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<span>Etymology</span> </div> </a> <ul id="toc-Etymology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Calculation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Calculation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Calculation</span> </div> </a> <ul id="toc-Calculation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Examples</span> </div> </a> <ul id="toc-Examples-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mean_average" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mean_average"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Mean average</span> </div> </a> <ul id="toc-Mean_average-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Climatic_effect" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Climatic_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Climatic effect</span> </div> </a> <ul id="toc-Climatic_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Exoplanets" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Exoplanets"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Exoplanets</span> </div> </a> <ul id="toc-Exoplanets-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-Footnotes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Footnotes"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Footnotes</span> </div> </a> <ul id="toc-Footnotes-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">10</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">11</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">12</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">Orbital eccentricity</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 54 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-54" 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">54 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/Eksentrisiteit_(sterrekunde)" title="Eksentrisiteit (sterrekunde) – Afrikaans" lang="af" hreflang="af" data-title="Eksentrisiteit (sterrekunde)" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%86%D8%AD%D8%B1%D8%A7%D9%81_%D9%85%D8%AF%D8%A7%D8%B1%D9%8A" title="انحراف مداري – Arabic" lang="ar" hreflang="ar" data-title="انحراف مداري" 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/Excentricidat" title="Excentricidat – Aragonese" lang="an" hreflang="an" data-title="Excentricidat" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</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%89%E0%A7%8E%E0%A6%95%E0%A7%87%E0%A6%A8%E0%A7%8D%E0%A6%A6%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%95%E0%A6%A4%E0%A6%BE" title="কক্ষীয় উৎকেন্দ্রিকতা – Bangla" lang="bn" hreflang="bn" data-title="কক্ষীয় উৎকেন্দ্রিকতা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D0%BA%D1%81%D1%86%D1%8D%D0%BD%D1%82%D1%80%D1%8B%D1%81%D1%96%D1%82%D1%8D%D1%82_%D0%B0%D1%80%D0%B1%D1%96%D1%82%D1%8B" title="Эксцэнтрысітэт арбіты – Belarusian" lang="be" hreflang="be" data-title="Эксцэнтрысітэт арбіты" 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%95%D0%BA%D1%81%D1%86%D0%B5%D0%BD%D1%82%D1%80%D0%B8%D1%86%D0%B8%D1%82%D0%B5%D1%82_(%D0%BE%D1%80%D0%B1%D0%B8%D1%82%D0%B0)" title="Ексцентрицитет (орбита) – Bulgarian" lang="bg" hreflang="bg" data-title="Ексцентрицитет (орбита)" 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/Excentricitat_orbital" title="Excentricitat orbital – Catalan" lang="ca" hreflang="ca" data-title="Excentricitat orbital" 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/Excentricita_dr%C3%A1hy" title="Excentricita dráhy – Czech" lang="cs" hreflang="cs" data-title="Excentricita 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/Excentricitet_(astronomi)" title="Excentricitet (astronomi) – Danish" lang="da" hreflang="da" data-title="Excentricitet (astronomi)" 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/Exzentrizit%C3%A4t_(Astronomie)" title="Exzentrizität (Astronomie) – German" lang="de" hreflang="de" data-title="Exzentrizität (Astronomie)" 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_ekstsentrilisus" title="Orbiidi ekstsentrilisus – Estonian" lang="et" hreflang="et" data-title="Orbiidi ekstsentrilisus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Excentricidad_orbital" title="Excentricidad orbital – Spanish" lang="es" hreflang="es" data-title="Excentricidad orbital" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Eszentrikotasun_orbital" title="Eszentrikotasun orbital – Basque" lang="eu" hreflang="eu" data-title="Eszentrikotasun 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%AE%D8%B1%D9%88%D8%AC_%D8%A7%D8%B2_%D9%85%D8%B1%DA%A9%D8%B2_%D9%85%D8%AF%D8%A7%D8%B1%DB%8C" title="خروج از مرکز مداری – Persian" lang="fa" hreflang="fa" data-title="خروج از مرکز 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/Excentricit%C3%A9_orbitale" title="Excentricité orbitale – French" lang="fr" hreflang="fr" data-title="Excentricité orbitale" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</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_%EC%9D%B4%EC%8B%AC%EB%A5%A0" title="궤도 이심률 – Korean" lang="ko" hreflang="ko" data-title="궤도 이심률" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</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%B5%E0%A4%BF%E0%A4%95%E0%A5%87%E0%A4%A8%E0%A5%8D%E0%A4%A6%E0%A5%8D%E0%A4%B0%E0%A4%A4%E0%A4%BE" title="कक्षीय विकेन्द्रता – Hindi" lang="hi" hreflang="hi" data-title="कक्षीय विकेन्द्रता" 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/Ekscentri%C4%8Dnost_orbite" title="Ekscentričnost orbite – Croatian" lang="hr" hreflang="hr" data-title="Ekscentričnost 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/Eksentrisitas_orbit" title="Eksentrisitas orbit – Indonesian" lang="id" hreflang="id" data-title="Eksentrisitas orbit" 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/Eccentricit%C3%A0_orbitale" title="Eccentricità orbitale – Italian" lang="it" hreflang="it" data-title="Eccentricità orbitale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%AD%D0%BA%D1%81%D1%86%D0%B5%D0%BD%D1%82%D1%80%D0%B8%D1%81%D0%B8%D1%82%D0%B5%D1%82" title="Эксцентриситет – Kazakh" lang="kk" hreflang="kk" data-title="Эксцентриситет" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Orb%C4%ABtas_ekscentricit%C4%81te" title="Orbītas ekscentricitāte – Latvian" lang="lv" hreflang="lv" data-title="Orbītas ekscentricitāte" 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/Exzentrizit%C3%A9it_(Astronomie)" title="Exzentrizitéit (Astronomie) – Luxembourgish" lang="lb" hreflang="lb" data-title="Exzentrizitéit (Astronomie)" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Excentricit%C3%A1s_(csillag%C3%A1szat)" title="Excentricitás (csillagászat) – Hungarian" lang="hu" hreflang="hu" data-title="Excentricitás (csillagászat)" 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%9E%D1%80%D0%B1%D0%B8%D1%82%D0%B0%D0%BB%D0%BD%D0%BE_%D0%B7%D0%B0%D0%BD%D0%B5%D1%81%D1%83%D0%B2%D0%B0%D1%9A%D0%B5" title="Орбитално занесување – Macedonian" lang="mk" hreflang="mk" data-title="Орбитално занесување" 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%89%E0%B5%BD%E0%B4%95%E0%B5%87%E0%B4%A8%E0%B5%8D%E0%B4%A6%E0%B5%8D%E0%B4%B0%E0%B4%A4_(%E0%B4%9C%E0%B5%8D%E0%B4%AF%E0%B5%8B%E0%B4%A4%E0%B4%BF%E0%B4%B6%E0%B4%BE%E0%B4%B8%E0%B5%8D%E0%B4%A4%E0%B5%8D%E0%B4%B0%E0%B4%82)" title="ഉൽകേന്ദ്രത (ജ്യോതിശാസ്ത്രം) – Malayalam" lang="ml" hreflang="ml" data-title="ഉൽകേന്ദ്രത (ജ്യോതിശാസ്ത്രം)" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</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%80%E0%A4%AF_%E0%A4%B5%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%A4%E0%A4%BE_%E0%A4%A8%E0%A4%BF%E0%A4%B0%E0%A5%8D%E0%A4%A6%E0%A5%87%E0%A4%B6%E0%A4%BE%E0%A4%82%E0%A4%95" title="कक्षीय वक्रता निर्देशांक – Marathi" lang="mr" hreflang="mr" data-title="कक्षीय वक्रता निर्देशांक" 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/Kesipian_orbit" title="Kesipian orbit – Malay" lang="ms" hreflang="ms" data-title="Kesipian 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/Excentriciteit_(astronomie)" title="Excentriciteit (astronomie) – Dutch" lang="nl" hreflang="nl" data-title="Excentriciteit (astronomie)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%BB%8C%E9%81%93%E9%9B%A2%E5%BF%83%E7%8E%87" title="軌道離心率 – Japanese" lang="ja" hreflang="ja" data-title="軌道離心率" 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/Baneeksentrisitet" title="Baneeksentrisitet – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Baneeksentrisitet" 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/Eksentrisitet" title="Eksentrisitet – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Eksentrisitet" 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-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Excentricitat_orbitala" title="Excentricitat orbitala – Occitan" lang="oc" hreflang="oc" data-title="Excentricitat orbitala" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ekscentryczno%C5%9B%C4%87_(fizyka)" title="Ekscentryczność (fizyka) – Polish" lang="pl" hreflang="pl" data-title="Ekscentryczność (fizyka)" 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/Excentricidade_orbital" title="Excentricidade orbital – Portuguese" lang="pt" hreflang="pt" data-title="Excentricidade 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/Excentricitate_orbital%C4%83" title="Excentricitate orbitală – Romanian" lang="ro" hreflang="ro" data-title="Excentricitate 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 mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D0%BA%D1%81%D1%86%D0%B5%D0%BD%D1%82%D1%80%D0%B8%D1%81%D0%B8%D1%82%D0%B5%D1%82_%D0%BE%D1%80%D0%B1%D0%B8%D1%82%D1%8B" title="Эксцентриситет орбиты – Russian" lang="ru" hreflang="ru" data-title="Эксцентриситет орбиты" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9A%E0%B6%9A%E0%B7%8A%E0%B7%82%E0%B7%93%E0%B6%BA_%E0%B6%8B%E0%B6%AD%E0%B7%8A%E0%B6%9A%E0%B7%9A%E0%B6%B1%E0%B7%8A%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%92%E0%B6%BA%E0%B6%AD%E0%B7%8F%E0%B7%80%E0%B6%BA" title="කක්ෂීය උත්කේන්ද්‍රියතාවය – Sinhala" lang="si" hreflang="si" data-title="කක්ෂීය උත්කේන්ද්‍රියතාවය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Orbital_eccentricity" title="Orbital eccentricity – Simple English" lang="en-simple" hreflang="en-simple" data-title="Orbital eccentricity" 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/Excentricita_(astron%C3%B3mia)" title="Excentricita (astronómia) – Slovak" lang="sk" hreflang="sk" data-title="Excentricita (astronómia)" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Izsrednost_tira" title="Izsrednost tira – Slovenian" lang="sl" hreflang="sl" data-title="Izsrednost 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%95%D0%BA%D1%81%D1%86%D0%B5%D0%BD%D1%82%D1%80%D0%B8%D1%86%D0%B8%D1%82%D0%B5%D1%82_%D0%BE%D1%80%D0%B1%D0%B8%D1%82%D0%B5" title="Ексцентрицитет орбите – Serbian" lang="sr" hreflang="sr" data-title="Ексцентрицитет орбите" 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/Ekscentricitet_orbite" title="Ekscentricitet orbite – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Ekscentricitet orbite" 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-su mw-list-item"><a href="https://su.wikipedia.org/wiki/%C3%89ks%C3%A9ntrisitas_orbit" title="Ékséntrisitas orbit – Sundanese" lang="su" hreflang="su" data-title="Ékséntrisitas orbit" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Excentricitet_(astronomi)" title="Excentricitet (astronomi) – Swedish" lang="sv" hreflang="sv" data-title="Excentricitet (astronomi)" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AF%81%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AF%81%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%A4%E0%AF%88%E0%AE%AF%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%B5%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%B5%E0%AE%BF%E0%AE%B2%E0%AE%95%E0%AE%B2%E0%AF%8D" title="சுற்றுப்பாதையின் வட்டவிலகல் – Tamil" lang="ta" hreflang="ta" data-title="சுற்றுப்பாதையின் வட்டவிலகல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Annfal_amezzay" title="Annfal amezzay – Kabyle" lang="kab" hreflang="kab" data-title="Annfal amezzay" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B9%80%E0%B8%A2%E0%B8%B7%E0%B9%89%E0%B8%AD%E0%B8%87%E0%B8%A8%E0%B8%B9%E0%B8%99%E0%B8%A2%E0%B9%8C%E0%B8%81%E0%B8%A5%E0%B8%B2%E0%B8%87%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%A7%E0%B8%87%E0%B9%82%E0%B8%84%E0%B8%88%E0%B8%A3" title="ความเยื้องศูนย์กลางของวงโคจร – Thai" lang="th" hreflang="th" data-title="ความเยื้องศูนย์กลางของวงโคจร" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/D%C4%B1%C5%9F_merkezlik_(astronomi)" title="Dış merkezlik (astronomi) – Turkish" lang="tr" hreflang="tr" data-title="Dış merkezlik (astronomi)" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D0%BA%D1%81%D1%86%D0%B5%D0%BD%D1%82%D1%80%D0%B8%D1%81%D0%B8%D1%82%D0%B5%D1%82_%D0%BE%D1%80%D0%B1%D1%96%D1%82%D0%B8" title="Ексцентриситет орбіти – Ukrainian" lang="uk" hreflang="uk" data-title="Ексцентриситет орбіти" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BB%99_l%E1%BB%87ch_t%C3%A2m_qu%E1%BB%B9_%C4%91%E1%BA%A1o" title="Độ lệch tâm quỹ đạo – Vietnamese" lang="vi" hreflang="vi" 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<div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Amount by which an orbit deviates from a perfect circle</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">This article is about eccentricity in astrodynamics. For other uses, see <a href="/wiki/Eccentricity_(disambiguation)" class="mw-redirect mw-disambig" title="Eccentricity (disambiguation)">Eccentricity (disambiguation)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Kepler_orbits.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Kepler_orbits.svg/220px-Kepler_orbits.svg.png" decoding="async" width="220" height="267" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Kepler_orbits.svg/330px-Kepler_orbits.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Kepler_orbits.svg/440px-Kepler_orbits.svg.png 2x" data-file-width="494" data-file-height="600" /></a><figcaption>An elliptic, parabolic, and hyperbolic <a href="/wiki/Kepler_orbit" title="Kepler orbit">Kepler orbit</a>:<br /> <style data-mw-deduplicate="TemplateStyles:r981673959">.mw-parser-output .legend{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .legend-color{display:inline-block;min-width:1.25em;height:1.25em;line-height:1.25;margin:1px 0;text-align:center;border:1px solid black;background-color:transparent;color:black}.mw-parser-output .legend-text{}</style><span class="legend nowrap"><span class="legend-color mw-no-invert" style="border: 1px solid #770D18;background-color:red; color:black;"> </span> Elliptic (eccentricity = 0.7)</span><br /> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r981673959"><span class="legend nowrap"><span class="legend-color mw-no-invert" style="border: 1px solid black;background-color:limegreen; color:black;"> </span> Parabolic (eccentricity = 1)</span><br /> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r981673959"><span class="legend nowrap"><span class="legend-color mw-no-invert" style="border: 1px solid #444;background-color:blue; color:white;"> </span> Hyperbolic orbit (eccentricity = 1.3)</span> </figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Animation_of_Orbital_eccentricity.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Animation_of_Orbital_eccentricity.gif/250px-Animation_of_Orbital_eccentricity.gif" decoding="async" width="250" height="188" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Animation_of_Orbital_eccentricity.gif/375px-Animation_of_Orbital_eccentricity.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Animation_of_Orbital_eccentricity.gif/500px-Animation_of_Orbital_eccentricity.gif 2x" data-file-width="560" data-file-height="420" /></a><figcaption>Elliptic orbit by eccentricity<br /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r981673959"><span class="legend nowrap"><span class="legend-color mw-no-invert" style="background-color: OrangeRed ; color:black;"> </span> 0</span> <b>·</b> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r981673959"><span class="legend nowrap"><span class="legend-color mw-no-invert" style="background-color:Lime; color:black;"> </span> 0.2</span> <b>·</b> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r981673959"><span class="legend nowrap"><span class="legend-color mw-no-invert" style="background-color:Cyan; color:black;"> </span> 0.4</span> <b>·</b> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r981673959"><span class="legend nowrap"><span class="legend-color mw-no-invert" style="background-color:Gold; color:black;"> </span> 0.6</span> <b>·</b> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r981673959"><span class="legend nowrap"><span class="legend-color mw-no-invert" style="background-color:hotpink; color:black;"> </span> 0.8</span></figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1129693374">.