text{o}}\right)&0&-\cos \left(\phi _{\text{o}}\right)\\0&1&0\\\cos \left(\phi _{\text{o}}\right)&0&\sin \left(\phi _{\text{o}}\right)\end{bmatrix}}{\begin{bmatrix}\cos \left(\theta _{L}\right)&\sin \left(\theta _{L}\right)&0\\\sin \left(\theta _{L}\right)&-\cos \left(\theta _{L}\right)&0\\0&0&1\end{bmatrix}}{\begin{bmatrix}\cos \left(\delta \right)\cos \left(\alpha \right)\\\cos \left(\delta \right)\sin \left(\alpha \right)\\\sin \left(\delta \right)\end{bmatrix}};\\[6pt]\tan \left(h\right)&={\sin \left(A\right) \over \cos \left(A\right)\sin \left(\phi _{\text{o}}\right)+\tan \left(a\right)\cos \left(\phi _{\text{o}}\right)};\qquad {\begin{cases}\cos \left(\delta \right)\sin \left(h\right)=\cos \left(a\right)\sin \left(A\right);\\\cos \left(\delta \right)\cos \left(h\right)=\sin \left(a\right)\cos \left(\phi _{\text{o}}\right)+\cos \left(a\right)\cos \left(A\right)\sin \left(\phi _{\text{o}}\right)\end{cases}}\\[3pt]\sin \left(\delta \right)&=\sin \left(\phi _{\text{o}}\right)\sin \left(a\right)-\cos \left(\phi _{\text{o}}\right)\cos \left(a\right)\cos \left(A\right);\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt 0.9em 0.6em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>;</mo> </mtd> </mtr> <mtr> <mtd> <mi>tan</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>tan</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> <mo>;</mo> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> <mo>;</mo> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> <mo>;</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\begin{bmatrix}\cos \left(a\right)\cos \left(A\right)\\\cos \left(a\right)\sin \left(A\right)\\\sin \left(a\right)\end{bmatrix}}&={\begin{bmatrix}\sin \left(\phi _{\text{o}}\right)&0&-\cos \left(\phi _{\text{o}}\right)\\0&1&0\\\cos \left(\phi _{\text{o}}\right)&0&\sin \left(\phi _{\text{o}}\right)\end{bmatrix}}{\begin{bmatrix}\cos \left(\delta \right)\cos \left(h\right)\\\cos \left(\delta \right)\sin \left(h\right)\\\sin \left(\delta \right)\end{bmatrix}}\\&={\begin{bmatrix}\sin \left(\phi _{\text{o}}\right)&0&-\cos \left(\phi _{\text{o}}\right)\\0&1&0\\\cos \left(\phi _{\text{o}}\right)&0&\sin \left(\phi _{\text{o}}\right)\end{bmatrix}}{\begin{bmatrix}\cos \left(\theta _{L}\right)&\sin \left(\theta _{L}\right)&0\\\sin \left(\theta _{L}\right)&-\cos \left(\theta _{L}\right)&0\\0&0&1\end{bmatrix}}{\begin{bmatrix}\cos \left(\delta \right)\cos \left(\alpha \right)\\\cos \left(\delta \right)\sin \left(\alpha \right)\\\sin \left(\delta \right)\end{bmatrix}};\\[6pt]\tan \left(h\right)&={\sin \left(A\right) \over \cos \left(A\right)\sin \left(\phi _{\text{o}}\right)+\tan \left(a\right)\cos \left(\phi _{\text{o}}\right)};\qquad {\begin{cases}\cos \left(\delta \right)\sin \left(h\right)=\cos \left(a\right)\sin \left(A\right);\\\cos \left(\delta \right)\cos \left(h\right)=\sin \left(a\right)\cos \left(\phi _{\text{o}}\right)+\cos \left(a\right)\cos \left(A\right)\sin \left(\phi _{\text{o}}\right)\end{cases}}\\[3pt]\sin \left(\delta \right)&=\sin \left(\phi _{\text{o}}\right)\sin \left(a\right)-\cos \left(\phi _{\text{o}}\right)\cos \left(a\right)\cos \left(A\right);\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0b38b9e388153fa974a286f72be3bf6906a5fe3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -14.864ex; margin-bottom: -0.307ex; width:113.943ex; height:31.509ex;" alt="{\displaystyle {\begin{aligned}{\begin{bmatrix}\cos \left(a\right)\cos \left(A\right)\\\cos \left(a\right)\sin \left(A\right)\\\sin \left(a\right)\end{bmatrix}}&={\begin{bmatrix}\sin \left(\phi _{\text{o}}\right)&0&-\cos \left(\phi _{\text{o}}\right)\\0&1&0\\\cos \left(\phi _{\text{o}}\right)&0&\sin \left(\phi _{\text{o}}\right)\end{bmatrix}}{\begin{bmatrix}\cos \left(\delta \right)\cos \left(h\right)\\\cos \left(\delta \right)\sin \left(h\right)\\\sin \left(\delta \right)\end{bmatrix}}\\&={\begin{bmatrix}\sin \left(\phi _{\text{o}}\right)&0&-\cos \left(\phi _{\text{o}}\right)\\0&1&0\\\cos \left(\phi _{\text{o}}\right)&0&\sin \left(\phi _{\text{o}}\right)\end{bmatrix}}{\begin{bmatrix}\cos \left(\theta _{L}\right)&\sin \left(\theta _{L}\right)&0\\\sin \left(\theta _{L}\right)&-\cos \left(\theta _{L}\right)&0\\0&0&1\end{bmatrix}}{\begin{bmatrix}\cos \left(\delta \right)\cos \left(\alpha \right)\\\cos \left(\delta \right)\sin \left(\alpha \right)\\\sin \left(\delta \right)\end{bmatrix}};\\[6pt]\tan \left(h\right)&={\sin \left(A\right) \over \cos \left(A\right)\sin \left(\phi _{\text{o}}\right)+\tan \left(a\right)\cos \left(\phi _{\text{o}}\right)};\qquad {\begin{cases}\cos \left(\delta \right)\sin \left(h\right)=\cos \left(a\right)\sin \left(A\right);\\\cos \left(\delta \right)\cos \left(h\right)=\sin \left(a\right)\cos \left(\phi _{\text{o}}\right)+\cos \left(a\right)\cos \left(A\right)\sin \left(\phi _{\text{o}}\right)\end{cases}}\\[3pt]\sin \left(\delta \right)&=\sin \left(\phi _{\text{o}}\right)\sin \left(a\right)-\cos \left(\phi _{\text{o}}\right)\cos \left(a\right)\cos \left(A\right);\end{aligned}}}"></span><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Một lần nữa, khi giải phương trình <span class="texhtml">tan(<i>h</i>)</span> để tìm <span class="texhtml"><i>h</i></span>, nên sử dụng hàm arctan hai đối số để phù hợp với quy ước phương vị được tính từ phía nam và chiều dương tới phía tây, </p> <dl><dd><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=\arctan(x,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo>=</mo> <mi>arctan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h=\arctan(x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c681c53478905b51d2d10ccd5c6b1c267fdcc23" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.232ex; height:2.843ex;" alt="{\displaystyle