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<span>In astronomy</span> </div> </a> <ul id="toc-In_astronomy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_navigation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_navigation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>In navigation</span> </div> </a> <button aria-controls="toc-In_navigation-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle In navigation subsection</span> </button> <ul id="toc-In_navigation-sublist" class="vector-toc-list"> <li id="toc-True_north-based_azimuths" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#True_north-based_azimuths"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>True north-based azimuths</span> </div> </a> <ul id="toc-True_north-based_azimuths-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-In_geodesy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_geodesy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>In geodesy</span> </div> </a> <ul id="toc-In_geodesy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_cartography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#In_cartography"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>In cartography</span> </div> </a> <button aria-controls="toc-In_cartography-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle In cartography subsection</span> </button> <ul id="toc-In_cartography-sublist" class="vector-toc-list"> <li id="toc-Map_projections" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Map_projections"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Map projections</span> </div> </a> <ul id="toc-Map_projections-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Related_coordinates" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Related_coordinates"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Related coordinates</span> </div> </a> <button aria-controls="toc-Related_coordinates-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Related coordinates subsection</span> </button> <ul id="toc-Related_coordinates-sublist" class="vector-toc-list"> <li id="toc-Right_ascension" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Right_ascension"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Right ascension</span> </div> </a> <ul id="toc-Right_ascension-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Polar_coordinate" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Polar_coordinate"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Polar coordinate</span> </div> </a> <ul id="toc-Polar_coordinate-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Other_uses" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Other_uses"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Other uses</span> </div> </a> <ul id="toc-Other_uses-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Azimuth</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 76 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-76" 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">76 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Asimut" title="Asimut – Afrikaans" lang="af" hreflang="af" data-title="Asimut" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Azimut" title="Azimut – Alemannic" lang="gsw" hreflang="gsw" data-title="Azimut" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B3%D9%85%D8%AA" title="سمت – Arabic" lang="ar" hreflang="ar" data-title="سمت" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Acimut" title="Acimut – Asturian" lang="ast" hreflang="ast" data-title="Acimut" data-language-autonym="Asturianu" data-language-local-name="Asturian" 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/Azimut" title="Azimut – Azerbaijani" lang="az" hreflang="az" data-title="Azimut" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A6%E0%A6%BF%E0%A6%97%E0%A6%82%E0%A6%B6" title="দিগংশ – Bangla" lang="bn" hreflang="bn" data-title="দিগংশ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%90%D0%B7%D0%B8%D0%BC%D1%83%D1%82" title="Азимут – Bashkir" lang="ba" hreflang="ba" data-title="Азимут" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%B7%D1%96%D0%BC%D1%83%D1%82" title="Азімут – Belarusian" lang="be" hreflang="be" data-title="Азімут" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D0%B7%D0%B8%D0%BC%D1%83%D1%82" title="Азимут – Bulgarian" lang="bg" hreflang="bg" data-title="Азимут" data-language-autonym="Български" data-language-local-name="Bulgarian" 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/Azimut" title="Azimut – Catalan" lang="ca" hreflang="ca" data-title="Azimut" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Azimut" title="Azimut – Czech" lang="cs" hreflang="cs" data-title="Azimut" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Azimut" title="Azimut – German" lang="de" hreflang="de" data-title="Azimut" data-language-autonym="Deutsch" data-language-local-name="German" 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/Asimuut" title="Asimuut – Estonian" lang="et" hreflang="et" data-title="Asimuut" data-language-autonym="Eesti" data-language-local-name="Estonian" 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%91%CE%B6%CE%B9%CE%BC%CE%BF%CF%8D%CE%B8%CE%B9%CE%BF" title="Αζιμούθιο – Greek" lang="el" hreflang="el" data-title="Αζιμούθιο" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Acimut" title="Acimut – Spanish" lang="es" hreflang="es" data-title="Acimut" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Azimuto" title="Azimuto – Esperanto" lang="eo" hreflang="eo" data-title="Azimuto" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Azimu" title="Azimu – Extremaduran" lang="ext" hreflang="ext" data-title="Azimu" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Azimut" title="Azimut – Basque" lang="eu" hreflang="eu" data-title="Azimut" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B3%D9%85%D8%AA_(%D8%B3%D8%AA%D8%A7%D8%B1%D9%87%E2%80%8C%D8%B4%D9%86%D8%A7%D8%B3%DB%8C)" title="سمت (ستاره‌شناسی) – Persian" lang="fa" hreflang="fa" data-title="سمت (ستاره‌شناسی)" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Azimut" title="Azimut – French" lang="fr" hreflang="fr" data-title="Azimut" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Asamat" title="Asamat – Irish" lang="ga" hreflang="ga" data-title="Asamat" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Acimut" title="Acimut – Galician" lang="gl" hreflang="gl" data-title="Acimut" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%A9%EC%9C%84%EA%B0%81" title="방위각 – Korean" lang="ko" hreflang="ko" data-title="방위각" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%A6%D5%AB%D5%B4%D5%B8%D6%82%D5%BF" title="Ազիմուտ – Armenian" lang="hy" hreflang="hy" data-title="Ազիմուտ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A6%E0%A4%BF%E0%A4%97%E0%A4%82%E0%A4%B6" title="दिगंश – Hindi" lang="hi" hreflang="hi" data-title="दिगंश" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Azimut" title="Azimut – Croatian" lang="hr" hreflang="hr" data-title="Azimut" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Azimuto" title="Azimuto – Ido" lang="io" hreflang="io" data-title="Azimuto" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Azimut" title="Azimut – Indonesian" lang="id" hreflang="id" data-title="Azimut" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/%C3%81ttarhorn" title="Áttarhorn – Icelandic" lang="is" hreflang="is" data-title="Áttarhorn" data-language-autonym="Íslenska" data-language-local-name="Icelandic" 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/Azimut" title="Azimut – Italian" lang="it" hreflang="it" data-title="Azimut" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%96%D7%99%D7%9E%D7%95%D7%AA" title="אזימות – Hebrew" lang="he" hreflang="he" data-title="אזימות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%90%E1%83%96%E1%83%98%E1%83%9B%E1%83%A3%E1%83%A2%E1%83%98" title="აზიმუტი – Georgian" lang="ka" hreflang="ka" data-title="აზიმუტი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-csb