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 class="mw-selflink selflink">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 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>In <a href="/wiki/Astrodynamics" class="mw-redirect" title="Astrodynamics">astrodynamics</a>, the <b>orbital eccentricity</b> of an <a href="/wiki/Astronomical_object" title="Astronomical object">astronomical object</a> is a <a href="/wiki/Dimensionless_quantity" title="Dimensionless quantity">dimensionless parameter</a> that determines the amount by which its <a href="/wiki/Orbit" title="Orbit">orbit</a> around another body deviates from a perfect <a href="/wiki/Circle" title="Circle">circle</a>. A value of 0 is a <a href="/wiki/Circular_orbit" title="Circular orbit">circular orbit</a>, values between 0 and 1 form an <a href="/wiki/Elliptic_orbit" title="Elliptic orbit">elliptic orbit</a>, 1 is a <a href="/wiki/Parabola" title="Parabola">parabolic</a> <a href="/wiki/Escape_orbit" class="mw-redirect" title="Escape orbit">escape orbit</a> (or capture orbit), and greater than 1 is a <a href="/wiki/Hyperbola" title="Hyperbola">hyperbola</a>. The term derives its name from the parameters of <a href="/wiki/Conic_section" title="Conic section">conic sections</a>, as every <a href="/wiki/Kepler_orbit" title="Kepler orbit">Kepler orbit</a> is a conic section. It is normally used for the isolated <a href="/wiki/Two-body_problem" title="Two-body problem">two-body problem</a>, but extensions exist for objects following a <a href="/wiki/Klemperer_rosette" title="Klemperer rosette">rosette</a> orbit through the Galaxy. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Orbital_eccentricity&action=edit&section=1" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In a <a href="/wiki/Two-body_problem" title="Two-body problem">two-body problem</a> with inverse-square-law force, every <a href="/wiki/Orbit" title="Orbit">orbit</a> is a <a href="/wiki/Kepler_orbit" title="Kepler orbit">Kepler orbit</a>. The <a href="/wiki/Eccentricity_(mathematics)" title="Eccentricity (mathematics)">eccentricity</a> of this Kepler orbit is a <a href="/wiki/Non-negative_number" class="mw-redirect" title="Non-negative number">non-negative number</a> that defines its shape. </p><p>The eccentricity may take the following values: </p> <ul><li><a href="/wiki/Circular_orbit" title="Circular orbit">Circular orbit</a>: <i>e</i> = 0</li> <li><a href="/wiki/Elliptic_orbit" title="Elliptic orbit">Elliptic orbit</a>: 0 < <i>e</i> < 1</li> <li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Parabolic trajectory</a>: <i>e</i> = 1</li> <li><a href="/wiki/Hyperbolic_trajectory" title="Hyperbolic trajectory">Hyperbolic trajectory</a>: <i>e</i> > 1</li></ul> <p>The eccentricity <i>e</i> is given by<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> </p><p><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 e={\sqrt {1+{\frac {2EL^{2}}{m_{\text{red}}\,\alpha ^{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>E</mi> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>red</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <msup> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e={\sqrt {1+{\frac {2EL^{2}}{m_{\text{red}}\,\alpha ^{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d62016b789691e1c8d8535e54b1e8aaa2dc8063" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:18.835ex; height:7.509ex;" alt="{\displaystyle e={\sqrt {1+{\frac {2EL^{2}}{m_{\text{red}}\,\alpha ^{2}}}}}}"></span> </p><p>where <span