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class="vector-toc-numb">2</span> <span>Calculation</span> </div> </a> <ul id="toc-Calculation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Observations_and_theories" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Observations_and_theories"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Observations and theories</span> </div> </a> <ul id="toc-Observations_and_theories-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_meaning" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Other_meaning"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Other meaning</span> </div> </a> <ul id="toc-Other_meaning-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">5</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">6</span> <span>References</span> </div> </a> <ul id="toc-References-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">Orbital inclination</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 61 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-61" 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">61 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/Baanhelling" title="Baanhelling – Afrikaans" lang="af" hreflang="af" data-title="Baanhelling" 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/Bahnneigung" title="Bahnneigung – Alemannic" lang="gsw" hreflang="gsw" data-title="Bahnneigung" 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%B2%D8%A7%D9%88%D9%8A%D8%A9_%D9%85%D9%8A%D9%84%D8%A7%D9%86" title="زاوية ميلان – Arabic" lang="ar" hreflang="ar" data-title="زاوية ميلان" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Inclinaci%C3%B3n" title="Inclinación – Aragonese" lang="an" hreflang="an" data-title="Inclinación" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Encl%C3%ADn_orbital" title="Enclín orbital – Asturian" lang="ast" hreflang="ast" data-title="Enclín orbital" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%A8%E0%A6%A4%E0%A6%BF" title="কক্ষীয় নতি – Bangla" lang="bn" hreflang="bn" data-title="কক্ষীয় নতি" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/K%C3%BAi-t%C5%8D_kheng-si%C3%A2-kak" title="Kúi-tō kheng-siâ-kak – Minnan" lang="nan" hreflang="nan" data-title="Kúi-tō kheng-siâ-kak" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%98%D0%BD%D0%BA%D0%BB%D0%B8%D0%BD%D0%B0%D1%86%D0%B8%D1%8F" title="Инклинация – Bulgarian" lang="bg" hreflang="bg" data-title="Инклинация" 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/Inclinaci%C3%B3" title="Inclinació – Catalan" lang="ca" hreflang="ca" data-title="Inclinació" 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/Sklon_dr%C3%A1hy" title="Sklon dráhy – Czech" lang="cs" hreflang="cs" data-title="Sklon dráhy" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Baneh%C3%A6ldning" title="Banehældning – Danish" lang="da" hreflang="da" data-title="Banehældning" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Bahnneigung" title="Bahnneigung – German" lang="de" hreflang="de" data-title="Bahnneigung" 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/Orbiidi_kalle" title="Orbiidi kalle – Estonian" lang="et" hreflang="et" data-title="Orbiidi kalle" 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%9A%CE%BB%CE%AF%CF%83%CE%B7_%CF%84%CF%81%CE%BF%CF%87%CE%B9%CE%AC%CF%82" title="Κλίση τροχιάς – Greek" lang="el" hreflang="el" data-title="Κλίση τροχιάς" 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/Inclinaci%C3%B3n_orbital" title="Inclinación orbital – Spanish" lang="es" hreflang="es" data-title="Inclinación orbital" 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/Orbita_klineco" title="Orbita klineco – Esperanto" lang="eo" hreflang="eo" data-title="Orbita klineco" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Makurdura_orbital" title="Makurdura orbital – Basque" lang="eu" hreflang="eu" data-title="Makurdura orbital" 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%A7%D9%86%D8%AD%D8%B1%D8%A7%D9%81_%D9%85%D8%AF%D8%A7%D8%B1%DB%8C" title="انحراف مداری – Persian" lang="fa" hreflang="fa" data-title="انحراف مداری" 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/Inclinaison_orbitale" title="Inclinaison orbitale – French" lang="fr" hreflang="fr" data-title="Inclinaison orbitale" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Cleayn" title="Cleayn – Manx" lang="gv" hreflang="gv" data-title="Cleayn" data-language-autonym="Gaelg" data-language-local-name="Manx" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Inclinaci%C3%B3n_orbital" title="Inclinación orbital – Galician" lang="gl" hreflang="gl" data-title="Inclinación orbital" 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/%EA%B6%A4%EB%8F%84_%EA%B2%BD%EC%82%AC" title="궤도 경사 – Korean" lang="ko" hreflang="ko" data-title="궤도 경사" 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/%D5%88%D6%82%D5%B2%D5%A5%D5%AE%D6%80%D5%AB_%D5%A9%D5%A5%D6%84%D5%B8%D6%82%D5%B4" title="Ուղեծրի թեքում – Armenian" lang="hy" hreflang="hy" data-title="Ուղեծրի թեքում" 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%95%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%80%E0%A4%AF_%E0%A4%9D%E0%A5%81%E0%A4%95%E0%A4%BE%E0%A4%B5" title="कक्षीय झुकाव – Hindi" lang="hi" hreflang="hi" data-title="कक्षीय झुकाव" 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/Inklinacija_orbite" title="Inklinacija orbite – Croatian" lang="hr" hreflang="hr" data-title="Inklinacija orbite" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Inklinasi" title="Inklinasi – Indonesian" lang="id" hreflang="id" data-title="Inklinasi" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Inclinazione_orbitale" title="Inclinazione orbitale – Italian" lang="it" hreflang="it" data-title="Inclinazione orbitale" 