mw-list-item"><a href="https://csb.wikipedia.org/wiki/Azym%C3%B9t" title="Azymùt – Kashubian" lang="csb" hreflang="csb" data-title="Azymùt" data-language-autonym="Kaszëbsczi" data-language-local-name="Kashubian" class="interlanguage-link-target"><span>Kaszëbsczi</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D0%B7%D0%B8%D0%BC%D1%83%D1%82" title="Азимут – Kazakh" lang="kk" hreflang="kk" data-title="Азимут" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D0%B7%D0%B8%D0%BC%D1%83%D1%82" title="Азимут – Kyrgyz" lang="ky" hreflang="ky" data-title="Азимут" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Azimuts" title="Azimuts – Latvian" lang="lv" hreflang="lv" data-title="Azimuts" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Azimut" title="Azimut – Luxembourgish" lang="lb" hreflang="lb" data-title="Azimut" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Azimutas" title="Azimutas – Lithuanian" lang="lt" hreflang="lt" data-title="Azimutas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Azimut" title="Azimut – Hungarian" lang="hu" hreflang="hu" data-title="Azimut" data-language-autonym="Magyar" data-language-local-name="Hungarian" 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%90%D0%B7%D0%B8%D0%BC%D1%83%D1%82" title="Азимут – Macedonian" lang="mk" hreflang="mk" data-title="Азимут" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A6%E0%B4%BF%E0%B4%97%E0%B4%82%E0%B4%B6%E0%B4%82" title="ദിഗംശം – Malayalam" lang="ml" hreflang="ml" data-title="ദിഗംശം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Azimut" title="Azimut – Malay" lang="ms" hreflang="ms" data-title="Azimut" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%90%D0%B7%D0%B8%D0%BC%D1%83%D1%82%D1%81%D1%8C" title="Азимутсь – Moksha" lang="mdf" hreflang="mdf" data-title="Азимутсь" data-language-autonym="Мокшень" data-language-local-name="Moksha" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%90%D0%B7%D0%B8%D0%BC%D1%83%D1%82" title="Азимут – Mongolian" lang="mn" hreflang="mn" data-title="Азимут" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Azimut" title="Azimut – Dutch" lang="nl" hreflang="nl" data-title="Azimut" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%96%B9%E4%BD%8D%E8%A7%92" title="方位角 – Japanese" lang="ja" hreflang="ja" data-title="方位角" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Asimut" title="Asimut – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Asimut" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Asimut" title="Asimut – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Asimut" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Azimut" title="Azimut – Uzbek" lang="uz" hreflang="uz" data-title="Azimut" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%84%D9%88%D8%B1%DB%8C_%D9%8A%D8%A7_%D8%B3%D9%85%D8%AA(%D8%B3%D8%AA%D9%88%D8%B1%DB%8C_%D9%BE%DB%90%DA%98%D9%86%D8%AF%D9%86%D9%87)" title="لوری يا سمت(ستوری پېژندنه) – Pashto" lang="ps" hreflang="ps" data-title="لوری يا سمت(ستوری پېژندنه)" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Azymut" title="Azymut – Polish" lang="pl" hreflang="pl" data-title="Azymut" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Azimute" title="Azimute – Portuguese" lang="pt" hreflang="pt" data-title="Azimute" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Azimut" title="Azimut – Romanian" lang="ro" hreflang="ro" data-title="Azimut" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%B7%D0%B8%D0%BC%D1%83%D1%82" title="Азимут – Russian" lang="ru" hreflang="ru" data-title="Азимут" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%90%D0%B0%D0%B7%D0%B8%D0%BC%D1%83%D1%82" title="Аазимут – Yakut" lang="sah" hreflang="sah" data-title="Аазимут" data-language-autonym="Саха тыла" data-language-local-name="Yakut" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Azimuti" title="Azimuti – Albanian" lang="sq" hreflang="sq" data-title="Azimuti" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%B7%D8%B1%D9%81" title="طرف – Sindhi" lang="sd" hreflang="sd" data-title="طرف" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Azimut" title="Azimut – Slovenian" lang="sl" hreflang="sl" data-title="Azimut" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-cu badge-Q70893996 mw-list-item" title=""><a href="https://cu.wikipedia.org/wiki/%D0%93%D1%94%D1%A1%D0%BB%D0%BE%D0%B3%D1%97%D1%87%D1%8C%D1%81%D0%BA%D1%8A_%D1%AB%D0%B3%D1%8A%D0%BB%D1%8A" title="Гєѡлогїчьскъ ѫгълъ – Church Slavic" lang="cu" hreflang="cu" data-title="Гєѡлогїчьскъ ѫгълъ" data-language-autonym="Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ" data-language-local-name="Church Slavic" class="interlanguage-link-target"><span>Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%B3%DB%95%D9%85%D8%AA" title="سەمت – Central Kurdish" lang="ckb" hreflang="ckb" data-title="سەمت" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D0%B7%D0%B8%D0%BC%D1%83%D1%82" title="Азимут – Serbian" lang="sr" hreflang="sr" data-title="Азимут" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Azimut" title="Azimut – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Azimut" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Atsimuutti" title="Atsimuutti – Finnish" lang="fi" hreflang="fi" data-title="Atsimuutti" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Azimut" title="Azimut – Swedish" lang="sv" hreflang="sv" data-title="Azimut" data-language-autonym="Svenska" data-language-local-name="Swedish" 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/Azimuth" title="Azimuth – Tagalog" lang="tl" hreflang="tl" data-title="Azimuth" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AE%BF%E0%AE%9A%E0%AF%88%E0%AE%B5%E0%AE%BF%E0%AE%B2%E0%AF%8D" title="திசைவில் – Tamil" lang="ta" hreflang="ta" data-title="திசைவில்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%90%D0%B7%D0%B8%D0%BC%D1%83%D1%82_(%D0%B3%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D1%8F)" title="Азимут (геодезия) – Tatar" lang="tt" hreflang="tt" data-title="Азимут (геодезия)" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A1%E0%B8%B8%E0%B8%A1%E0%B8%97%E0%B8%B4%E0%B8%A8" title="มุมทิศ – Thai" lang="th" hreflang="th" data-title="มุมทิศ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A1%D0%B0%D0%BC%D1%82_(%D1%81%D0%B8%D1%82%D0%BE%D1%80%D0%B0%D1%88%D0%B8%D0%BD%D0%BE%D1%81%D3%A3)" title="Самт (ситорашиносӣ) – Tajik" lang="tg" hreflang="tg" data-title="Самт (ситорашиносӣ)" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Azimut" title="Azimut – Turkish" lang="tr" hreflang="tr" data-title="Azimut" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D0%B7%D0%B8%D0%BC%D1%83%D1%82" title="Азимут – Ukrainian" lang="uk" hreflang="uk" data-title="Азимут" data-language-autonym="Українська" data-language-local-name="Ukrainian" 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%A7%D9%81%D9%82%DB%8C_%D8%B2%D8%A7%D9%88%DB%8C%DB%81" title="افقی زاویہ – Urdu" lang="ur" hreflang="ur" data-title="افقی زاویہ" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/G%C3%B3c_ph%C6%B0%C6%A1ng_v%E1%BB%8B" title="Góc phương vị – Vietnamese" lang="vi" hreflang="vi" data-title="Góc phương vị" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%96%B9%E4%BD%8D%E8%A7%92" title="方位角 – Wu" lang="wuu" hreflang="wuu" data-title="方位角" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%9C%B0%E5%B9%B3%E7%B6%93%E5%BA%A6" title="地平經度 – Cantonese" lang="yue" hreflang="yue" data-title="地平經度" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%96%B9%E4%BD%8D%E8%A7%92" title="方位角 – Chinese" lang="zh" hreflang="zh" data-title="方位角" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q124274#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</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="Namespaces"> <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/Azimuth" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Horizontal angle from north or other reference cardinal direction</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Azimuth_(disambiguation)" class="mw-disambig" title="Azimuth (disambiguation)">Azimuth (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Azimuth-Altitude_schematic.