h=\arctan(x,y)}"></span>,</dd></dl> <p>trong đó </p> <dl><dd><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{aligned}x&=\sin \left(\phi _{\text{o}}\right)\cos \left(a\right)\cos \left(A\right)+\cos \left(\phi _{\text{o}}\right)\sin \left(a\right)\\y&=\cos \left(a\right)\sin \left(A\right)\\[3pt]{\begin{bmatrix}\cos \left(\delta \right)\cos \left(h\right)\\\cos \left(\delta \right)\sin \left(h\right)\\\sin \left(\delta \right)\end{bmatrix}}&={\begin{bmatrix}\sin \left(\phi _{\text{o}}\right)&0&\cos \left(\phi _{\text{o}}\right)\\0&1&0\\-\cos \left(\phi _{\text{o}}\right)&0&\sin \left(\phi _{\text{o}}\right)\end{bmatrix}}{\begin{bmatrix}\cos \left(a\right)\cos \left(A\right)\\\cos \left(a\right)\sin \left(A\right)\\\sin \left(a\right)\end{bmatrix}}\\{\begin{bmatrix}\cos \left(\delta \right)\cos \left(\alpha \right)\\\cos \left(\delta \right)\sin \left(\alpha \right)\\\sin \left(\delta \right)\end{bmatrix}}&={\begin{bmatrix}\cos \left(\theta _{L}\right)&\sin \left(\theta _{L}\right)&0\\\sin \left(\theta _{L}\right)&-\cos \left(\theta _{L}\right)&0\\0&0&1\end{bmatrix}}{\begin{bmatrix}\sin \left(\phi _{\text{o}}\right)&0&\cos \left(\phi _{\text{o}}\right)\\0&1&0\\-\cos \left(\phi _{\text{o}}\right)&0&\sin \left(\phi _{\text{o}}\right)\end{bmatrix}}{\begin{bmatrix}\cos \left(a\right)\cos \left(A\right)\\\cos \left(a\right)\sin \left(A\right)\\\sin \left(a\right)\end{bmatrix}}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt 0.6em 0.3em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>x</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>o</mtext> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>A</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}x&=\sin \left(\phi _{\text{o}}\right)\cos \left(a\right)\cos \left(A\right)+\cos \left(\phi _{\text{o}}\right)\sin \left(a\right)\\y&=\cos \left(a\right)\sin \left(A\right)\\[3pt]{\begin{bmatrix}\cos \left(\delta \right)\cos \left(h\right)\\\cos \left(\delta \right)\sin \left(h\right)\\\sin \left(\delta \right)\end{bmatrix}}&={\begin{bmatrix}\sin \left(\phi _{\text{o}}\right)&0&\cos \left(\phi _{\text{o}}\right)\\0&1&0\\-\cos \left(\phi _{\text{o}}\right)&0&\sin \left(\phi _{\text{o}}\right)\end{bmatrix}}{\begin{bmatrix}\cos \left(a\right)\cos \left(A\right)\\\cos \left(a\right)\sin \left(A\right)\\\sin \left(a\right)\end{bmatrix}}\\{\begin{bmatrix}\cos \left(\delta \right)\cos \left(\alpha \right)\\\cos \left(\delta \right)\sin \left(\alpha \right)\\\sin \left(\delta \right)\end{bmatrix}}&={\begin{bmatrix}\cos \left(\theta _{L}\right)&\sin \left(\theta _{L}\right)&0\\\sin \left(\theta _{L}\right)&-\cos \left(\theta _{L}\right)&0\\0&0&1\end{bmatrix}}{\begin{bmatrix}\sin \left(\phi _{\text{o}}\right)&0&\cos \left(\phi _{\text{o}}\right)\\0&1&0\\-\cos \left(\phi _{\text{o}}\right)&0&\sin \left(\phi _{\text{o}}\right)\end{bmatrix}}{\begin{bmatrix}\cos \left(a\right)\cos \left(A\right)\\\cos \left(a\right)\sin \left(A\right)\\\sin \left(a\right)\end{bmatrix}}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e80cd665d08444dadd652d53b0f1bfd9bb35e9c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -12.671ex; width:91.321ex; height:26.509ex;" alt="{\displaystyle {\begin{aligned}x&=\sin \left(\phi _{\text{o}}\right)\cos \left(a\right)\cos \left(A\right)+\cos \left(\phi _{\text{o}}\right)\sin \left(a\right)\\y&=\cos \left(a\right)\sin \left(A\right)\\[3pt]{\begin{bmatrix}\cos \left(\delta \right)\cos \left(h\right)\\\cos \left(\delta \right)\sin \left(h\right)\\\sin \left(\delta \right)\end{bmatrix}}&={\begin{bmatrix}\sin \left(\phi _{\text{o}}\right)&0&\cos \left(\phi _{\text{o}}\right)\\0&1&0\\-\cos \left(\phi _{\text{o}}\right)&0&\sin \left(\phi _{\text{o}}\right)\end{bmatrix}}{\begin{bmatrix}\cos \left(a\right)\cos \left(A\right)\\\cos \left(a\right)\sin \left(A\right)\\\sin \left(a\right)\end{bmatrix}}\\{\begin{bmatrix}\cos \left(\delta \right)\cos \left(\alpha \right)\\\cos \left(\delta \right)\sin \left(\alpha \right)\\\sin \left(\delta \right)\end{bmatrix}}&={\begin{bmatrix}\cos \left(\theta _{L}\right)&\sin \left(\theta _{L}\right)&0\\\sin \left(\theta _{L}\right)&-\cos \left(\theta _{L}\right)&0\\0&0&1\end{bmatrix}}{\begin{bmatrix}\sin \left(\phi _{\text{o}}\right)&0&\cos \left(\phi _{\text{o}}\right)\\0&1&0\\-\cos \left(\phi _{\text{o}}\right)&0&\sin \left(\phi _{\text{o}}\right)\end{bmatrix}}{\begin{bmatrix}\cos \left(a\right)\cos \left(A\right)\\\cos \left(a\right)\sin \left(A\right)\\\sin \left(a\right)\end{bmatrix}}.\end{aligned}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Xích_đạo_↔_thiên_hà"><span id="X.C3.ADch_.C4.91.E1.BA.A1o_.E2.86.94_thi.C3.AAn_h.C3.A0"></span>Xích đạo ↔ thiên hà</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=7" title="Sửa đổi phần “Xích đạo ↔ thiên hà”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=7" title="Sửa mã nguồn tại đề mục: Xích đạo ↔ thiên hà"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Các phương trình bên dưới<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> được dùng để chuyển đổi tọa độ xích đạo sang tọa độ thiên hà. </p> <dl><dd><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{aligned}\cos \left(l_{\text{NCP}}-l\right)\cos(b)&=\sin \left(\delta \right)\cos \left(\delta _{\text{G}}\right)-\cos \left(\delta \right)\sin \left(\delta _{\text{G}}\right)\cos \left(\alpha -\alpha _{\text{G}}\right)\\\sin \left(l_{\text{NCP}}-l\right)\cos(b)&=\cos(\delta )\sin \left(\alpha -\alpha _{\text{G}}\right)\\\sin \left(b\right)&=\sin \left(\delta \right)\sin \left(\delta _{\text{G}}\right)+\cos \left(\delta \right)\cos \left(\delta _{\text{G}}\right)\cos \left(\alpha -\alpha _{\text{G}}\right)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>NCP</mtext> </mrow> </msub> <mo>−</mo> <mi>l</mi> </mrow> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi>α</mi> <mo>−</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>NCP</mtext> </mrow> </msub> <mo>−</mo> <mi>l</mi> </mrow> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi>α</mi> <mo>−</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi>α</mi> <mo>−</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\cos \left(l_{\text{NCP}}-l\right)\cos(b)&=\sin \left(\delta \right)\cos \left(\delta _{\text{G}}\right)-\cos \left(\delta \right)\sin \left(\delta _{\text{G}}\right)\cos \left(\alpha -\alpha _{\text{G}}\right)\\\sin \left(l_{\text{NCP}}-l\right)\cos(b)&=\cos(\delta )\sin \left(\alpha -\alpha _{\text{G}}\right)\\\sin \left(b\right)&=\sin \left(\delta \right)\sin \left(\delta _{\text{G}}\right)+\cos \left(\delta \right)\cos \left(\delta _{\text{G}}\right)\cos \left(\alpha -\alpha _{\text{G}}\right)\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78994b1e8705517659dd8b13f262157d178e8bd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:65.71ex; height:9.176ex;" alt="{\displaystyle {\begin{aligned}\cos \left(l_{\text{NCP}}-l\right)\cos(b)&=\sin \left(\delta \right)\cos \left(\delta _{\text{G}}\right)-\cos \left(\delta \right)\sin \left(\delta _{\text{G}}\right)\cos \left(\alpha -\alpha _{\text{G}}\right)\\\sin \left(l_{\text{NCP}}-l\right)\cos(b)&=\cos(\delta )\sin \left(\alpha -\alpha _{\text{G}}\right)\\\sin \left(b\right)&=\sin \left(\delta \right)\sin \left(\delta _{\text{G}}\right)+\cos \left(\delta \right)\cos \left(\delta _{\text{G}}\right)\cos \left(\alpha -\alpha _{\text{G}}\right)\end{aligned}}}"></span></dd></dl> <p><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 _{\text{G}},\delta _{\text{G}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> <mo>,</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha _{\text{G}},\delta _{\text{G}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7737134f568aa3fa4819f07bc987cc7a38d1f0a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.599ex; height:2.676ex;" alt="{\displaystyle \alpha _{\text{G}},\delta _{\text{G}}}"></span> là tọa độ xích đạo của <a href="/wiki/Thi%C3%AAn_c%E1%BB%B1c" title="Thiên cực">Thiên cực Bắc</a> và <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_{\text{NCP}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>NCP</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{\text{NCP}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/209d2070bf725ee618f562e417c381ed52164b65" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.464ex; height:2.509ex;" alt="{\displaystyle l_{\text{NCP}}}"></span> là kinh độ thiên hà của Thiên cực Bắc. Các giá trị này tham chiếu theo <a href="/wiki/K%E1%BB%B7_nguy%C3%AAn_(thi%C3%AAn_v%C4%83n_h%E1%BB%8Dc)" title="Kỷ nguyên (thiên văn học)">J2000.0</a> là: </p> <dl><dd><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 _{G}=192.85948^{\circ }\qquad \delta _{G}=27.12825^{\circ }\qquad l_{\text{NCP}}=122.93192^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> </msub> <mo>=</mo> <msup> <mn>192.85948</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mspace width="2em" /> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> </mrow> </msub> <mo>=</mo> <msup> <mn>27.12825</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mspace width="2em" /> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>NCP</mtext> </mrow> </msub> <mo>=</mo> <msup> <mn>122.93192</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha _{G}=192.85948^{\circ }\qquad \delta _{G}=27.12825^{\circ }\qquad l_{\text{NCP}}=122.93192^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22238e19106e46827927d43047ec4a02431da4c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:60.457ex; height:2.676ex;" alt="{\displaystyle \alpha _{G}=192.85948^{\circ }\qquad \delta _{G}=27.12825^{\circ }\qquad l_{\text{NCP}}=122.93192^{\circ }}"></span></dd></dl> <p>Nếu các tọa độ xích đạo được tham chiếu tới <a href="/wiki/%C4%90i%E1%BB%83m_ph%C3%A2n_(t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n)" class="mw-redirect" title="Điểm phân (tọa độ thiên văn)">điểm phân</a> mốc khác thì chúng phải được chỉnh <a href="/wiki/Ti%E1%BA%BFn_%C4%91%E1%BB%99ng" title="Tiến động">tuế sai</a> tới vị trí của chúng tại kỷ nguyên J2000.0 trước khi áp dụng các công thức trên. </p><p>Các phương trình sau chuyển đổi sang tọa độ xích đạo được tham chiếu theo <a href="/wiki/K%E1%BB%B7_nguy%C3%AAn_(thi%C3%AAn_v%C4%83n_h%E1%BB%8Dc)" title="Kỷ nguyên (thiên văn học)">B2000.0</a>. </p> <dl><dd><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{aligned}\sin \left(\alpha -\alpha _{\text{G}}\right)\cos \left(\delta \right)&=\cos \left(b\right)\sin \left(l_{\text{NCP}}-l\right)\\\cos \left(\alpha -\alpha _{\text{G}}\right)\cos \left(\delta \right)&=\sin \left(b\right)\cos \left(\delta _{\text{G}}\right)-\cos \left(b\right)\sin \left(\delta _{\text{G}}\right)\cos \left(l_{\text{NCP}}-l\right)\\\sin \left(\delta \right)&=\sin \left(b\right)\sin \left(\delta _{\text{G}}\right)+\cos \left(b\right)\cos \left(\delta _{\text{G}}\right)\cos \left(l_{\text{NCP}}-l\right)\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi>α</mi> <mo>−</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>NCP</mtext> </mrow> </msub> <mo>−</mo> <mi>l</mi> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi>α</mi> <mo>−</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>NCP</mtext> </mrow> </msub> <mo>−</mo> <mi>l</mi> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>δ</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>G</mtext> </mrow> </msub> <mo>)</mo> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>NCP</mtext> </mrow> </msub> <mo>−</mo> <mi>l</mi> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\sin \left(\alpha -\alpha _{\text{G}}\right)\cos \left(\delta \right)&=\cos \left(b\right)\sin \left(l_{\text{NCP}}-l\right)\\\cos \left(\alpha -\alpha _{\text{G}}\right)\cos \left(\delta \right)&=\sin \left(b\right)\cos \left(\delta _{\text{G}}\right)-\cos \left(b\right)\sin \left(\delta _{\text{G}}\right)\cos \left(l_{\text{NCP}}-l\right)\\\sin \left(\delta \right)&=\sin \left(b\right)\sin \left(\delta _{\text{G}}\right)+\cos \left(b\right)\cos \left(\delta _{\text{G}}\right)\cos \left(l_{\text{NCP}}-l\right)\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fa4c034f04f6b86c445367c1e21650fbd8d33c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:65.659ex; height:9.176ex;" alt="{\displaystyle {\begin{aligned}\sin \left(\alpha -\alpha _{\text{G}}\right)\cos \left(\delta \right)&=\cos \left(b\right)\sin \left(l_{\text{NCP}}-l\right)\\\cos \left(\alpha -\alpha _{\text{G}}\right)\cos \left(\delta \right)&=\sin \left(b\right)\cos \left(\delta _{\text{G}}\right)-\cos \left(b\right)\sin \left(\delta _{\text{G}}\right)\cos \left(l_{\text{NCP}}-l\right)\\\sin \left(\delta \right)&=\sin \left(b\right)\sin \left(\delta _{\text{G}}\right)+\cos \left(b\right)\cos \left(\delta _{\text{G}}\right)\cos \left(l_{\text{NCP}}-l\right)\end{aligned}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Thiên_hà_↔_siêu_thiên_hà"><span id="Thi.C3.AAn_h.C3.A0_.E2.86.94_si.C3.AAu_thi.C3.AAn_h.C3.A0"></span>Thiên hà ↔ siêu thiên hà</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=8" title="Sửa đổi phần “Thiên hà ↔ siêu thiên hà”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=8" title="Sửa mã nguồn tại đề mục: Thiên hà ↔ siêu thiên hà"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r72019635"><div role="note" class="hatnote navigation-not-searchable">Bài chi tiết: <a href="/wiki/H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_si%C3%AAu_thi%C3%AAn_h%C3%A0" title="Hệ tọa độ siêu thiên hà">Hệ tọa độ siêu thiên hà</a></div> <div class="mw-heading mw-heading3"><h3 id="Lưu_ý_khi_chuyển_đổi"><span id="L.C6.B0u_.C3.BD_khi_chuy.E1.BB.83n_.C4.91.E1.BB.95i"></span>Lưu ý khi chuyển đổi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=9" title="Sửa đổi phần “Lưu ý khi chuyển đổi”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=9" title="Sửa mã nguồn tại đề mục: Lưu ý khi chuyển đổi"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Góc viết theo <a href="/wiki/%C4%90%E1%BB%99_(g%C3%B3c)" title="Độ (góc)">độ</a> (°), phút (′), và giây (″) trong hệ lục thập phân phải được chuyển đổi sang số thập phân trước khi thực hiện tính toán. Việc chúng cần phải được chuyển đổi thành độ thập phân hay <a href="/wiki/Radian" title="Radian">radian</a> phụ thuộc vào chương trình hay máy tính riêng biệt thực hiện tính toán. Giá trị góc âm cần phải được nhập cẩn thận; <span class="nowrap">–10° 20′ 30″</span> phải chuyển thành <span class="nowrap">−10° −20′ −30″</span>.</li> <li>Góc theo giờ (<sup>h</sup>), phút (<sup>m</sup>), và giây (<sup>s</sup>), ví dụ <a href="/wiki/G%C3%B3c_gi%E1%BB%9D" title="Góc giờ">góc giờ</a> hay xích kinh, cũng cần phải được chuyển sang <a href="/wiki/%C4%90%E1%BB%99_(g%C3%B3c)" title="Độ (góc)">độ</a> thập phân hay <a href="/wiki/Radian" title="Radian">radian</a> trước khi thực hiện tính toán. 1<sup>h</sup> = 15°; 1<sup>m</sup> = 15′; 1<sup>s</sup> = 15″</li> <li>Góc lớn hơn 360° (2<span class="texhtml">π</span>) hoặc nhỏ hơn 0°Có thể cần được tối giản trong khoảng 0°~360° (0~2<span class="texhtml">π</span>) tùy thuộc chương trình hoặc máy tính thực hiện tính toán.</li> <li>Cosin của một vĩ độ (độ cao, xích vĩ, hoàng vĩ và vĩ độ thiên hà) không bao giờ âm theo định nghĩa, vì vĩ độ chỉ thay đổi trong khoảng giữa −90° và +90°.</li> <li>Các <a href="/wiki/H%C3%A0m_l%C6%B0%E1%BB%A3ng_gi%C3%A1c_ng%C6%B0%E1%BB%A3c" class="mw-redirect" title="Hàm lượng giác ngược">hàm lượng giác ngược</a> arcsin, arccos và arctan có thể cho giá trị góc nhưng không xác định rõ góc phần tư chứa góc đó, nên kết quả cần được đánh giá cẩn thận. Việc sử dụng <a href="/w/index.php?title=Atan2&action=edit&redlink=1" class="new" title="Atan2 (trang không tồn tại)">hàm arctan hai đối số</a> (ký hiệu trên máy tính có thể là <style data-mw-deduplicate="TemplateStyles:r68144455">.mw-parser-output .monospaced{font-family:monospace,monospace}</style><span class="monospaced">atn2(<i>y</i>,<i>x</i>)</span> hoặc <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r68144455"><span class="monospaced">atan2(<i>y</i>,<i>x</i>)</span>, tính arctan của <span class="texhtml"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r68144636"><span class="sfrac"><span class="tion"><span class="num"><i>y</i></span><span class="sr-only">/</span><span class="den"><i>x</i></span></span></span></span> và sử dụng dấu của cả hai đối số để xác định góc phần tư đúng) được khuyến khích khi tính toán kinh độ/xích kinh/phương vị. Một phương trình tìm giá trị <a href="/wiki/Sin" title="Sin">sin</a>, sau đó đưa vào <a href="/wiki/H%C3%A0m_l%C6%B0%E1%BB%A3ng_gi%C3%A1c" title="Hàm lượng giác">hàm arcsin</a> nên được sử dụng khi tính toán vĩ độ/xích vĩ/độ cao.