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%A0%D7%98%D7%99%D7%99%D7%AA_%D7%9E%D7%A1%D7%9C%D7%95%D7%9C" title="נטיית מסלול – Hebrew" lang="he" hreflang="he" data-title="נטיית מסלול" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Gumiwang_Orbit" title="Gumiwang Orbit – Javanese" lang="jv" hreflang="jv" data-title="Gumiwang Orbit" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Mwinamo_wa_mzunguko" title="Mwinamo wa mzunguko – Swahili" lang="sw" hreflang="sw" data-title="Mwinamo wa mzunguko" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Inclinatio_orbitalis" title="Inclinatio orbitalis – Latin" lang="la" hreflang="la" data-title="Inclinatio orbitalis" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Orb%C4%ABtas_sl%C4%ABpums" title="Orbītas slīpums – Latvian" lang="lv" hreflang="lv" data-title="Orbītas slīpums" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Inklin%C3%A1ci%C3%B3" title="Inklináció – Hungarian" lang="hu" hreflang="hu" data-title="Inklináció" 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%9D%D0%B0%D0%BA%D0%BB%D0%BE%D0%BD_(%D0%BE%D1%80%D0%B1%D0%B8%D1%82%D0%B0)" title="Наклон (орбита) – Macedonian" lang="mk" hreflang="mk" data-title="Наклон (орбита)" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%95%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%87%E0%A4%9A%E0%A4%BE_%E0%A4%95%E0%A4%B2" title="कक्षेचा कल – Marathi" lang="mr" hreflang="mr" data-title="कक्षेचा कल" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kecondongan_orbit" title="Kecondongan orbit – Malay" lang="ms" hreflang="ms" data-title="Kecondongan orbit" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Glooiingshoek" title="Glooiingshoek – Dutch" lang="nl" hreflang="nl" data-title="Glooiingshoek" 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/%E8%BB%8C%E9%81%93%E5%82%BE%E6%96%9C%E8%A7%92" title="軌道傾斜角 – Japanese" lang="ja" hreflang="ja" data-title="軌道傾斜角" 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/Inklinasjon" title="Inklinasjon – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Inklinasjon" 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/Banehelling" title="Banehelling – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Banehelling" 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-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Bahnnegen" title="Bahnnegen – Low German" lang="nds" hreflang="nds" data-title="Bahnnegen" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Inklinacja" title="Inklinacja – Polish" lang="pl" hreflang="pl" data-title="Inklinacja" 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/Inclina%C3%A7%C3%A3o_orbital" title="Inclinação orbital – Portuguese" lang="pt" hreflang="pt" data-title="Inclinação orbital" 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/%C3%8Enclina%C8%9Bie_orbital%C4%83" title="Înclinație orbitală – Romanian" lang="ro" hreflang="ro" data-title="Înclinație orbitală" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q70894304 mw-list-item" title=""><a href="https://ru.wikipedia.org/wiki/%D0%9D%D0%B0%D0%BA%D0%BB%D0%BE%D0%BD%D0%B5%D0%BD%D0%B8%D0%B5_(%D0%B0%D1%81%D1%82%D1%80%D0%BE%D0%BD%D0%BE%D0%BC%D0%B8%D1%8F)" title="Наклонение (астрономия) – Russian" lang="ru" hreflang="ru" data-title="Наклонение (астрономия)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Orbital_inclination" title="Orbital inclination – Simple English" lang="en-simple" hreflang="en-simple" data-title="Orbital inclination" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Sklon_dr%C3%A1hy" title="Sklon dráhy – Slovak" lang="sk" hreflang="sk" data-title="Sklon dráhy" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Naklon_tira" title="Naklon tira – Slovenian" lang="sl" hreflang="sl" data-title="Naklon tira" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%98%D0%BD%D0%BA%D0%BB%D0%B8%D0%BD%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Инклинација – Serbian" lang="sr" hreflang="sr" data-title="Инклинација" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li 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tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" 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.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">"Inclination" redirects here. For other uses, see <a href="/wiki/Inclination_(disambiguation)" class="mw-disambig" title="Inclination (disambiguation)">Inclination (disambiguation)</a>.</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Orbit1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Orbit1.svg/300px-Orbit1.svg.png" decoding="async" width="300" height="270" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Orbit1.svg/450px-Orbit1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Orbit1.svg/600px-Orbit1.svg.png 2x" data-file-width="555" data-file-height="500" /></a><figcaption>Fig. 1: Orbital inclination represented by <i><b>i</b></i> (dark green), along with other fundamental <a href="/wiki/Orbital_parameters" class="mw-redirect" title="Orbital parameters">orbital parameters</a></figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist 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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 class="mw-selflink selflink">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 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Astrodynamics" title="Template:Astrodynamics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Astrodynamics" title="Template talk:Astrodynamics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Astrodynamics" title="Special:EditPage/Template:Astrodynamics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Orbital inclination</b> measures the tilt of an object's <a href="/wiki/Orbit" title="Orbit">orbit</a> around a celestial body. It is expressed as the <a href="/wiki/Angle" title="Angle">angle</a> between