class="texhtml"><i>E</i></span> is the total <a href="/wiki/Orbital_energy" class="mw-redirect" title="Orbital energy">orbital energy</a>, <span class="texhtml"><i>L</i></span> is the <a href="/wiki/Angular_momentum" title="Angular momentum">angular momentum</a>, <span class="texhtml"><i>m</i><sub>red</sub></span> is the <a href="/wiki/Reduced_mass" title="Reduced mass">reduced mass</a>, and <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 }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> the coefficient of the inverse-square law <a href="/wiki/Central_force" title="Central force">central force</a> such as in the theory of <a href="/wiki/Gravity" title="Gravity">gravity</a> or <a href="/wiki/Electrostatics" title="Electrostatics">electrostatics</a> in <a href="/wiki/Classical_physics" title="Classical physics">classical physics</a>: <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 F={\frac {\alpha }{r^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>α</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F={\frac {\alpha }{r^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7de79d511a8adc03e76e31ddf64c7f3972e8bed" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:7.778ex; height:5.009ex;" alt="{\displaystyle F={\frac {\alpha }{r^{2}}}}"></span> (<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 }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> is negative for an attractive force, positive for a repulsive one; related to the <a href="/wiki/Kepler_problem" title="Kepler problem">Kepler problem</a>) </p><p>or in the case of a gravitational force:<sup id="cite_ref-BateEtAl_2-0" class="reference"><a href="#cite_note-BateEtAl-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 24">: 24 </span></sup> <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 e={\sqrt {1+{\frac {2\varepsilon h^{2}}{\mu ^{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>ε</mi> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e={\sqrt {1+{\frac {2\varepsilon h^{2}}{\mu ^{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56bf173b613ed5a2cc8485714c210108884d2c31" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:15.984ex; height:7.676ex;" alt="{\displaystyle e={\sqrt {1+{\frac {2\varepsilon h^{2}}{\mu ^{2}}}}}}"></span> </p><p>where <span class="texhtml"><i>ε</i></span> is the <a href="/wiki/Specific_orbital_energy" title="Specific orbital energy">specific orbital energy</a> (total energy divided by the reduced mass), <span class="texhtml"><i>μ</i></span> the <a href="/wiki/Standard_gravitational_parameter" title="Standard gravitational parameter">standard gravitational parameter</a> based on the total mass, and <span class="texhtml"><i>h</i></span> the <a href="/wiki/Specific_relative_angular_momentum" class="mw-redirect" title="Specific relative angular momentum">specific relative angular momentum</a> (<a href="/wiki/Angular_momentum" title="Angular momentum">angular momentum</a> divided by the reduced mass).<sup id="cite_ref-BateEtAl_2-1" class="reference"><a href="#cite_note-BateEtAl-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 12–17">: 12–17 </span></sup> </p><p>For values of <i>e</i> from 0 to 1 the orbit's shape is an increasingly elongated (or flatter) ellipse; for values of <i>e</i> from 1 to infinity the orbit is a <a href="/wiki/Hyperbola" title="Hyperbola">hyperbola</a> branch making a total turn of <span class="nowrap">2 <a href="/wiki/Inverse_trigonometric_functions" title="Inverse trigonometric functions">arccsc</a>(<i>e</i>)</span>, decreasing from 180 to 0 degrees. Here, the total turn is analogous to <a href="/wiki/Winding_number#Turning_number" title="Winding number">turning number</a>, but for open curves (an angle covered by velocity vector). The limit case between an ellipse and a hyperbola, when <i>e</i> equals 1, is parabola. </p><p>Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits have zero angular momentum and hence eccentricity equal to one. Keeping the energy constant and reducing the angular momentum, elliptic, parabolic, and hyperbolic orbits each tend to the corresponding