</li> <li>Góc phương vị (<span class="texhtml"><i>A</i></span>) ở đây được tham chiếu tới điểm nam trên đường <a href="/wiki/Ch%C3%A2n_tr%E1%BB%9Di" title="Chân trời">chân trời</a>, theo quy ước thiên văn thông dụng. Theo cách dùng này một vật thể nằm trên đường <a href="/wiki/Kinh_tuy%E1%BA%BFn_(thi%C3%AAn_v%C4%83n_h%E1%BB%8Dc)" title="Kinh tuyến (thiên văn học)">kinh tuyến</a> ở phía nam so với người quan sát có <span class="texhtml"><i>A</i></span> = <span class="texhtml"><i>a</i></span> = 0°. Tuy nhiên trong hệ AltAz của <a href="/w/index.php?title=Astropy&action=edit&redlink=1" class="new" title="Astropy (trang không tồn tại)">Astropy</a>, trong quy ước file <a href="/wiki/FITS" title="FITS">FITS</a> của <a href="/w/index.php?title=Large_Binocular_Telescope&action=edit&redlink=1" class="new" title="Large Binocular Telescope (trang không tồn tại)">Kính viễn vọng ống nhòm lớn</a> (LBT), trong <a href="/w/index.php?title=XEphem&action=edit&redlink=1" class="new" title="XEphem (trang không tồn tại)">XEphem</a>, trong thư viện <a href="/w/index.php?title=SOFA_(astronomy)&action=edit&redlink=1" class="new" title="SOFA (astronomy) (trang không tồn tại)">Standards of Fundamental Astronomy</a> của <a href="/wiki/International_Astronomical_Union" class="mw-redirect" title="International Astronomical Union">IAU</a> và Phần B của <a href="/w/index.php?title=Astronomical_Almanac&action=edit&redlink=1" class="new" title="Astronomical Almanac (trang không tồn tại)">Astronomical Almanac</a> chẳng hạn, phương vị theo chiều Đông từ phía Bắc. Trong định hướng và một số ngành khác, phương vị được tính từ phía bắc.</li> <li>Các phương trình cho độ cao (<span class="texhtml"><i>a</i></span>) chưa tính đến ảnh hưởng của <a href="/w/index.php?title=Kh%C3%BAc_x%E1%BA%A1_kh%C3%AD_quy%E1%BB%83n&action=edit&redlink=1" class="new" title="Khúc xạ khí quyển (trang không tồn tại)">khúc xạ khí quyển</a>.</li> <li>Các phương trình cho tọa độ chân trời chưa tính đến <a href="/wiki/Th%E1%BB%8B_sai" title="Thị sai">thị sai ngày</a>, tức là, sự sai lệch nhỏ trong vị trí của một thiên thể gây ra bởi vị trí của người quan sát trên bề mặt <a href="/wiki/Tr%C3%A1i_%C4%90%E1%BA%A5t" title="Trái Đất">Trái Đất</a>. Hiệu ứng này là đáng kể đối với <a href="/wiki/M%E1%BA%B7t_Tr%C4%83ng" title="Mặt Trăng">Mặt Trăng</a>, ít hơn đối với các <a href="/wiki/H%E1%BB%87_M%E1%BA%B7t_Tr%E1%BB%9Di" title="Hệ Mặt Trời">hành tinh</a>, và cực kỳ nhỏ đối với các <a href="/wiki/Sao" title="Sao">ngôi sao</a> hay các thiên thể xa hơn.</li> <li>Vĩ độ của người quan sát (<span class="texhtml"><i>λ</i><sub>o</sub></span>) ở đây được đo theo chiều dương về phía tây so với <a href="/wiki/Kinh_tuy%E1%BA%BFn_g%E1%BB%91c" title="Kinh tuyến gốc">kinh tuyến gốc</a>; trái với tiêu chuẩn <a href="/wiki/International_Astronomical_Union" class="mw-redirect" title="International Astronomical Union">IAU</a> hiện hành.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Xem_thêm"><span id="Xem_th.C3.AAm"></span>Xem thêm</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=10" title="Sửa đổi phần “Xem thêm”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=10" title="Sửa mã nguồn tại đề mục: Xem thêm"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/G%C3%B3c_ph%C6%B0%C6%A1ng_v%E1%BB%8B" title="Góc phương vị">Góc phương vị</a> – góc giữa mặt phẳng tham chiếu và một điểm</li> <li><a href="/w/index.php?title=H%E1%BB%87_quy_chi%E1%BA%BFu_thi%C3%AAn_th%E1%BB%83_barycentric&action=edit&redlink=1" class="new" title="Hệ quy chiếu thiên thể barycentric (trang không tồn tại)">Hệ quy chiếu thiên thể barycentric</a> (BCRS)</li> <li><a href="/wiki/Thi%C3%AAn_c%E1%BA%A7u" title="Thiên cầu">Thiên cầu</a> – Mặt cầu tưởng tượng với bán kính rất lớn, đồng tâm với người quan sát</li> <li><a href="/w/index.php?title=H%E1%BB%87_th%E1%BB%91ng_tham_chi%E1%BA%BFu_Thi%C3%AAn_th%E1%BB%83_Qu%E1%BB%91c_t%E1%BA%BF&action=edit&redlink=1" class="new" title="Hệ thống tham chiếu Thiên thể Quốc tế (trang không tồn tại)">Hệ thống tham chiếu Thiên thể Quốc tế</a> (ICRS) và <a href="/w/index.php?title=H%E1%BB%87_quy_chi%E1%BA%BFu_Thi%C3%AAn_th%E1%BB%83_Qu%E1%BB%91c_t%E1%BA%BF&action=edit&redlink=1" class="new" title="Hệ quy chiếu Thiên thể Quốc tế (trang không tồn tại)">Hệ quy chiếu Thiên thể Quốc tế</a> (ICRF) – hệ thống quy ước tham chiếu tiêu chuẩn hiện hành.</li> <li><a href="/wiki/Tham_s%E1%BB%91_qu%E1%BB%B9_%C4%91%E1%BA%A1o" title="Tham số quỹ đạo">Tham số quỹ đạo</a></li> <li><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_h%C3%A0nh_tinh&action=edit&redlink=1" class="new" title="Hệ tọa độ hành tinh (trang không tồn tại)">Hệ tọa độ hành tinh</a></li> <li><a href="/w/index.php?title=H%E1%BB%87_quy_chi%E1%BA%BFu_tr%C3%A1i_%C4%91%E1%BA%A5t&action=edit&redlink=1" class="new" title="Hệ quy chiếu trái đất (trang không tồn tại)">Hệ quy chiếu trái đất</a> (TRF)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Chú_thích"><span id="Ch.C3.BA_th.C3.ADch"></span>Chú thích</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=11" title="Sửa đổi phần “Chú thích”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=11" title="Sửa mã nguồn tại đề mục: Chú thích"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-12"><b><a href="#cite_ref-12">^</a></b> <span class="reference-text">Depending on the azimuth convention in use, the signs of <span class="texhtml">cos <i>A</i></span> and <span class="texhtml">sin <i>A</i></span> appear in all four different combinations. Karttunen et al.,<sup id="cite_ref-Karttunen_7-0" class="reference"><a href="#cite_note-Karttunen-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Taff,<sup id="cite_ref-Taff_8-0" class="reference"><a href="#cite_note-Taff-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and Roth<sup id="cite_ref-Roth_9-0" class="reference"><a href="#cite_note-Roth-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> define <span