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Azimuth-Altitude_schematic.svg/220px-Azimuth-Altitude_schematic.svg.png" decoding="async" width="220" height="212" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Azimuth-Altitude_schematic.svg/330px-Azimuth-Altitude_schematic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Azimuth-Altitude_schematic.svg/440px-Azimuth-Altitude_schematic.svg.png 2x" data-file-width="436" data-file-height="420" /></a><figcaption>The azimuth is the angle formed between a reference direction (in this example north) and a <a href="/wiki/Sightline" class="mw-redirect" title="Sightline">line</a> from the observer to a point of interest projected on the same plane as the reference direction orthogonal to the <a href="/wiki/Zenith" title="Zenith">zenith</a>.</figcaption></figure> <p>An <b>azimuth</b> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="/æ/: 'a' in 'bad'">æ</span><span title="'z' in 'zoom'">z</span><span title="/ə/: 'a' in 'about'">ə</span><span title="'m' in 'my'">m</span><span title="/ə/: 'a' in 'about'">ə</span><span title="/θ/: 'th' in 'thigh'">θ</span></span>/</a></span> <span class="noprint"><span class="ext-phonos"><span data-nosnippet="" id="ooui-php-1" class="ext-phonos-PhonosButton noexcerpt ext-phonos-PhonosButton-emptylabel oo-ui-widget oo-ui-widget-enabled oo-ui-buttonElement oo-ui-buttonElement-frameless oo-ui-iconElement oo-ui-buttonWidget" data-ooui="{"_":"mw.Phonos.PhonosButton","href":"\/\/upload.wikimedia.org\/wikipedia\/commons\/transcoded\/c\/c4\/En-us-azimuth.ogg\/En-us-azimuth.ogg.mp3","rel":["nofollow"],"framed":false,"icon":"volumeUp","data":{"ipa":"","text":"","lang":"en","wikibase":"","file":"En-us-azimuth.ogg"},"classes":["ext-phonos-PhonosButton","noexcerpt","ext-phonos-PhonosButton-emptylabel"]}"><a role="button" tabindex="0" href="//upload.wikimedia.org/wikipedia/commons/transcoded/c/c4/En-us-azimuth.ogg/En-us-azimuth.ogg.mp3" rel="nofollow" aria-label="Play audio" title="Play audio" class="oo-ui-buttonElement-button"><span class="oo-ui-iconElement-icon oo-ui-icon-volumeUp"></span><span class="oo-ui-labelElement-label"></span><span class="oo-ui-indicatorElement-indicator oo-ui-indicatorElement-noIndicator"></span></a></span><sup class="ext-phonos-attribution noexcerpt navigation-not-searchable"><a href="/wiki/File:En-us-azimuth.ogg" title="File:En-us-azimuth.ogg">ⓘ</a></sup></span></span></span>; from <a href="/wiki/Arabic_language" class="mw-redirect" title="Arabic language">Arabic</a>: <span lang="ar" dir="rtl">اَلسُّمُوت</span>, <small><a href="/wiki/Romanization_of_Arabic" title="Romanization of Arabic">romanized</a>: </small><span title="Arabic-language romanization"><i lang="ar-Latn">as-sumūt</i></span>, <small><a href="/wiki/Literal_translation" title="Literal translation">lit.</a> </small>'the directions')<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> is the <a href="/wiki/Horizon" title="Horizon">horizontal</a> <a href="/wiki/Angle#Measuring_angles" title="Angle">angle</a> from a <a href="/wiki/Cardinal_direction" title="Cardinal direction">cardinal direction</a>, most commonly <a href="/wiki/North" title="North">north</a>, in a local or observer-centric <a href="/wiki/Spherical_coordinate_system" title="Spherical coordinate system">spherical coordinate system</a>. </p><p>Mathematically, the <a href="/wiki/Relative_position" class="mw-redirect" title="Relative position">relative position</a> <a href="/wiki/Vector_(physics_and_mathematics)" class="mw-redirect" title="Vector (physics and mathematics)">vector</a> from an observer (<a href="/wiki/Origin_(mathematics)" title="Origin (mathematics)">origin</a>) to a point of interest is <a href="/wiki/Graphical_projection" class="mw-redirect" title="Graphical projection">projected</a> <a href="/wiki/Perpendicular" title="Perpendicular">perpendicularly</a> onto a <a href="/wiki/Reference_plane" class="mw-redirect" title="Reference plane">reference plane</a> (the <a href="/wiki/Horizontal_plane" class="mw-redirect" title="Horizontal plane">horizontal plane</a>); the angle between the projected vector and a reference vector on the reference plane is called the azimuth. </p><p>When used as a <a href="/wiki/Horizontal_coordinate_system" title="Horizontal coordinate system">celestial coordinate</a>, the azimuth is the <a href="/wiki/Horizon" title="Horizon">horizontal</a> direction of a <a href="/wiki/Star" title="Star">star</a> or other <a href="/wiki/Astronomical_object" title="Astronomical object">astronomical object</a> in the <a href="/wiki/Sky" title="Sky">sky</a>. The star is the point of interest, the reference plane is the local area (e.g. a circular area with a 5 km radius at <a href="/wiki/Sea_level" title="Sea level">sea level</a>) around an observer on <a href="/wiki/Planetary_surface" title="Planetary surface">Earth's surface</a>, and the reference vector points to <a href="/wiki/True_north" title="True north">true north</a>. The azimuth is the angle between the north vector and the star's vector on the <a href="/wiki/Horizontal_plane" class="mw-redirect" title="Horizontal plane">horizontal plane</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Azimuth is usually measured in <a href="/wiki/Degree_(angle)" title="Degree (angle)">degrees</a> (°), in the positive range 0° to 360° or in the signed range -180° to +180°. The concept is used in <a href="/wiki/Navigation" title="Navigation">navigation</a>, <a href="/wiki/Astrometry" title="Astrometry">astronomy</a>, <a href="/wiki/Engineering" title="Engineering">engineering</a>, <a href="/wiki/Map" title="Map">mapping</a>, <a href="/wiki/Mining" title="Mining">mining</a>, and <a href="/wiki/Ballistics" title="Ballistics">ballistics</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etymology">Etymology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=1" title="Edit section: Etymology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The word azimuth is used in all European languages today. It originates from medieval Arabic السموت (<i>al-sumūt</i>, pronounced <i>as-sumūt</i>), meaning "the directions" (plural of Arabic السمت <i>al-samt</i> = "the direction"). The Arabic word entered late medieval Latin in an astronomy context and in particular in the use of the Arabic version of the <a href="/wiki/Astrolabe" title="Astrolabe">astrolabe</a> astronomy instrument. Its first recorded use in English is in the 1390s in <a href="/wiki/Geoffrey_Chaucer" title="Geoffrey Chaucer">Geoffrey Chaucer</a>'s <i><a href="/wiki/Treatise_on_the_Astrolabe" class="mw-redirect" title="Treatise on the Astrolabe">Treatise on the Astrolabe</a></i>. The first known record in any Western language is in Spanish in the 1270s in an astronomy book that was largely derived from Arabic sources, the <i><a href="/wiki/Libros_del_saber_de_astronom%C3%ADa" title="Libros del saber de astronomía">Libros del saber de astronomía</a></i> commissioned by <a href="/wiki/King_Alfonso_X" class="mw-redirect" title="King Alfonso X">King Alfonso X</a> of Castile.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="In_astronomy">In astronomy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=2" title="Edit section: In astronomy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Horizontal_coordinate_system" title="Horizontal coordinate system">Horizontal coordinate system</a></div> <p>In the <a href="/wiki/Horizontal_coordinate_system" title="Horizontal coordinate system">horizontal coordinate system</a>, used in <a href="/wiki/Celestial_navigation" title="Celestial navigation">celestial navigation</a>, azimuth is one of the two <a href="/wiki/Coordinate_system" title="Coordinate system">coordinates</a>.