type of radial trajectory while <i>e</i> tends to 1 (or in the parabolic case, remains 1). </p><p>For a repulsive force only the hyperbolic trajectory, including the radial version, is applicable. </p><p>For elliptical orbits, a simple proof shows that <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 \arcsin(e)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>arcsin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>e</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \arcsin(e)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d97c5c4792d3a33b1f701e373a8308454226480" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.855ex; height:2.843ex;" alt="{\displaystyle \arcsin(e)}"></span> yields the projection angle of a perfect circle to an <a href="/wiki/Ellipse" title="Ellipse">ellipse</a> of eccentricity <i>e</i>. For example, to view the eccentricity of the planet Mercury (<i>e</i> = 0.2056), one must simply calculate the <a href="/wiki/Inverse_trigonometric_functions" title="Inverse trigonometric functions">inverse sine</a> to find the projection angle of 11.86 degrees. Then, tilting any circular object by that angle, the apparent ellipse of that object projected to the viewer's eye will be of the same eccentricity. </p> <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=Orbital_eccentricity&action=edit&section=2" title="Edit section: Etymology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The word "eccentricity" comes from <a href="/wiki/Medieval_Latin" title="Medieval Latin">Medieval Latin</a> <i>eccentricus</i>, derived from <a href="/wiki/Ancient_Greek_language" class="mw-redirect" title="Ancient Greek language">Greek</a> <span title="Ancient Greek (to 1453)-language text"><span lang="grc">ἔκκεντρος</span></span> <i>ekkentros</i> "out of the center", from <span title="Ancient Greek (to 1453)-language text"><span lang="grc">ἐκ-</span></span> <i>ek-</i>, "out of" + <span title="Ancient Greek (to 1453)-language text"><span lang="grc">κέντρον</span></span> <i>kentron</i> "center". "Eccentric" first appeared in English in 1551, with the definition "...a circle in which the earth, sun. etc. deviates from its center".<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. (November 2017)">citation needed</span></a></i>]</sup> In 1556, five years later, an adjectival form of the word had developed. </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_eccentricity&action=edit&section=3" title="Edit section: Calculation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The eccentricity of an orbit can be calculated from the <a href="/wiki/Orbital_state_vectors" title="Orbital state vectors">orbital state vectors</a> as the <a href="/wiki/Magnitude_(mathematics)#Euclidean_vector_space" title="Magnitude (mathematics)">magnitude</a> of the <a href="/wiki/Eccentricity_vector" title="Eccentricity vector">eccentricity vector</a>: <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 e=\left|\mathbf {e} \right|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>=</mo> <mrow> <mo>|</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">e</mi> </mrow> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e=\left|\mathbf {e} \right|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c093a492d9d4b09ece25d6ded7ae9f6988b976f4" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.701ex; height:2.843ex;" alt="{\displaystyle e=\left|\mathbf {e} \right|}"></span> where: </p> <ul><li><b><span class="texhtml">e</span></b> is the eccentricity vector (<i>"Hamilton's vector"</i>).