a <a href="/wiki/Plane_of_reference" class="mw-redirect" title="Plane of reference">reference plane</a> and the <a href="/wiki/Orbital_plane" title="Orbital plane">orbital plane</a> or <a href="/wiki/Axis_of_rotation" class="mw-redirect" title="Axis of rotation">axis</a> of direction of the orbiting object. </p><p>For a satellite orbiting the Earth directly above the <a href="/wiki/Equator" title="Equator">Equator</a>, the plane of the satellite's orbit is the same as the Earth's equatorial plane, and the satellite's orbital inclination is 0°. The general case for a circular orbit is that it is tilted, spending half an orbit over the northern hemisphere and half over the southern. If the orbit swung between 20° north <a href="/wiki/Latitude" title="Latitude">latitude</a> and 20° south latitude, then its orbital inclination would be 20°. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Orbits">Orbits</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Orbital_inclination&action=edit&section=1" title="Edit section: Orbits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The inclination is one of the six <a href="/wiki/Orbital_elements" title="Orbital elements">orbital elements</a> describing the shape and orientation of a celestial <a href="/wiki/Orbit" title="Orbit">orbit</a>. It is the <a href="/wiki/Angle" title="Angle">angle</a> between the orbital plane and the <a href="/wiki/Plane_of_reference" class="mw-redirect" title="Plane of reference">plane of reference</a>, normally stated in <a href="/wiki/Degree_(angle)" title="Degree (angle)">degrees</a>. For a satellite orbiting a <a href="/wiki/Planet" title="Planet">planet</a>, the plane of reference is usually the plane containing the planet's <a href="/wiki/Equator" title="Equator">equator</a>. For planets in the Solar System, the plane of reference is usually the <a href="/wiki/Ecliptic" title="Ecliptic">ecliptic</a>, the plane in which the Earth orbits the Sun.<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><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> This reference plane is most practical for Earth-based observers. Therefore, Earth's inclination is, by definition, zero. </p><p>Inclination can instead be measured with respect to another plane, such as the <a href="/wiki/Sun" title="Sun">Sun</a>'s equator or the <a href="/wiki/Invariable_plane" title="Invariable plane">invariable plane</a> (the plane that represents the angular momentum of the Solar System, approximately the orbital plane of <a href="/wiki/Jupiter" title="Jupiter">Jupiter</a>). </p> <div class="mw-heading mw-heading3"><h3 id="Natural_and_artificial_satellites">Natural and artificial satellites</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Orbital_inclination&action=edit&section=2" title="Edit section: Natural and artificial satellites"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The inclination of orbits of <a href="/wiki/Natural_satellite" title="Natural satellite">natural</a> or <a href="/wiki/Artificial_satellite" class="mw-redirect" title="Artificial satellite">artificial satellites</a> is measured relative to the equatorial plane of the body they orbit, if they orbit sufficiently closely. The equatorial plane is the plane perpendicular to the axis of rotation of the central body. </p><p>An inclination of 30° could also be described using an angle of 150°. The convention is that the normal orbit is <a href="/wiki/Direct_motion" class="mw-redirect" title="Direct motion">prograde</a>, an orbit in the same direction as the planet rotates. Inclinations greater than 90° describe <a href="/wiki/Retrograde_motion" class="mw-redirect" title="Retrograde motion">retrograde orbits</a> (backward). Thus: </p> <ul><li>An inclination of 0° means the orbiting body has a prograde orbit in the planet's equatorial plane.</li> <li>An inclination greater than 0° and less than 90° also describes a prograde orbit.</li> <li>An inclination of 63.4° is often called a <b>critical inclination</b>, when describing artificial satellites orbiting the Earth, because they have <a href="/wiki/Orbital_perturbation_analysis#Perturbation_of_the_orbital_plane_2" class="mw-redirect" title="Orbital perturbation analysis">zero apogee drift</a>.<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></li> <li>An inclination of exactly 90° is a <a href="/wiki/Polar_orbit" title="Polar orbit">polar orbit</a>, in which the spacecraft passes over the poles of the planet.</li> <li>An inclination greater than 90° and less than 180° is a retrograde orbit.</li> <li>An inclination of exactly 180° is a retrograde equatorial orbit.</li></ul> <p>For impact-generated moons of <a href="/wiki/Terrestrial_planet" title="Terrestrial planet">terrestrial planets</a> not too far from their star, with a large planet–moon distance, the orbital planes of moons tend to be aligned with the planet's orbit around the star due to tides from the star, but if the planet–moon distance is small, it may be inclined. For <a href="/wiki/Gas_giant" title="Gas giant">gas giants</a>, the orbits of moons tend to be aligned with the giant planet's equator, because these formed in circumplanetary disks.<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> Strictly speaking, this applies only to regular satellites. Captured bodies on distant orbits vary widely in their inclinations, while captured bodies in relatively close orbits tend to have low inclinations owing to tidal effects and perturbations by large regular satellites. </p> <div class="mw-heading mw-heading3"><h3 id="Exoplanets_and_multiple_star_systems">Exoplanets and multiple star systems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Orbital_inclination&action=edit&section=3" title="Edit section: Exoplanets and multiple star systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The inclination of <a href="/wiki/Exoplanet" title="Exoplanet">exoplanets</a> or members of <a href="/wiki/Star_system" title="Star system">multi-star star systems</a> is the angle of the plane of the orbit relative to the plane perpendicular to the line of sight from Earth to the object.