<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> The other is <i><a href="/wiki/Altitude_(astronomy)" class="mw-redirect" title="Altitude (astronomy)">altitude</a></i>, sometimes called elevation above the horizon. It is also used for <a href="/wiki/Satellite_dish" title="Satellite dish">satellite dish</a> installation (see also: <a href="/wiki/Sat_finder" class="mw-redirect" title="Sat finder">sat finder</a>). In modern <a href="/wiki/Astronomy" title="Astronomy">astronomy</a> azimuth is nearly always measured from the north. </p> <div class="mw-heading mw-heading2"><h2 id="In_navigation">In navigation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=3" title="Edit section: In navigation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Azimuth_(navigation)" class="mw-redirect" title="Azimuth (navigation)">Azimuth (navigation)</a></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:True_North_Mount_Allen.fw.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/True_North_Mount_Allen.fw.png/220px-True_North_Mount_Allen.fw.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/True_North_Mount_Allen.fw.png/330px-True_North_Mount_Allen.fw.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/True_North_Mount_Allen.fw.png/440px-True_North_Mount_Allen.fw.png 2x" data-file-width="3264" data-file-height="2448" /></a><figcaption>Azimuth marker, Mount Allen (<a href="/wiki/Sandstone_Peak" title="Sandstone Peak">Sandstone Peak</a>), southern California, US</figcaption></figure><p> In land navigation, azimuth is usually denoted <a href="/wiki/Alpha" title="Alpha">alpha</a>, <i>α</i>, and defined as a horizontal angle measured <a href="/wiki/Clockwise_and_counterclockwise" class="mw-redirect" title="Clockwise and counterclockwise">clockwise</a> from a north base line or <i><a href="/wiki/Meridian_(geography)" title="Meridian (geography)">meridian</a></i>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> <i>Azimuth</i> has also been more generally defined as a horizontal angle measured clockwise from any fixed reference plane or easily established base direction line.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Today, the reference plane for an azimuth is typically <a href="/wiki/True_north" title="True north">true north</a>, measured as a 0° azimuth, though other angular units (<a href="/wiki/Grad_(angle)" class="mw-redirect" title="Grad (angle)">grad</a>, <a href="/wiki/Angular_mil" class="mw-redirect" title="Angular mil">mil</a>) can be used. Moving clockwise on a 360 degree circle, east has azimuth 90°, south 180°, and west 270°. There are exceptions: some navigation systems use south as the reference vector. Any direction can be the reference vector, as long as it is clearly defined. </p><p>Quite commonly, azimuths or compass bearings are stated in a system in which either north or south can be the zero, and the angle may be measured clockwise or anticlockwise from the zero. For example, a bearing might be described as "(from) south, (turn) thirty degrees (toward the) east" (the words in brackets are usually omitted), abbreviated "S30°E", which is the bearing 30 degrees in the eastward direction from south, i.e. the bearing 150 degrees clockwise from north. The reference direction, stated first, is always north or south, and the turning direction, stated last, is east or west. The directions are chosen so that the angle, stated between them, is positive, between zero and 90 degrees. If the bearing happens to be exactly in the direction of one of the <a href="/wiki/Cardinal_point" class="mw-redirect" title="Cardinal point">cardinal points</a>, a different notation, e.g. "due east", is used instead. </p> <div class="mw-heading mw-heading3"><h3 id="True_north-based_azimuths">True north-based azimuths</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=4" title="Edit section: True north-based azimuths"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="display:inline-table; margin-right:2em;"> <table class="wikitable" style="text-align:center;"> <caption>From north, eastern side </caption> <tbody><tr> <th scope="col">Direction </th> <th scope="col">Azimuth </th></tr> <tr> <th scope="row">North </th> <td>0° </td></tr> <tr> <th scope="row">North-northeast </th> <td>22.5° </td></tr> <tr> <th scope="row">Northeast </th> <td>45° </td></tr> <tr> <th scope="row">East-northeast </th> <td>67.5° </td></tr> <tr> <th scope="row">East </th> <td>90° </td></tr> <tr> <th scope="row">East-southeast </th> <td>112.5° </td></tr> <tr> <th scope="row">Southeast </th> <td>135° </td></tr> <tr> <th scope="row">South-southeast </th> <td>157.5° </td></tr></tbody></table> </div> <div style="display:inline-table"> <table class="wikitable" style="text-align:center;"> <caption>From north, western side </caption> <tbody><tr> <th scope="col">Direction </th> <th scope="col">Azimuth </th></tr> <tr> <th scope="row">South </th> <td>180° </td></tr> <tr> <th scope="row">South-southwest </th> <td>202.5° </td></tr> <tr> <th scope="row">Southwest </th> <td>225° </td></tr> <tr> <th scope="row">West-southwest </th> <td>247.5° </td></tr> <tr> <th scope="row">West </th> <td>270° </td></tr> <tr> <th scope="row">West-northwest </th> <td>292.5° </td></tr> <tr> <th scope="row">Northwest </th> <td>315° </td></tr> <tr> <th scope="row">North-northwest </th> <td>337.5° </td></tr></tbody></table> </div> <div class="mw-heading mw-heading2"><h2 id="In_geodesy">In geodesy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=5" title="Edit section: In geodesy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Inverse_geodetic_problem" class="mw-redirect" title="Inverse geodetic problem">Inverse geodetic problem</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Earth_section_paths#Inverse_problem" title="Earth section paths">Earth section paths § Inverse problem</a>, <a href="/wiki/Vincenty%27s_formulae#Inverse_problem" title="Vincenty's formulae">Vincenty's formulae § Inverse problem</a>, and <a href="/wiki/Geographical_distance#Ellipsoidal-surface_formulae" title="Geographical distance">Geographical distance § Ellipsoidal-surface formulae</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Bearing_and_azimuth_along_the_geodesic.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Bearing_and_azimuth_along_the_geodesic.png/220px-Bearing_and_azimuth_along_the_geodesic.png" decoding="async" width="220" height="278" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Bearing_and_azimuth_along_the_geodesic.png/330px-Bearing_and_azimuth_along_the_geodesic.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/Bearing_and_azimuth_along_the_geodesic.png/440px-Bearing_and_azimuth_along_the_geodesic.png 2x" data-file-width="632" data-file-height="800" /></a><figcaption>The azimuth between <a href="/wiki/Cape_Town" title="Cape Town">Cape Town</a> and <a href="/wiki/Melbourne" title="Melbourne">Melbourne</a> along the <a href="/wiki/Geodesic" title="Geodesic">geodesic</a> (the shortest route) changes from 141° to 42°. <a href="/wiki/Orthographic_projection_in_cartography" class="mw-redirect" title="Orthographic projection in cartography">Azimuthal orthographic projection</a> and <a href="/wiki/Miller_cylindrical_projection" title="Miller cylindrical projection">Miller cylindrical projection</a>.