class="texhtml"><i>A</i></span> clockwise from the south. Lang<sup id="cite_ref-Lang_10-0" class="reference"><a href="#cite_note-Lang-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> defines it north through east, Smart<sup id="cite_ref-Smart_11-0" class="reference"><a href="#cite_note-Smart-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> north through west. Meeus (1991),<sup id="cite_ref-Meeus_2-1" class="reference"><a href="#cite_note-Meeus-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> p. 89: <span class="texhtml">sin <i>δ</i> = sin <i>φ</i> sin <i>a</i> − cos <i>φ</i> cos <i>a</i> cos <i>A</i></span>; <i>Explanatory Supplement</i> (1961),<sup id="cite_ref-ExplSupp_3-1" class="reference"><a href="#cite_note-ExplSupp-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> p. 26: <span class="texhtml">sin <i>δ</i> = sin <i>a</i> sin <i>φ</i> + cos <i>a</i> cos <i>A</i> cos <i>φ</i></span>.</span> </li> </ol> <div class="mw-heading mw-heading2"><h2 id="Tham_khảo"><span id="Tham_kh.E1.BA.A3o"></span>Tham khảo</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=12" title="Sửa đổi phần “Tham khảo”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=12" title="Sửa mã nguồn tại đề mục: Tham khảo"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r71728118">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><b><a href="#cite_ref-1">^</a></b> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r72042645">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"“""”""‘""’"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFMajewski" class="citation web cs1">Majewski, Steve. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160312195329/http://faculty.virginia.edu/ASTR5610/lectures/COORDS/coords.html">“Coordinate Systems”</a>. UVa Department of Astronomy. <a rel="nofollow" class="external text" href="http://www.faculty.virginia.edu/ASTR5610/lectures/COORDS/coords.html">Bản gốc</a> lưu trữ ngày 12 tháng 3 năm 2016<span class="reference-accessdate">. Truy cập ngày 19 tháng 3 năm 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Coordinate+Systems&rft.pub=UVa+Department+of+Astronomy&rft.aulast=Majewski&rft.aufirst=Steve&rft_id=http%3A%2F%2Fwww.faculty.virginia.edu%2FASTR5610%2Flectures%2FCOORDS%2Fcoords.html&rfr_id=info%3Asid%2Fvi.wikipedia.org%3AH%E1%BB%87+t%E1%BB%8Da+%C4%91%E1%BB%99+thi%C3%AAn+v%C4%83n" class="Z3988"></span></span> </li> <li id="cite_note-Meeus-2">^ <a href="#cite_ref-Meeus_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Meeus_2-1"><sup><i><b>b</b></i></sup></a> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r72042645"><cite id="CITEREFMeeus1991" class="citation book cs1">Meeus, Jean (1991). <i>Astronomical Algorithms</i>. Willmann-Bell, Inc., Richmond, VA. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Ngu%E1%BB%93n_s%C3%A1ch/0-943396-35-2" title="Đặc biệt:Nguồn sách/0-943396-35-2"><bdi>0-943396-35-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Astronomical+Algorithms&rft.pub=Willmann-Bell%2C+Inc.%2C+Richmond%2C+VA&rft.date=1991&rft.isbn=0-943396-35-2&rft.aulast=Meeus&rft.aufirst=Jean&rfr_id=info%3Asid%2Fvi.wikipedia.org%3AH%E1%BB%87+t%E1%BB%8Da+%C4%91%E1%BB%99+thi%C3%AAn+v%C4%83n" class="Z3988"></span>, chap. 12</span> </li> <li id="cite_note-ExplSupp-3">^ <a href="#cite_ref-ExplSupp_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ExplSupp_3-1"><sup><i><b>b</b></i></sup></a> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r72042645"><cite id="CITEREFU.S._Naval_ObservatoryH.M._Nautical_Almanac_Office1961" class="citation book cs1">U.S. Naval Observatory, Nautical Almanac Office; H.M. Nautical Almanac Office (1961). <i>Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac</i>. H.M. Stationery Office, London.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Explanatory+Supplement+to+the+Astronomical+Ephemeris+and+the+American+Ephemeris+and+Nautical+Almanac&rft.pub=H.M.+Stationery+Office%2C+London&rft.date=1961&rft.aulast=U.S.+Naval+Observatory&rft.aufirst=Nautical+Almanac+Office&rft.au=H.M.+Nautical+Almanac+Office&rfr_id=info%3Asid%2Fvi.wikipedia.org%3AH%E1%BB%87+t%E1%BB%8Da+%C4%91%E1%BB%99+thi%C3%AAn+v%C4%83n" class="Z3988"></span>, sec. 2A</span> </li> <li id="cite_note-4"><b><a href="#cite_ref-4">^</a></b> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r72042645"><cite id="CITEREFU.S._Naval_Observatory1992" class="citation book cs1">U.S. Naval Observatory, Nautical Almanac Office (1992). P. Kenneth Seidelmann (biên tập). <a rel="nofollow" class="external text" href="https://archive.org/details/explanatorysuppl0003unse"><i>Explanatory Supplement to the Astronomical Almanac</i></a>. University Science Books, Mill Valley, CA. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Ngu%E1%BB%93n_s%C3%A1ch/0-935702-68-7" title="Đặc biệt:Nguồn sách/0-935702-68-7"><bdi>0-935702-68-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Explanatory+Supplement+to+the+Astronomical+Almanac&rft.pub=University+Science+Books%2C+Mill+Valley%2C+CA&rft.date=1992&rft.isbn=0-935702-68-7&rft.aulast=U.S.+Naval+Observatory&rft.aufirst=Nautical+Almanac+Office&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fexplanatorysuppl0003unse&rfr_id=info%3Asid%2Fvi.wikipedia.org%3AH%E1%BB%87+t%E1%BB%8Da+%C4%91%E1%BB%99+thi%C3%AAn+v%C4%83n" class="Z3988"></span>, section 11.43</span> </li> <li id="cite_note-5"><b><a href="#cite_ref-5">^</a></b> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r72042645"><cite id="CITEREFMontenbruckPfleger2000" class="citation book cs1">Montenbruck, Oliver; Pfleger, Thomas (2000). <i>Astronomy on the Personal Computer</i>. Springer-Verlag Berlin Heidelberg. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Ngu%E1%BB%93n_s%C3%A1ch/978-3-540-67221-0" title="Đặc biệt:Nguồn sách/978-3-540-67221-0"><bdi>978-3-540-67221-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Astronomy+on+the+Personal+Computer&rft.pub=Springer-Verlag+Berlin+Heidelberg&rft.date=2000&rft.isbn=978-3-540-67221-0&rft.aulast=Montenbruck&rft.aufirst=Oliver&rft.au=Pfleger%2C+Thomas&rfr_id=info%3Asid%2Fvi.wikipedia.org%3AH%E1%BB%87+t%E1%BB%8Da+%C4%91%E1%BB%99+thi%C3%AAn+v%C4%83n" class="Z3988"></span>, pp 35-37</span> </li> <li id="cite_note-6"><b><a href="#cite_ref-6">^</a></b> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r72042645"><cite id="CITEREFU.S._Naval_ObservatoryU.K._Hydrographic_Office2008" class="citation book cs1">U.S. Naval Observatory, Nautical Almanac Office; U.K. Hydrographic Office, H.M. Nautical Almanac Office (2008). <i>The Astronomical Almanac for the Year 2010</i>. U.S. Govt. Printing Office. tr. M18. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Ngu%E1%BB%93n_s%C3%A1ch/978-0160820083" title="Đặc biệt:Nguồn sách/978-0160820083"><bdi>978-0160820083</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Astronomical+Almanac+for+the+Year+2010&rft.pages=M18&rft.pub=U.S.+Govt.+Printing+Office&rft.date=2008&rft.isbn=978-0160820083&rft.aulast=U.S.+Naval+Observatory&rft.aufirst=Nautical+Almanac+Office&rft.au=U.K.+Hydrographic+Office%2C+H.M.+Nautical+Almanac+Office&rfr_id=info%3Asid%2Fvi.wikipedia.org%3AH%E1%BB%87+t%E1%BB%8Da+%C4%91%E1%BB%99+thi%C3%AAn+v%C4%83n" class="Z3988"></span></span> </li> <li id="cite_note-Karttunen-7"><b><a href="#cite_ref-Karttunen_7-0">^</a></b> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r72042645"><cite id="CITEREFKarttunenKrögerOjaPoutanen2006" class="citation book cs1">Karttunen, H.; Kröger, P.; Oja, H.; Poutanen, M.; Donner, H. J. (2006). <i>Fundamental Astronomy</i> (ấn bản thứ 5). <a href="/wiki/Bibcode_(%C4%91%E1%BB%8Bnh_danh)" class="mw-redirect" title="Bibcode (định danh)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2003fuas.book.....K">2003fuas.book.....K</a>. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Ngu%E1%BB%93n_s%C3%A1ch/978-3-540-34143-7" title="Đặc biệt:Nguồn sách/978-3-540-34143-7"><bdi>978-3-540-34143-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamental+Astronomy&rft.edition=5&rft.date=2006&rft_id=info%3Abibcode%2F2003fuas.book.....K&rft.isbn=978-3-540-34143-7&rft.aulast=Karttunen&rft.aufirst=H.&rft.au=Kr%C3%B6ger%2C+P.&rft.au=Oja%2C+H.&rft.au=Poutanen%2C+M.&rft.au=Donner%2C+H.+J.&rfr_id=info%3Asid%2Fvi.wikipedia.org%3AH%E1%BB%87+t%E1%BB%8Da+%C4%91%E1%BB%99+thi%C3%AAn+v%C4%83n" class="Z3988"></span></span> </li> <li id="cite_note-Taff-8"><b><a href="#cite_ref-Taff_8-0">^</a></b> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r72042645"><cite id="CITEREFTaff1981" class="citation book cs1">Taff, L. G. (1981). <a rel="nofollow" class="external text" href="https://archive.org/details/computationalsph0000taff"><i>Computational spherical astronomy</i></a>. Wiley. <a href="/wiki/Bibcode_(%C4%91%E1%BB%8Bnh_danh)" class="mw-redirect" title="Bibcode (định danh)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1981csa..book.....T">1981csa..book.....T</a>. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Ngu%E1%BB%93n_s%C3%A1ch/0-471-06257-X" title="Đặc biệt:Nguồn sách/0-471-06257-X"><bdi>0-471-06257-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computational+spherical+astronomy&rft.pub=Wiley&rft.date=1981&rft_id=info%3Abibcode%2F1981csa..book.....T&rft.isbn=0-471-06257-X&rft.aulast=Taff&rft.aufirst=L.+G.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcomputationalsph0000taff&rfr_id=info%3Asid%2Fvi.wikipedia.org%3AH%E1%BB%87+t%E1%BB%8Da+%C4%91%E1%BB%99+thi%C3%AAn+v%C4%83n" class="Z3988"></span></span> </li> <li id="cite_note-Roth-9"><b><a href="#cite_ref-Roth_9-0">^</a></b> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r72042645"><cite id="CITEREFRoth1989" class="citation book cs1">Roth, G. D. (ngày 23 tháng 10 năm 1989). <i>Handbuch für Sternenfreunde</i>. Springer. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Ngu%E1%BB%93n_s%C3%A1ch/3-540-19436-3" title="Đặc biệt:Nguồn sách/3-540-19436-3"><bdi>3-540-19436-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Handbuch+f%C3%BCr+Sternenfreunde&rft.pub=Springer&rft.date=1989-10-23&rft.isbn=3-540-19436-3&rft.aulast=Roth&rft.aufirst=G.+D.&rfr_id=info%3Asid%2Fvi.wikipedia.org%3AH%E1%BB%87+t%E1%BB%8Da+%C4%91%E1%BB%99+thi%C3%AAn+v%C4%83n" class="Z3988"></span></span> </li> <li id="cite_note-Lang-10"><b><a href="#cite_ref-Lang_10-0">^</a></b> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r72042645"><cite id="CITEREFLang1978" class="citation book cs1">Lang, Kenneth R. (1978). <i>Astrophysical Formulae</i>. Springer. <a href="/wiki/Bibcode_(%C4%91%E1%BB%8Bnh_danh)" class="mw-redirect" title="Bibcode (định danh)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1978afcp.book.....L">1978afcp.book.....L</a>. <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Ngu%E1%BB%93n_s%C3%A1ch/3-540-09064-9" title="Đặc biệt:Nguồn sách/3-540-09064-9"><bdi>3-540-09064-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Astrophysical+Formulae&rft.pub=Springer&rft.date=1978&rft_id=info%3Abibcode%2F1978afcp.book.....L&rft.isbn=3-540-09064-9&rft.aulast=Lang&rft.aufirst=Kenneth+R.