<sup id="cite_ref-Campante_5-0" class="reference"><a href="#cite_note-Campante-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <ul><li>An inclination of 0° is a face-on orbit, meaning the plane of the exoplanet's orbit is perpendicular to the line of sight with Earth.</li> <li>An inclination of 90° is an edge-on orbit, meaning the plane of the exoplanet's orbit is parallel to the line of sight with Earth.</li></ul> <p>Since the word "inclination" is used in exoplanet studies for this line-of-sight inclination, the angle between the planet's orbit and its star's rotational axis is expressed using the term the "spin-orbit angle" or "spin-orbit alignment".<sup id="cite_ref-Campante_5-1" class="reference"><a href="#cite_note-Campante-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In most cases the orientation of the star's rotational axis is unknown. </p><p>Because the <a href="/wiki/Doppler_spectroscopy" title="Doppler spectroscopy">radial-velocity method</a> more easily finds planets with orbits closer to edge-on, most exoplanets found by this method have inclinations between 45° and 135°, although in most cases the inclination is not known. Consequently, most exoplanets found by radial velocity have <a href="/wiki/Binary_mass_function" title="Binary mass function">true masses</a> no more than 40% greater than their <a href="/wiki/Minimum_mass" title="Minimum mass">minimum masses</a>.<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. (May 2014)">citation needed</span></a></i>]</sup> If the orbit is almost face-on, especially for superjovians detected by radial velocity, then those objects may actually be <a href="/wiki/Brown_dwarf" title="Brown dwarf">brown dwarfs</a> or even <a href="/wiki/Red_dwarf" title="Red dwarf">red dwarfs</a>. One particular example is <a href="/wiki/HD_33636" title="HD 33636">HD 33636</a> B, which has true mass 142 M<sub>J</sub>, corresponding to an M6V star, while its minimum mass was 9.28 M<sub>J</sub>. </p><p>If the orbit is almost edge-on, then the planet can be seen <a href="/wiki/Transit_method" class="mw-redirect" title="Transit method">transiting</a> its star. </p> <div class="mw-heading mw-heading2"><h2 id="Calculation">Calculation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Orbital_inclination&action=edit&section=4" title="Edit section: Calculation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Orbital_inclination_from_momentum_vector.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Orbital_inclination_from_momentum_vector.gif/220px-Orbital_inclination_from_momentum_vector.gif" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Orbital_inclination_from_momentum_vector.gif/330px-Orbital_inclination_from_momentum_vector.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/2/28/Orbital_inclination_from_momentum_vector.gif 2x" data-file-width="389" data-file-height="291" /></a><figcaption>Components of the calculation of the orbital inclination from the momentum vector</figcaption></figure> <p>In <a href="/wiki/Astrodynamics" class="mw-redirect" title="Astrodynamics">astrodynamics</a>, the inclination <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> can be computed from the <a href="/wiki/Orbital_momentum_vector" class="mw-redirect" title="Orbital momentum vector">orbital momentum vector</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}"></span> (or any vector perpendicular to the <a href="/wiki/Orbital_plane_(astronomy)" class="mw-redirect" title="Orbital plane (astronomy)">orbital plane</a>) as <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i=\arccos {\frac {h_{z}}{\left|h\right|}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>=</mo> <mi>arccos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mrow> <mo>|</mo> <mi>h</mi> <mo>|</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i=\arccos {\frac {h_{z}}{\left|h\right|}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9da25a1e357520c04a7ddc2bf3ee7fb41ea65c32" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:13.974ex; height:6.176ex;" alt="{\displaystyle i=\arccos {\frac {h_{z}}{\left|h\right|}}}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{z}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{z}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/453e3ca341aeff78130e772d48b352a68eaadfd7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.341ex; height:2.509ex;" alt="{\displaystyle h_{z}}"></span> is the z-component of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}"></span>. </p><p>Mutual inclination of two orbits may be calculated from their inclinations to another plane using <a href="/wiki/Spherical_law_of_cosines" title="Spherical law of cosines">cosine rule for angles</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Observations_and_theories">Observations and theories</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Orbital_inclination&action=edit&section=5" title="Edit section: Observations and theories"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Most planetary orbits in the Solar System have relatively small inclinations, both in relation to each other and to the Sun's equator: </p> <table class="wikitable" style="text-align:right;"> <tbody><tr> <th rowspan="2" colspan="2" style="background:#DDEEFF;">Body </th> <th colspan="10">Inclination to </th></tr> <tr style="font-size:smaller;"> <th><a href="/wiki/Ecliptic" title="Ecliptic">Ecliptic</a> </th> <th>Sun's <br />equator </th> <th><a href="/wiki/Invariable_plane" title="Invariable plane">Invariable<br /> plane</a><sup id="cite_ref-meanplane_6-0" class="reference"><a href="#cite_note-meanplane-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </th></tr> <tr> <th rowspan="4" style="background:#DDEEFF;"><a href="/wiki/Terrestrial_planet" title="Terrestrial planet">Terre-<br />strials</a> </th> <td style="text-align:left;"><a href="/wiki/Mercury_(planet)" title="Mercury (planet)">Mercury</a> </td> <td>7.01° </td> <td>3.38° </td> <td>6.34° </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/Venus" title="Venus">Venus</a> </td> <td>3.39° </td> <td>3.86° </td> <td>2.19° </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/Earth" title="Earth">Earth</a> </td> <td><div class="center" style="width:auto; margin-left:auto; margin-right:auto;">0°</div> </td> <td>7.25°<sup id="cite_ref-NASA_7-0" class="reference"><a href="#cite_note-NASA-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </td> <td>1.57° </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/Mars" title="Mars">Mars</a> </td> <td>1.85° </td> <td>5.65° </td> <td>1.67° </td></tr> <tr> <th rowspan="4" style="background:#DDEEFF;"><a href="/wiki/Gas_giant" title="Gas giant">Gas &</a><br /><a href="/wiki/Ice_giant" title="Ice giant">ice<br />giants</a> </th> <td style="text-align:left;"><a href="/wiki/Jupiter" title="Jupiter">Jupiter</a> </td> <td>1.31° </td> <td>6.09° </td> <td>0.32° </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/Saturn" title="Saturn">Saturn</a> </td> <td>2.49° </td> <td>5.51° </td> <td>0.93° </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/Uranus" title="Uranus">Uranus</a> </td> <td>0.77° </td> <td>6.48° </td> <td>1.02° </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/Neptune" title="Neptune">Neptune</a> </td> <td>1.77° </td> <td>6.43° </td> <td>0.72° </td></tr> <tr> <th rowspan="4" style="background:#DDEEFF;"><a href="/wiki/Minor_planet" title="Minor planet">Minor<br />planets</a> </th> <td style="text-align:left;"><a href="/wiki/Pluto" title="Pluto">Pluto</a> </td> <td>17.14° </td> <td>11.88° </td> <td>15.55° </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/Ceres_(dwarf_planet)" title="Ceres (dwarf planet)">Ceres</a> </td> <td>10.59° </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">  </td> <td>9.20° </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/2_Pallas" title="2 Pallas">Pallas</a> </td> <td>34.83° </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">  </td> <td>34.21° </td></tr> <tr> <td style="text-align:left;"><a href="/wiki/4_Vesta" title="4 Vesta">Vesta</a> </td> <td>5.58° </td> <td data-sort-value="" style="background: var(--background-color-interactive, #ececec); color: var(--color-base, inherit); vertical-align: middle; text-align: center;" class="table-na">  </td> <td>7.13° </td></tr></tbody></table> <p>On the other hand, the <a href="/wiki/Dwarf_planet" title="Dwarf planet">dwarf planets</a> <a href="/wiki/Pluto" title="Pluto">Pluto</a> and <a href="/wiki/Eris_(dwarf_planet)" title="Eris (dwarf planet)">Eris</a> have inclinations to the ecliptic of 17° and 44° respectively, and the large <a href="/wiki/Asteroid" title="Asteroid">asteroid</a> <a href="/wiki/2_Pallas" title="2 Pallas">Pallas</a> is inclined at 34°. </p><p>In 1966, <a href="/wiki/Peter_Goldreich" title="Peter Goldreich">Peter Goldreich</a> published a classic paper on the evolution of <a href="/wiki/Orbit_of_the_Moon" title="Orbit of the Moon">the Moon's orbit</a> and on the orbits of other moons in the Solar System.<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> He showed that, for each planet, there is a distance such that moons closer to the planet than that distance maintain an almost constant orbital inclination with respect to the planet's equator (with an <a href="/wiki/Nodal_precession" title="Nodal precession">orbital precession</a> mostly due to the tidal influence of the planet), whereas moons farther away maintain an almost constant orbital inclination with respect to the <a href="/wiki/Ecliptic" title="Ecliptic">ecliptic</a> (with precession due mostly to the tidal influence of the sun). The moons in the first category, with the exception of <a href="/wiki/Neptune" title="Neptune">Neptune</a>'s moon <a href="/wiki/Triton_(moon)" title="Triton (moon)">Triton</a>, orbit near the equatorial plane. He concluded that these moons formed from equatorial <a href="/wiki/Accretion_disk" title="Accretion disk">accretion disks</a>. But he found that the Moon, although it was once inside the critical distance from the Earth, never had an equatorial orbit as would be expected from various <a href="/wiki/Origin_of_the_Moon" title="Origin of the Moon">scenarios for its origin</a>. This is called the lunar inclination problem, to which various solutions have since been proposed.<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> <div class="mw-heading mw-heading2"><h2 id="Other_meaning">Other meaning</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Orbital_inclination&action=edit&section=6" title="Edit section: Other meaning"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For planets and other rotating celestial bodies, the angle of the equatorial plane relative to the orbital plane – such as the tilt of the Earth's poles toward or away from the Sun – is sometimes also called inclination, but less ambiguous terms are <a href="/wiki/Axial_tilt" title="Axial tilt">axial tilt</a> or obliquity. </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=Orbital_inclination&action=edit&section=7" title="Edit section: See also"><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/inclination" class="extiw" title="wiktionary:inclination">inclination</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <ul><li><a