</figcaption></figure> <p>We are standing at latitude <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7daf493c8f6ef669c04c7b9715532fc35d12d60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.574ex; height:2.176ex;" alt="{\displaystyle \varphi _{1}}"></span>, longitude zero; we want to find the azimuth from our viewpoint to Point 2 at latitude <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c08631714273b6c8edaa9573ef3d8c548314a930" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.574ex; height:2.176ex;" alt="{\displaystyle \varphi _{2}}"></span>, longitude <i>L</i> (positive eastward). We can get a fair approximation by assuming the Earth is a sphere, in which case the azimuth <i>α</i> is given by </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 \tan \alpha ={\frac {\sin L}{\cos \varphi _{1}\tan \varphi _{2}-\sin \varphi _{1}\cos L}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>L</mi> </mrow> <mrow> <mi>cos</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mi>L</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan \alpha ={\frac {\sin L}{\cos \varphi _{1}\tan \varphi _{2}-\sin \varphi _{1}\cos L}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/932f343d8a785838aae407d2f5d005ea89a72328" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:36.075ex; height:5.676ex;" alt="{\displaystyle \tan \alpha ={\frac {\sin L}{\cos \varphi _{1}\tan \varphi _{2}-\sin \varphi _{1}\cos L}}}"></span></dd></dl> <p>A better approximation assumes the Earth is a slightly-squashed sphere (an <i><a href="/wiki/Oblate_spheroid" class="mw-redirect" title="Oblate spheroid">oblate spheroid</a></i>); <i>azimuth</i> then has at least two very slightly different meanings. <b><a href="/wiki/Earth_normal_section" class="mw-redirect" title="Earth normal section">Normal-section</a> azimuth</b> is the angle measured at our viewpoint by a <a href="/wiki/Theodolite" title="Theodolite">theodolite</a> whose axis is perpendicular to the surface of the spheroid; <b>geodetic azimuth</b> (or <b>geodesic azimuth</b>) is the angle between north and the <a href="/wiki/Ellipsoidal_geodesic" class="mw-redirect" title="Ellipsoidal geodesic">ellipsoidal geodesic</a> (the shortest path on the surface of the spheroid from our viewpoint to Point 2). The difference is usually negligible: less than 0.03 arc second for distances less than 100 km.<sup id="cite_ref-T&G_10-0" class="reference"><a href="#cite_note-T&G-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Normal-section azimuth can be calculated as follows:<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2022)">citation needed</span></a></i>]</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}e^{2}&=f(2-f)\\1-e^{2}&=(1-f)^{2}\\\Lambda &=\left(1-e^{2}\right){\frac {\tan \varphi _{2}}{\tan \varphi _{1}}}+e^{2}{\sqrt {\frac {1+\left(1-e^{2}\right)\left(\tan \varphi _{2}\right)^{2}}{1+\left(1-e^{2}\right)\left(\tan \varphi _{1}\right)^{2}}}}\\\tan \alpha &={\frac {\sin L}{(\Lambda -\cos L)\sin \varphi _{1}}}\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> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mo>−</mo> <mi>f</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> <mtd> <mi></mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>f</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <mi mathvariant="normal">Λ</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>L</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Λ</mi> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mi>L</mi> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}e^{2}&=f(2-f)\\1-e^{2}&=(1-f)^{2}\\\Lambda &=\left(1-e^{2}\right){\frac {\tan \varphi _{2}}{\tan \varphi _{1}}}+e^{2}{\sqrt {\frac {1+\left(1-e^{2}\right)\left(\tan \varphi _{2}\right)^{2}}{1+\left(1-e^{2}\right)\left(\tan \varphi _{1}\right)^{2}}}}\\\tan \alpha &={\frac {\sin L}{(\Lambda -\cos L)\sin \varphi _{1}}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/598caaa71e94ddb4a9e3406f290abc62fede2cf1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -9.616ex; margin-bottom: -0.222ex; width:55.598ex; height:20.843ex;" alt="{\displaystyle {\begin{aligned}e^{2}&=f(2-f)\\1-e^{2}&=(1-f)^{2}\\\Lambda &=\left(1-e^{2}\right){\frac {\tan \varphi _{2}}{\tan \varphi _{1}}}+e^{2}{\sqrt {\frac {1+\left(1-e^{2}\right)\left(\tan \varphi _{2}\right)^{2}}{1+\left(1-e^{2}\right)\left(\tan \varphi _{1}\right)^{2}}}}\\\tan \alpha &={\frac {\sin L}{(\Lambda -\cos L)\sin \varphi _{1}}}\end{aligned}}}"></span></dd></dl> <p>where <i>f</i> is the flattening and <i>e</i> the eccentricity for the chosen spheroid (e.g., <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num">1</span>⁄<span class="den"><span class="nowrap"><span data-sort-value="7002298257223563000♠"></span>298.257<span style="margin-left:.25em;">223</span><span style="margin-left:.25em;">563</span></span></span></span> for <a href="/wiki/World_Geodetic_System" title="World Geodetic System">WGS84</a>). If <i>φ</i><sub>1</sub> = 0 then </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 \tan \alpha ={\frac {\sin L}{\left(1-e^{2}\right)\tan \varphi _{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mi>L</mi> </mrow> <mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mi>tan</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan \alpha ={\frac {\sin L}{\left(1-e^{2}\right)\tan \varphi _{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42fcfaa7e73bf729ec2d5c2e379cb041a54603a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:23.827ex; height:6.009ex;" alt="{\displaystyle \tan \alpha ={\frac {\sin L}{\left(1-e^{2}\right)\tan \varphi _{2}}}}"></span></dd></dl> <p>To calculate the azimuth of the Sun or a star given its <a href="/wiki/Declination" title="Declination">declination</a> and <a href="/wiki/Hour_angle" title="Hour angle">hour angle</a> at a specific location, modify the formula for a spherical Earth. Replace <i>φ</i><sub>2</sub> with declination and longitude difference with hour angle, and change the sign (since the hour angle is positive westward instead of east).<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2022)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="In_cartography">In cartography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=6" title="Edit section: In cartography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Brunton.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Brunton.JPG/220px-Brunton.JPG" decoding="async" width="220" height="156" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Brunton.JPG/330px-Brunton.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Brunton.JPG/440px-Brunton.JPG 2x" data-file-width="3648" data-file-height="2593" /></a><figcaption>A standard Brunton Geo <a href="/wiki/Compass" title="Compass">compass</a>, commonly used by geologists and surveyors to measure azimuth</figcaption></figure> <p>The <b>cartographical azimuth</b> or <b>grid azimuth</b> (in decimal degrees) can be calculated when the coordinates of 2 points are known in a flat plane (<a href="/wiki/Spatial_reference_system" title="Spatial reference system">cartographical coordinates</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 \alpha ={\frac {180}{\pi }}\operatorname {atan2} (X_{2}-X_{1},Y_{2}-Y_{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>180</mn> <mi>π</mi> </mfrac> </mrow> <mi>atan2</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ={\frac {180}{\pi }}\operatorname {atan2} (X_{2}-X_{1},Y_{2}-Y_{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e674fc0bf4b1eff38a3c3c399b0864f7fe68612" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:34.272ex; height:5.176ex;" alt="{\displaystyle \alpha ={\frac {180}{\pi }}\operatorname {atan2} (X_{2}-X_{1},Y_{2}-Y_{1})}"></span></dd></dl> <p>Remark that the reference axes are swapped relative to the (counterclockwise) mathematical <a href="/wiki/Polar_coordinate_system" title="Polar coordinate system">polar coordinate system</a> and that the azimuth is clockwise relative to the north. This is the reason why the X and Y axis in the above formula are swapped. If the azimuth becomes negative, one can always add 360°. </p><p>The formula in <a href="/wiki/Radian" title="Radian">radians</a> would be slightly easier: </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 =\operatorname {atan2} (X_{2}-X_{1},Y_{2}-Y_{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> <mi>atan2</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha =\operatorname {atan2} (X_{2}-X_{1},Y_{2}-Y_{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3647a3fed22ea218b98dc4300e74c5c7cd4d4ef1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:29.561ex; height:2.843ex;" alt="{\displaystyle \alpha =\operatorname {atan2} (X_{2}-X_{1},Y_{2}-Y_{1})}"></span></dd></dl> <p>Note the swapped <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41cf50e4a314ca8e2c30964baa8d26e5be7a9386" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.328ex; height:2.843ex;" alt="{\displaystyle (x,y)}"></span> in contrast to the normal <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 (y,x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>y</mi> <mo>,</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (y,x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec736777360ba7cbdabf050bc448d33ec5e266b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.328ex; height:2.843ex;" alt="{\displaystyle (y,x)}"></span> <a href="/wiki/Atan2" title="Atan2">atan2</a> input order. </p><p>The opposite problem occurs when the coordinates (<i>X</i><sub>1</sub>, <i>Y</i><sub>1</sub>) of one point, the distance <i>D</i>, and the azimuth <i>α</i> to another point (<i>X</i><sub>2</sub>, <i>Y</i><sub>2</sub>) are known, one can calculate its coordinates: </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_{2}&=X_{1}+D\sin \alpha \\Y_{2}&=Y_{1}+D\cos \alpha \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> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>D</mi> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi>D</mi> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}X_{2}&=X_{1}+D\sin \alpha \\Y_{2}&=Y_{1}+D\cos \alpha \end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b352cb255c124478144a259ce854defcdabe4385" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:19.689ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}X_{2}&=X_{1}+D\sin \alpha \\Y_{2}&=Y_{1}+D\cos \alpha \end{aligned}}}"></span></dd></dl> <p>This is typically used in <a href="/wiki/Triangulation" title="Triangulation">triangulation</a> and azimuth identification (AzID), especially in <a href="/wiki/Radar" title="Radar">radar</a> applications. </p> <div class="mw-heading mw-heading3"><h3 id="Map_projections">Map projections</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=7" title="Edit section: Map projections"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There is a wide variety of <a href="/wiki/Map_projection#Azimuthal_.28projections_onto_a_plane.29" title="Map projection">azimuthal map projections</a>. They all have the property that directions (the azimuths) from a central point are preserved. Some navigation systems use south as the reference plane. However, any direction can serve as the plane of reference, as long as it is clearly defined for everyone using that system. </p> <table align="left"> <tbody><tr> <td><div class="thumb tnone" style="margin-left:auto;margin-right:auto;overflow:hidden;width:auto;max-width:828px"><div class="thumbinner"><div class="noresize" style="overflow:auto"><span typeof="mw:File"><a href="/wiki/File:Comparison_azimuthal_projections.svg" class="mw-file-description" title="Comparison of some azimuthal projections centred on 90° N at the same scale, ordered by projection altitude in Earth radii. (click for detail)"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Comparison_azimuthal_projections.svg/820px-Comparison_azimuthal_projections.svg.png" decoding="async" width="820" height="274" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Comparison_azimuthal_projections.svg/1230px-Comparison_azimuthal_projections.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Comparison_azimuthal_projections.svg/1640px-Comparison_azimuthal_projections.svg.png 2x" data-file-width="512" data-file-height="171" /></a></span></div><div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Comparison_azimuthal_projections.svg" title="File:Comparison azimuthal projections.svg"> </a></div>Comparison of some azimuthal projections centred on 90° N at the same scale, ordered by projection altitude in Earth radii. <a class="external text" href="https://upload.wikimedia.org/wikipedia/commons/b/ba/Comparison_azimuthal_projections.svg">(click for detail)</a></div></div></div> </td></tr></tbody></table> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2"><h2 id="Related_coordinates">Related coordinates</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=8" title="Edit section: Related coordinates"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Right_ascension">Right ascension</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=9" title="Edit section: Right ascension"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If, instead of measuring from and along the horizon, the angles are measured from and along the <a href="/wiki/Celestial_equator" title="Celestial equator">celestial equator</a>, the angles are called <a href="/wiki/Right_ascension" title="Right ascension">right ascension</a> if referenced to the Vernal Equinox, or hour angle if referenced to the <a href="/wiki/Celestial_meridian" class="mw-redirect" title="Celestial meridian">celestial meridian</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Polar_coordinate">Polar coordinate</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=10" title="Edit section: Polar coordinate"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In mathematics, the azimuth angle of a point in <a href="/wiki/Cylindrical_coordinate_system" title="Cylindrical coordinate system">cylindrical coordinates</a> or <a href="/wiki/Spherical_coordinate_system" title="Spherical coordinate system">spherical coordinates</a> is the anticlockwise <a href="/wiki/Angle" title="Angle">angle</a> between the positive <i>x</i>-axis and the projection of the <a href="/wiki/Vector_(geometry)" class="mw-redirect" title="Vector (geometry)">vector</a> onto the <i>xy</i>-<a href="/wiki/Plane_(mathematics)" title="Plane (mathematics)">plane</a>. A special case of an azimuth angle is the angle in <a href="/wiki/Polar_coordinates" class="mw-redirect" title="Polar coordinates">polar coordinates</a> of the component of the vector in the <i>xy</i>-plane, although this angle is normally measured in <a href="/wiki/Radian" title="Radian">radians</a> rather than degrees and denoted by <i>θ</i> rather than <i>φ</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Other_uses">Other uses</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=11" title="Edit section: Other uses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For <a href="/wiki/Tape_drive" title="Tape drive">magnetic tape drives</a>, <i>azimuth</i> refers to the angle between the tape head(s) and tape. </p><p>In <a href="/wiki/Sound_localization" title="Sound localization">sound localization</a> experiments and literature, the <i>azimuth</i> refers to the angle the sound source makes compared to the imaginary straight line that is drawn from within the head through the area between the eyes. </p><p>An <a href="/wiki/Azimuth_thruster" title="Azimuth thruster">azimuth thruster</a> in <a href="/wiki/Shipbuilding" title="Shipbuilding">shipbuilding</a> is a <a href="/wiki/Propeller" title="Propeller">propeller</a> that can be rotated horizontally. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=12" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 21em;"> <ul><li><a href="/wiki/Altitude_(astronomy)" class="mw-redirect" title="Altitude (astronomy)">Altitude (astronomy)</a></li> <li><a href="/wiki/Angular_displacement" title="Angular displacement">Angular displacement</a></li> <li><a href="/wiki/Azimuthal_quantum_number" title="Azimuthal quantum number">Azimuthal quantum number</a></li> <li><a href="/wiki/Azimuthal_equidistant_projection" title="Azimuthal equidistant projection">Azimuthal equidistant projection</a></li> <li><a href="/wiki/Azimuth_recording" title="Azimuth recording">Azimuth recording</a></li> <li><a href="/wiki/Bearing_(navigation)" title="Bearing (navigation)">Bearing (navigation)</a></li> <li><a href="/wiki/Clock_position" title="Clock position">Clock position</a></li> <li><a href="/wiki/Course_(navigation)" 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a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle">Astrodynamics</th></tr><tr><td class="sidebar-image" style="padding-bottom:0.85em;"><span typeof="mw:File"><a href="/wiki/File:Orbit_mechanics_icon.