&rfr_id=info%3Asid%2Fvi.wikipedia.org%3AH%E1%BB%87+t%E1%BB%8Da+%C4%91%E1%BB%99+thi%C3%AAn+v%C4%83n" class="Z3988"></span></span> </li> <li id="cite_note-Smart-11"><b><a href="#cite_ref-Smart_11-0">^</a></b> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r72042645"><cite id="CITEREFSmart1949" class="citation book cs1">Smart, William Marshall (1949). <i>Text-book on spherical astronomy</i>. <a href="/wiki/Cambridge_University_Press" class="mw-redirect" title="Cambridge University Press">Cambridge University Press</a>. <a href="/wiki/Bibcode_(%C4%91%E1%BB%8Bnh_danh)" class="mw-redirect" title="Bibcode (định danh)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1965tbsa.book.....S">1965tbsa.book.....S</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Text-book+on+spherical+astronomy&rft.pub=Cambridge+University+Press&rft.date=1949&rft_id=info%3Abibcode%2F1965tbsa.book.....S&rft.aulast=Smart&rft.aufirst=William+Marshall&rfr_id=info%3Asid%2Fvi.wikipedia.org%3AH%E1%BB%87+t%E1%BB%8Da+%C4%91%E1%BB%99+thi%C3%AAn+v%C4%83n" class="Z3988"></span></span> </li> <li id="cite_note-13"><b><a href="#cite_ref-13">^</a></b> <span class="reference-text"><cite style="font-style:normal" class="">Poleski, Radosław (2013). "Transformation of the equatorial proper motion to the Galactic system".  <i><a href="/wiki/ArXiv" title="ArXiv">arΧiv</a>:<a rel="nofollow" class="external text" href="http://www.arxiv.org/abs/1306.2945">1306.2945</a></i> [astro-ph.IM].</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.btitle=Transformation+of+the+equatorial+proper+motion+to+the+Galactic+system&rft.atitle=&rft.aulast=Poleski&rft.aufirst=Rados%C5%82aw&rft.au=Poleski%2C+Rados%C5%82aw&rft.date=2013&rfr_id=info:sid/vi.wikipedia.org:H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n"><span style="display: none;"> </span></span></span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Tham_khảo_sách"><span id="Tham_kh.E1.BA.A3o_s.C3.A1ch"></span>Tham khảo sách</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=13" title="Sửa đổi phần “Tham khảo sách”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=13" title="Sửa mã nguồn tại đề mục: Tham khảo sách"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>(bằng <a href="/wiki/Ti%E1%BA%BFng_Anh" title="Tiếng Anh">tiếng Anh</a>) </p> <ul><li>The Astronomical Almanac, 1984, "The Introduction of the Improved IAU System of Astronomical Constants, Time Scales and Reference Frame into the Astronomical Almanac", Supplement section, pp. S1-S39, U. S. Government Printing Office, Washington and Her Majesty's Stationery Office, London.</li> <li>Hohenkerk, C.Y., Yallop, B.D., Smith, C.A., Sinclair, A.T., 1992, "Celestial Reference Systems", Chapter 3, p. 167, Explanatory Supplement to the Astronomical Almanac, Seidelmann, P.K., Ed., U. S. Naval Observatory, University Science Books, Mill Valley, CA.</li> <li>Archinal, B.A., 1992, "Terrestrial Coordinates and the Rotation of the Earth", Chapter 4, p. 255, Explanatory Supplement to the Astronomical Almanac Seidelmann, P.K., Ed., U. S. Naval Observatory, University Science Books, Mill Valley, CA.</li> <li>Seidelmann, P.K., Guinot, B., Dogget, L.E., 1992, "Time", Chapter 2, p. 42, Explanatory Supplement to the Astronomical Almanac, Seidelmann, P.K., Ed., U. S. Naval Observatory, University Science Books, Mill Valley, CA.</li> <li>Standish, E.M., Newhall, X X, Williams, J.G. and Folkner, W.F.: 1995, "JPL Planetary and Lunar Ephemerides, DE403/LE403", JPL IOM 314.10-127.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Liên_kết_ngoài"><span id="Li.C3.AAn_k.E1.BA.BFt_ngo.C3.A0i"></span>Liên kết ngoài</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&veaction=edit&section=14" title="Sửa đổi phần “Liên kết ngoài”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=H%E1%BB%87_t%E1%BB%8Da_%C4%91%E1%BB%99_thi%C3%AAn_v%C4%83n&action=edit&section=14" title="Sửa mã nguồn tại đề mục: Liên kết ngoài"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r71936381">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r70981351">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons có thêm hình ảnh và phương tiện truyền tải về <i><b><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Celestial_coordinate_systems?uselang=vi">Hệ tọa độ thiên văn</a></b></i>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://aa.usno.navy.mil/software/novas/novas_info.php">NOVAS</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150628034916/http://aa.usno.navy.mil/software/novas/novas_info.php">Lưu trữ</a> 2015-06-28 tại <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, the <a href="/w/index.php?title=U.S._Naval_Observatory&action=edit&redlink=1" class="new" title="U.S. Naval Observatory (trang không tồn tại)">U.S. Naval Observatory</a>'s Vector Astrometry Software, an integrated package of subroutines and functions for computing various commonly needed quantities in positional astronomy.</li> <li><a rel="nofollow" class="external text" href="http://www.iausofa.org/">SOFA</a>, the <a href="/wiki/International_Astronomical_Union" class="mw-redirect" title="International Astronomical Union">IAU</a>'s Standards of Fundamental Astronomy, an accessible and authoritative set of algorithms and procedures that implement standard models used in fundamental astronomy.</li> <li><i>This article was originally based on Jason Harris' Astroinfo, which comes along with <a href="/w/index.php?title=KStars&action=edit&redlink=1" class="new" title="KStars (trang không tồn tại)">KStars</a>, a <a rel="nofollow" class="external text" href="http://edu.kde.org/kstars/">KDE Desktop Planetarium</a> for <a href="/wiki/Linux" title="Linux">Linux</a>/<a href="/wiki/KDE" title="KDE">KDE</a>.</i></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r70958518">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl 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