href="/wiki/Horizontal_coordinate_system" title="Horizontal coordinate system">Horizontal coordinate system</a></li> <li><a href="/wiki/Axial_parallelism" title="Axial parallelism">Axial parallelism</a></li> <li><a href="/wiki/Axial_tilt" title="Axial tilt">Axial tilt</a></li> <li><a href="/wiki/Azimuth" title="Azimuth">Azimuth</a></li> <li><a href="/wiki/Beta_angle" title="Beta angle">Beta angle</a></li> <li><a href="/wiki/Kepler_orbit" title="Kepler orbit">Kepler orbits</a></li> <li><a href="/wiki/Kozai_mechanism" title="Kozai mechanism">Kozai mechanism</a></li> <li><a href="/wiki/Orbital_inclination_change" title="Orbital inclination change">Orbital inclination change</a></li> <li><a href="/wiki/Orbital_pole" title="Orbital pole">Orbital pole</a></li> <li><a href="/wiki/Space_Shuttle_Columbia_disaster#Possible_emergency_procedures" title="Space Shuttle Columbia disaster">Space Shuttle Columbia disaster: Possible emergency procedures</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Orbital_inclination&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFChobotov2002" class="citation book cs1">Chobotov, Vladimir A. 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Retrieved <span class="nowrap">23 November</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Solex+10&rft.pub=Universit%C3%A0+degli+Studi+di+Napoli+Federico+II&rft.aulast=Vitagliano&rft.aufirst=Aldo&rft_id=http%3A%2F%2Fchemistry.unina.it%2F~alvitagl%2Fsolex%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+inclination" class="Z3988"></span></span> </li> <li id="cite_note-NASA-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-NASA_7-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://nssdc.gsfc.nasa.gov/planetary/planetfact.html">Planetary Fact Sheets</a>, at <a rel="nofollow" class="external free" href="https://nssdc.gsfc.nasa.gov">http://nssdc.gsfc.nasa.gov</a></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPeter_Goldreich1966" class="citation journal cs1">Peter Goldreich (November 1966). "History of the Lunar Orbit". <i><a href="/wiki/Reviews_of_Geophysics" title="Reviews of Geophysics">Reviews of Geophysics</a></i>. <b>4</b> (4): 411–439. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1966RvGSP...4..411G">1966RvGSP...4..411G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1029%2FRG004i004p00411">10.1029/RG004i004p00411</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Reviews+of+Geophysics&rft.atitle=History+of+the+Lunar+Orbit&rft.volume=4&rft.issue=4&rft.pages=411-439&rft.date=1966-11&rft_id=info%3Adoi%2F10.1029%2FRG004i004p00411&rft_id=info%3Abibcode%2F1966RvGSP...4..411G&rft.au=Peter+Goldreich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+inclination" class="Z3988"></span> Termed "classic" by <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJihad_Touma_&_Jack_Wisdom1994" class="citation journal cs1"><a href="/w/index.php?title=Jihad_Touma&action=edit&redlink=1" class="new" title="Jihad Touma (page does not exist)">Jihad Touma</a> & <a href="/wiki/Jack_Wisdom" title="Jack Wisdom">Jack Wisdom</a> (November 1994). <a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F117209">"Evolution of the Earth-Moon system"</a>. <i><a href="/wiki/The_Astronomical_Journal" title="The Astronomical Journal">The Astronomical Journal</a></i>. <b>108</b>: 1943. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1994AJ....108.1943T">1994AJ....108.1943T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F117209">10.1086/117209</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Astronomical+Journal&rft.atitle=Evolution+of+the+Earth-Moon+system&rft.volume=108&rft.pages=1943&rft.date=1994-11&rft_id=info%3Adoi%2F10.1086%2F117209&rft_id=info%3Abibcode%2F1994AJ....108.1943T&rft.au=Jihad+Touma+%26+Jack+Wisdom&rft_id=https%3A%2F%2Fdoi.org%2F10.1086%252F117209&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+inclination" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKaveh_Pahlevan_&_Alessandro_Morbidelli2015" class="citation journal cs1">Kaveh Pahlevan & Alessandro Morbidelli (26 November 2015). "Collisionless encounters and the origin of the lunar inclination". <i>Nature</i>. <b>527</b> (7579): 492–494. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1603.06515">1603.06515</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2015Natur.527..492P">2015Natur.527..492P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnature16137">10.1038/nature16137</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/26607544">26607544</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4456736">4456736</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Collisionless+encounters+and+the+origin+of+the+lunar+inclination&rft.volume=527&rft.issue=7579&rft.pages=492-494&rft.date=2015-11-26&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4456736%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2015Natur.527..492P&rft_id=info%3Aarxiv%2F1603.06515&rft_id=info%3Apmid%2F26607544&rft_id=info%3Adoi%2F10.1038%2Fnature16137&rft.au=Kaveh+Pahlevan+%26+Alessandro+Morbidelli&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+inclination" class="Z3988"></span></span> </li> </ol></div></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style 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tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Gravitational_orbits" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Orbits" title="Template:Orbits"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Orbits" title="Template talk:Orbits"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Orbits" title="Special:EditPage/Template:Orbits"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Gravitational_orbits" style="font-size:114%;margin:0 