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Orbit_mechanics_icon.svg/60px-Orbit_mechanics_icon.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Orbit_mechanics_icon.svg/90px-Orbit_mechanics_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Orbit_mechanics_icon.svg/120px-Orbit_mechanics_icon.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span></td></tr><tr><th class="sidebar-heading" style="padding-bottom:0.55em;"> <div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Orbital_mechanics" title="Orbital mechanics"><span style="font-size:110%;">Orbital mechanics</span></a></div></th></tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Orbital_elements" title="Orbital elements">Orbital elements</a></div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"> <ul><li><a href="/wiki/Apsis" title="Apsis">Apsis</a></li> <li><a href="/wiki/Argument_of_periapsis" title="Argument of periapsis">Argument of periapsis</a></li> <li><a href="/wiki/Orbital_eccentricity" title="Orbital eccentricity">Eccentricity</a></li> <li><a href="/wiki/Orbital_inclination" title="Orbital inclination">Inclination</a></li> <li><a href="/wiki/Mean_anomaly" title="Mean anomaly">Mean anomaly</a></li> <li><a href="/wiki/Orbital_node" title="Orbital node">Orbital nodes</a></li> <li><a href="/wiki/Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">Semi-major axis</a></li> <li><a href="/wiki/True_anomaly" title="True anomaly">True anomaly</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Types of <a href="/wiki/Two-body_problem" title="Two-body problem">two-body orbits</a> by <br />eccentricity</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"> <ul><li><a href="/wiki/Circular_orbit" title="Circular orbit">Circular orbit</a></li> <li><a href="/wiki/Elliptic_orbit" title="Elliptic orbit">Elliptic orbit</a></li></ul> <div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Transfer_orbit" title="Transfer orbit">Transfer orbit</a> <div class="hlist" style="font-size:90%"><ul><li>(<a href="/wiki/Hohmann_transfer_orbit" title="Hohmann transfer orbit">Hohmann transfer orbit</a></li><li><a href="/wiki/Bi-elliptic_transfer" title="Bi-elliptic transfer">Bi-elliptic transfer orbit</a>)</li></ul></div></div> <ul><li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Parabolic orbit</a></li> <li><a href="/wiki/Hyperbolic_trajectory" title="Hyperbolic trajectory">Hyperbolic orbit</a></li> <li><a href="/wiki/Radial_trajectory" title="Radial trajectory">Radial orbit</a></li> <li><a href="/wiki/Orbital_decay" title="Orbital decay">Decaying orbit</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Equations</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"> <ul><li><a href="/wiki/Dynamical_friction" title="Dynamical friction">Dynamical friction</a></li> <li><a href="/wiki/Escape_velocity" title="Escape velocity">Escape velocity</a></li> <li><a href="/wiki/Kepler%27s_equation" title="Kepler's equation">Kepler's equation</a></li> <li><a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws of planetary motion</a></li> <li><a href="/wiki/Orbital_period" title="Orbital period">Orbital period</a></li> <li><a href="/wiki/Orbital_speed" title="Orbital speed">Orbital velocity</a></li> <li><a href="/wiki/Surface_gravity" title="Surface gravity">Surface gravity</a></li> <li><a href="/wiki/Specific_orbital_energy" title="Specific orbital energy">Specific orbital energy</a></li> <li><a href="/wiki/Vis-viva_equation" title="Vis-viva equation">Vis-viva equation</a></li></ul></div></div></td> </tr><tr><th class="sidebar-heading" style="padding-bottom:0.55em;"> <div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Celestial_mechanics" title="Celestial mechanics"><span style="font-size:110%;">Celestial mechanics</span></a></div></th></tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Gravitational influences</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"> <ul><li><a href="/wiki/Barycenter" class="mw-redirect" title="Barycenter">Barycenter</a></li> <li><a href="/wiki/Hill_sphere" title="Hill sphere">Hill sphere</a></li> <li><a href="/wiki/Perturbation_(astronomy)" title="Perturbation (astronomy)">Perturbations</a></li> <li><a href="/wiki/Sphere_of_influence_(astrodynamics)" title="Sphere of influence (astrodynamics)">Sphere of influence</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/N-body_problem" title="N-body problem">N-body orbits</a></div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Lagrange_point" title="Lagrange point">Lagrangian points</a> <div class="hlist" style="font-size:90%"><ul><li>(<a href="/wiki/Halo_orbit" title="Halo orbit">Halo orbits</a>)</li></ul></div></div> <ul><li><a href="/wiki/Lissajous_orbit" title="Lissajous orbit">Lissajous orbits</a></li> <li><a href="/wiki/Lyapunov_stability" title="Lyapunov stability">Lyapunov orbits</a></li></ul></div></div></td> </tr><tr><th class="sidebar-heading" style="padding-bottom:0.55em;"> <div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Aerospace_engineering" title="Aerospace engineering"><span style="font-size:110%;">Engineering and efficiency</span></a></div></th></tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Preflight engineering</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"> <ul><li><a href="/wiki/Mass_ratio" title="Mass ratio">Mass ratio</a></li> <li><a href="/wiki/Payload_fraction" title="Payload fraction">Payload fraction</a></li> <li><a href="/wiki/Propellant_mass_fraction" title="Propellant mass fraction">Propellant mass fraction</a></li> <li><a href="/wiki/Tsiolkovsky_rocket_equation" title="Tsiolkovsky rocket equation">Tsiolkovsky rocket equation</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Efficiency measures</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"> <ul><li><a href="/wiki/Gravity_assist" title="Gravity assist">Gravity assist</a></li> <li><a href="/wiki/Oberth_effect" title="Oberth effect">Oberth effect</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Propulsive maneuvers</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"> <ul><li><a href="/wiki/Orbital_maneuver" title="Orbital maneuver">Orbital maneuver</a></li> <li><a href="/wiki/Orbit_insertion" title="Orbit insertion">Orbit insertion</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 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class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=13" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">The singular form of the noun is <a href="/wiki/Arabic_language" class="mw-redirect" title="Arabic language">Arabic</a>: <span lang="ar" dir="rtl">السَّمْت</span>, <small><a href="/wiki/Romanization_of_Arabic" title="Romanization of Arabic">romanized</a>: </small><span title="Arabic-language romanization"><i lang="ar-Latn">as-samt</i></span>, <small><a href="/wiki/Literal_translation" title="Literal translation">lit.</a> </small>'the direction'.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation encyclopaedia cs1"><a rel="nofollow" class="external text" href="https://www.dictionary.com/browse/azimuth">"azimuth"</a>. <i><a href="/wiki/Dictionary.com" title="Dictionary.com">Dictionary.com Unabridged</a></i> (Online). n.d.