4em">Gravitational <a href="/wiki/Orbit" title="Orbit">orbits</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_orbits" title="List of orbits">Types</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Box_orbit" title="Box orbit">Box</a></li> <li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Capture</a></li> <li><a href="/wiki/Circular_orbit" title="Circular orbit">Circular</a></li> <li><a href="/wiki/Elliptic_orbit" title="Elliptic orbit">Elliptical</a> / <a href="/wiki/Highly_elliptical_orbit" title="Highly elliptical orbit">Highly elliptical</a></li> <li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Escape</a></li> <li><a href="/wiki/Horseshoe_orbit" title="Horseshoe orbit">Horseshoe</a></li> <li><a href="/wiki/Hyperbolic_trajectory" title="Hyperbolic trajectory">Hyperbolic trajectory</a></li> <li><a href="/wiki/Inclined_orbit" title="Inclined orbit">Inclined</a> / <a href="/wiki/Non-inclined_orbit" class="mw-redirect" title="Non-inclined orbit">Non-inclined</a></li> <li><a href="/wiki/Kepler_orbit" title="Kepler orbit">Kepler</a></li> <li><a href="/wiki/Lagrange_point" title="Lagrange point">Lagrange point</a></li> <li><a href="/wiki/Osculating_orbit" title="Osculating orbit">Osculating</a></li> <li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Parabolic trajectory</a></li> <li><a href="/wiki/Parking_orbit" title="Parking orbit">Parking</a></li> <li><a href="/wiki/Retrograde_and_prograde_motion" title="Retrograde and prograde motion">Prograde / Retrograde</a></li> <li><a href="/wiki/Synchronous_orbit" title="Synchronous orbit">Synchronous</a> <ul><li><a href="/wiki/Semi-synchronous_orbit" title="Semi-synchronous orbit">semi</a></li> <li><a href="/wiki/Subsynchronous_orbit" title="Subsynchronous orbit">sub</a></li></ul></li> <li><a href="/wiki/Hohmann_transfer_orbit" title="Hohmann transfer orbit">Transfer orbit</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em"><a href="/wiki/Geocentric_orbit" title="Geocentric orbit">Geocentric</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Geosynchronous_orbit" title="Geosynchronous orbit">Geosynchronous</a> <ul><li><a href="/wiki/Geostationary_orbit" title="Geostationary orbit">Geostationary</a></li> <li><a href="/wiki/Geostationary_transfer_orbit" title="Geostationary transfer orbit">Geostationary transfer</a></li></ul></li> <li><a href="/wiki/Graveyard_orbit" title="Graveyard orbit">Graveyard</a></li> <li><a href="/wiki/High_Earth_orbit" title="High Earth orbit">High Earth</a></li> <li><a href="/wiki/Low_Earth_orbit" title="Low Earth orbit">Low Earth</a></li> <li><a href="/wiki/Medium_Earth_orbit" title="Medium Earth orbit">Medium Earth</a></li> <li><a href="/wiki/Molniya_orbit" title="Molniya orbit">Molniya</a></li> <li><a href="/wiki/Near-equatorial_orbit" title="Near-equatorial orbit">Near-equatorial</a></li> <li><a href="/wiki/Orbit_of_the_Moon" title="Orbit of the Moon">Orbit of the Moon</a></li> <li><a href="/wiki/Polar_orbit" title="Polar orbit">Polar</a></li> <li><a href="/wiki/Sun-synchronous_orbit" title="Sun-synchronous orbit">Sun-synchronous</a></li> <li><a href="/wiki/Transatmospheric_orbit" title="Transatmospheric orbit">Transatmospheric</a></li> <li><a href="/wiki/Tundra_orbit" title="Tundra orbit">Tundra</a></li> <li><a href="/wiki/Very_low_Earth_orbit" title="Very low Earth orbit">Very low Earth</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">About<br />other points</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li>Mars <ul><li><a href="/wiki/Areocentric_orbit" title="Areocentric orbit">Areocentric</a></li> <li><a href="/wiki/Areosynchronous_orbit" title="Areosynchronous orbit">Areosynchronous</a></li> <li><a href="/wiki/Areostationary_orbit" title="Areostationary orbit">Areostationary</a></li></ul></li> <li>Lagrange points <ul><li><a href="/wiki/Distant_retrograde_orbit" title="Distant retrograde orbit">Distant retrograde</a></li> <li><a href="/wiki/Halo_orbit" title="Halo orbit">Halo</a></li> <li><a href="/wiki/Lissajous_orbit" title="Lissajous orbit">Lissajous</a></li> <li><a href="/wiki/Libration_point_orbit" title="Libration point orbit">Libration</a></li></ul></li> <li><a href="/wiki/Lunar_orbit" title="Lunar orbit">Lunar</a></li> <li>Sun <ul><li><a href="/wiki/Heliocentric_orbit" title="Heliocentric orbit">Heliocentric</a> <ul><li><a href="/wiki/Earth%27s_orbit" title="Earth's orbit">Earth's orbit</a></li></ul></li> <li><a href="/wiki/Mars_cycler" title="Mars cycler">Mars cycler</a></li> <li><a href="/wiki/Sun-synchronous_orbit" title="Sun-synchronous orbit">Heliosynchronous</a></li></ul></li> <li>Other <ul><li><a href="/wiki/Lunar_cycler" title="Lunar cycler">Lunar cycler</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Orbital_elements" title="Orbital elements">Parameters</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em"><div class="hlist"><ul><li>Shape</li><li>Size</li></ul></div></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">e</span>  <a href="/wiki/Orbital_eccentricity" title="Orbital eccentricity">Eccentricity</a></li> <li><span class="texhtml mvar" style="font-style:italic;">a</span>  <a href="/wiki/Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">Semi-major axis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">b</span>  <a href="/wiki/Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">Semi-minor axis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">Q</span>, <span class="texhtml mvar" style="font-style:italic;">q</span>  <a href="/wiki/Apsis" title="Apsis">Apsides</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">Orientation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">i</span>  <a class="mw-selflink selflink">Inclination</a></li> <li><span class="texhtml mvar" style="font-style:italic;">Ω</span>  <a href="/wiki/Longitude_of_the_ascending_node" title="Longitude of the ascending node">Longitude of the ascending node</a></li> <li><span class="texhtml mvar" style="font-style:italic;">ω</span>  <a href="/wiki/Argument_of_periapsis" title="Argument of periapsis">Argument of periapsis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">ϖ</span>  <a href="/wiki/Longitude_of_the_periapsis" class="mw-redirect" title="Longitude of the periapsis">Longitude of the periapsis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">Position</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">M</span>  <a href="/wiki/Mean_anomaly" title="Mean anomaly">Mean anomaly</a></li> <li><span class="texhtml mvar" style="font-style:italic;">ν</span>, <span class="texhtml mvar" style="font-style:italic;">θ</span>, <span class="texhtml mvar" style="font-style:italic;">f</span>  <a href="/wiki/True_anomaly" title="True anomaly">True anomaly</a></li> <li><span class="texhtml mvar" style="font-style:italic;">E</span>  <a href="/wiki/Eccentric_anomaly" title="Eccentric anomaly">Eccentric anomaly</a></li> <li><span class="texhtml mvar" style="font-style:italic;">L</span>  <a href="/wiki/Mean_longitude" title="Mean longitude">Mean longitude</a></li> <li><span class="texhtml mvar" style="font-style:italic;">l</span>  <a href="/wiki/True_longitude" title="True longitude">True longitude</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">Variation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">T</span>  <a href="/wiki/Orbital_period" title="Orbital period">Orbital period</a></li> <li><span class="texhtml mvar" style="font-style:italic;">n</span>  <a href="/wiki/Mean_motion" title="Mean motion">Mean motion</a></li> <li><span class="texhtml mvar" style="font-style:italic;">v</span>  <a href="/wiki/Orbital_speed" title="Orbital speed">Orbital speed</a></li> <li><span class="texhtml"><i>t</i><sub>0</sub></span>  <a href="/wiki/Epoch_(astronomy)" title="Epoch (astronomy)">Epoch</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Orbital_maneuver" title="Orbital maneuver">Maneuvers</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bi-elliptic_transfer" title="Bi-elliptic transfer">Bi-elliptic transfer</a></li> <li><a href="/wiki/Collision_avoidance_(spacecraft)" title="Collision avoidance (spacecraft)">Collision avoidance (spacecraft)</a></li> <li><a href="/wiki/Delta-v" title="Delta-v">Delta-v</a></li> <li><a href="/wiki/Delta-v_budget" title="Delta-v budget">Delta-v budget</a></li> <li><a href="/wiki/Gravity_assist" title="Gravity assist">Gravity assist</a></li> <li><a href="/wiki/Gravity_turn" title="Gravity turn">Gravity turn</a></li> <li><a href="/wiki/Hohmann_transfer_orbit" title="Hohmann transfer orbit">Hohmann transfer</a></li> <li><a href="/wiki/Orbital_inclination_change" title="Orbital inclination change">Inclination change</a></li> <li><a href="/wiki/Low-energy_transfer" title="Low-energy transfer">Low-energy transfer</a></li> <li><a href="/wiki/Oberth_effect" title="Oberth effect">Oberth effect</a></li> <li><a href="/wiki/Orbit_phasing" title="Orbit phasing">Phasing</a></li> <li><a href="/wiki/Tsiolkovsky_rocket_equation" title="Tsiolkovsky rocket equation">Rocket equation</a></li> <li><a href="/wiki/Space_rendezvous" title="Space rendezvous">Rendezvous</a></li> <li><a href="/wiki/Trans-lunar_injection" title="Trans-lunar injection">Trans-lunar injection</a></li> <li><a href="/wiki/Transposition,_docking,_and_extraction" title="Transposition, docking, and extraction">Transposition, docking, and extraction</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Orbital_mechanics" title="Orbital mechanics">Orbital<br />mechanics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Astronomical_coordinate_systems" title="Astronomical coordinate systems">Astronomical coordinate systems</a></li> <li><a href="/wiki/Characteristic_energy" title="Characteristic energy">Characteristic energy</a></li> <li><a href="/wiki/Escape_velocity" title="Escape velocity">Escape velocity</a></li> <li><a href="/wiki/Ephemeris" title="Ephemeris">Ephemeris</a></li> <li><a href="/wiki/Equatorial_coordinate_system" title="Equatorial coordinate system">Equatorial coordinate system</a></li> <li><a href="/wiki/Ground_track" class="mw-redirect" title="Ground track">Ground track</a></li> <li><a href="/wiki/Hill_sphere" title="Hill sphere">Hill sphere</a></li> <li><a href="/wiki/Interplanetary_Transport_Network" title="Interplanetary Transport Network">Interplanetary Transport Network</a></li> <li><a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws of planetary motion</a></li> <li><a href="/wiki/Lagrange_point" title="Lagrange point">Lagrangian point</a></li> <li><a href="/wiki/N-body_problem" title="N-body problem"><i>n</i>-body problem</a></li> <li><a href="/wiki/Orbit_equation" title="Orbit equation">Orbit equation</a></li> <li><a href="/wiki/Orbital_state_vectors" title="Orbital state vectors">Orbital state vectors</a></li> <li><a href="/wiki/Perturbation_(astronomy)" title="Perturbation (astronomy)">Perturbation</a></li> <li><a href="/wiki/Retrograde_and_prograde_motion" title="Retrograde and prograde motion">Retrograde and prograde motion</a></li> <li><a href="/wiki/Specific_orbital_energy" title="Specific orbital energy">Specific orbital energy</a></li> <li><a href="/wiki/Specific_angular_momentum" title="Specific angular momentum">Specific angular momentum</a></li> <li><a href="/wiki/Two-line_element_set" title="Two-line element set">Two-line elements</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="List-Class article"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/16px-Symbol_list_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" 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