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=azimuth&rft.btitle=Dictionary.com+Unabridged&rft_id=https%3A%2F%2Fwww.dictionary.com%2Fbrowse%2Fazimuth&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAzimuth" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">"Azimuth" at <a rel="nofollow" class="external text" href="https://archive.org/stream/oed01arch#page/602/mode/1up"><i>New English Dictionary on Historical Principles</i></a>; "azimut" at <a rel="nofollow" class="external text" href="http://www.cnrtl.fr/definition/azimut"><i>Centre National de Ressources Textuelles et Lexicales</i></a>; "al-Samt" at <a rel="nofollow" class="external text" href="http://referenceworks.brillonline.com/entries/encyclopaedia-of-islam-2/al-samt-SIM_6591"><i>Brill's Encyclopedia of Islam</i></a>; "azimuth" at <a rel="nofollow" class="external text" href="http://englishwordsofarabicancestry.wordpress.com/#cite_note-39">EnglishWordsOfArabicAncestry.wordpress.com</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140102020035/http://englishwordsofarabicancestry.wordpress.com/#cite_note-39">Archived</a> January 2, 2014, at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. In Arabic the written <i>al-sumūt</i> is always pronounced <i>as-sumūt</i> (see <a href="/wiki/Sun_and_moon_letters" title="Sun and moon letters">pronunciation of "al-" in Arabic</a>).</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Rutstrum, Carl, <i>The Wilderness Route Finder</i>, University of Minnesota Press (2000), <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8166-3661-3" title="Special:BookSources/0-8166-3661-3">0-8166-3661-3</a>, p. 194</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">U.S. Army, <i>Map Reading and Land Navigation</i>, FM 21-26, Headquarters, Dept. of the Army, Washington, D.C. (7 May 1993), ch. 6, p. 2</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">U.S. Army, <i>Map Reading and Land Navigation</i>, FM 21-26, Headquarters, Dept. of the Army, Washington, D.C. (28 March 1956), ch. 3, p. 63</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">U.S. Army, ch. 6 p. 2</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">U.S. Army, <i>Advanced Map and Aerial Photograph Reading</i>, Headquarters, War Department, Washington, D.C. (17 September 1941), pp. 24–25</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">U.S. Army, <i>Advanced Map and Aerial Photograph Reading</i>, Headquarters, War Department, Washington, D.C. (23 December 1944), p. 15</span> </li> <li id="cite_note-T&G-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-T&G_10-0">^</a></b></span> <span class="reference-text">Torge & Müller (2012) Geodesy, De Gruyter, eq.6.70, p.248</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=14" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Rutstrum, Carl, <i>The Wilderness Route Finder</i>, University of Minnesota Press (2000), <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8166-3661-3" title="Special:BookSources/0-8166-3661-3">0-8166-3661-3</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuth&action=edit&section=15" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.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><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/azimuth" class="extiw" title="wiktionary:azimuth">azimuth</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1"><span class="cs1-ws-icon" title="s:1911 Encyclopædia Britannica/Azimuth"><a class="external text" href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Azimuth">"Azimuth" </a></span>. <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i> (11th ed.). 1911.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Azimuth&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.edition=11th&rft.date=1911&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAzimuth" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1"><span class="cs1-ws-icon" title="s:Collier's New Encyclopedia (1921)/Azimuth"><a class="external text" href="https://en.wikisource.org/wiki/Collier%27s_New_Encyclopedia_(1921)/Azimuth">"Azimuth" </a></span>. <i><a href="/wiki/Collier%27s_Encyclopedia" title="Collier's Encyclopedia">Collier's New Encyclopedia</a></i>. 1921.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Azimuth&rft.btitle=Collier%27s+New+Encyclopedia&rft.date=1921&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAzimuth" class="Z3988"></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r1130092004">.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;justify-content:center;align-items:baseline}.mw-parser-output .portal-bar-bordered{padding:0 2em;background-color:#fdfdfd;border:1px solid #a2a9b1;clear:both;margin:1em auto 0}.mw-parser-output .portal-bar-related{font-size:100%;justify-content:flex-start}.mw-parser-output .portal-bar-unbordered{padding:0 1.7em;margin-left:0}.mw-parser-output .portal-bar-header{margin:0 1em 0 0.5em;flex:0 0 auto;min-height:24px}.mw-parser-output .portal-bar-content{display:flex;flex-flow:row wrap;flex:0 1 auto;padding:0.15em 0;column-gap:1em;align-items:baseline;margin:0;list-style:none}.mw-parser-output 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.sister-bar+style+.portal-bar,.mw-parser-output .portal-bar+.navbox-styles+.navbox,.mw-parser-output .portal-bar+.navbox-styles+.sister-bar{margin-top:-1px}</style><div class="portal-bar noprint metadata noviewer portal-bar-bordered" role="navigation" aria-label="Portals"><span class="portal-bar-header"><a href="/wiki/Wikipedia:Contents/Portals" title="Wikipedia:Contents/Portals">Portals</a>:</span><ul class="portal-bar-content"><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Terra.png/19px-Terra.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Terra.png/29px-Terra.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Terra.png/38px-Terra.png 2x" data-file-width="600" data-file-height="600" /></span></span> </span><a href="/wiki/Portal:Geography" title="Portal:Geography">Geography</a></li><li 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src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/19px-Crab_Nebula.jpg" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/29px-Crab_Nebula.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/38px-Crab_Nebula.jpg 2x" data-file-width="3864" data-file-height="3864" /></span></span> </span><a href="/wiki/Portal:Astronomy" title="Portal:Astronomy">Astronomy</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><a href="/wiki/File:He1523a.jpg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/He1523a.jpg/16px-He1523a.jpg" decoding="async" width="16" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/He1523a.jpg/25px-He1523a.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/He1523a.jpg/33px-He1523a.jpg 2x" data-file-width="180" data-file-height="207" /></a></span> </span><a href="/wiki/Portal:Stars" title="Portal:Stars">Stars</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/19px-RocketSunIcon.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/29px-RocketSunIcon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/38px-RocketSunIcon.svg.png 2x" data-file-width="128" data-file-height="128" /></span></span> </span><a href="/wiki/Portal:Spaceflight" title="Portal:Spaceflight">Spaceflight</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/21px-Earth-moon.jpg" decoding="async" width="21" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/32px-Earth-moon.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Earth-moon.jpg/42px-Earth-moon.jpg 2x" data-file-width="3000" data-file-height="2400" /></span></span> </span><a href="/wiki/Portal:Outer_space" title="Portal:Outer space">Outer space</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><a href="/wiki/File:Nuvola_apps_kalzium.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/19px-Nuvola_apps_kalzium.svg.png" decoding="async" width="19" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/29px-Nuvola_apps_kalzium.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Nuvola_apps_kalzium.svg/38px-Nuvola_apps_kalzium.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> </span><a 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autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q124274#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q124274#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" 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