<sup id="cite_ref-BateEtAl_2-2" class="reference"><a href="#cite_note-BateEtAl-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 25, 62–63">: 25, 62–63 </span></sup></li></ul> <p>For <a href="/wiki/Elliptical_orbit" class="mw-redirect" title="Elliptical orbit">elliptical orbits</a> it can also be calculated from the <a href="/wiki/Periapsis" class="mw-redirect" title="Periapsis">periapsis</a> and <a href="/wiki/Apoapsis" class="mw-redirect" title="Apoapsis">apoapsis</a> since <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 r_{\text{p}}=a\,(1-e)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> <mo>=</mo> <mi>a</mi> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>e</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{\text{p}}=a\,(1-e)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52d677da10c1d2f2e8832cacdd4c730d73ca458e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.806ex; height:3.009ex;" alt="{\displaystyle r_{\text{p}}=a\,(1-e)}"></span> and <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 r_{\text{a}}=a\,(1+e)\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <mo>=</mo> <mi>a</mi> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>e</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{\text{a}}=a\,(1+e)\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad2838661225593b31452ce1649b2817091f804e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.748ex; height:2.843ex;" alt="{\displaystyle r_{\text{a}}=a\,(1+e)\,,}"></span> where <span class="texhtml mvar" style="font-style:italic;">a</span> is the length of the <a href="/wiki/Semi-major_axis" class="mw-redirect" title="Semi-major axis">semi-major axis</a>.<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 {\begin{aligned}e&={\frac {r_{\text{a}}-r_{\text{p}}}{r_{\text{a}}+r_{\text{p}}}}\\\,\\&={\frac {r_{\text{a}}/r_{\text{p}}-1}{r_{\text{a}}/r_{\text{p}}+1}}\\\,\\&=1-{\frac {2}{\;{\frac {r_{\text{a}}}{r_{\text{p}}}}+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> <mi>e</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> </mrow> <mrow> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace" /> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mspace width="thinmathspace" /> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mrow> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mn>1</mn> <mspace width="thickmathspace" /> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}e&={\frac {r_{\text{a}}-r_{\text{p}}}{r_{\text{a}}+r_{\text{p}}}}\\\,\\&={\frac {r_{\text{a}}/r_{\text{p}}-1}{r_{\text{a}}/r_{\text{p}}+1}}\\\,\\&=1-{\frac {2}{\;{\frac {r_{\text{a}}}{r_{\text{p}}}}+1\;}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb13bba463ad0e6db9b52ccfec264e308c3297cb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -12.505ex; width:17.549ex; height:26.009ex;" alt="{\displaystyle {\begin{aligned}e&={\frac {r_{\text{a}}-r_{\text{p}}}{r_{\text{a}}+r_{\text{p}}}}\\\,\\&={\frac {r_{\text{a}}/r_{\text{p}}-1}{r_{\text{a}}/r_{\text{p}}+1}}\\\,\\&=1-{\frac {2}{\;{\frac {r_{\text{a}}}{r_{\text{p}}}}+1\;}}\end{aligned}}}"></span> where: </p> <ul><li><span class="texhtml mvar" style="font-style:italic;">r</span><sub>a</sub> is the radius at <a href="/wiki/Apoapsis" class="mw-redirect" title="Apoapsis">apoapsis</a> (also "apofocus", "aphelion", "apogee"), i.e., the farthest distance of the orbit to the <a href="/wiki/Center_of_mass" title="Center of mass">center of mass</a> of the system, which is a <a href="/wiki/Focus_(geometry)" title="Focus (geometry)">focus</a> of the ellipse.</li> <li><span class="texhtml mvar" style="font-style:italic;">r</span><sub>p</sub> is the radius at <a href="/wiki/Periapsis" class="mw-redirect" title="Periapsis">periapsis</a> (or "perifocus" etc.), the closest distance.</li></ul> <p>The semi-major axis, a, is also the path-averaged distance to the centre of mass, <sup id="cite_ref-BateEtAl_2-3" class="reference"><a href="#cite_note-BateEtAl-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 24–25">: 24–25 </span></sup> while the time-averaged distance is a(1 + e e / 2).<a rel="nofollow" class="external autonumber" href="https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Celestial_Mechanics_(Tatum)/09%3A_The_Two_Body_Problem_in_Two_Dimensions/9.10%3A_Mean_Distance_in_an_Elliptic_Orbit">[1]</a> </p><p>The eccentricity of an elliptical orbit can be used to obtain the ratio of the <a href="/wiki/Apoapsis" class="mw-redirect" title="Apoapsis">apoapsis</a> radius to the <a href="/wiki/Periapsis" class="mw-redirect" title="Periapsis">periapsis</a> radius: <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 {\frac {r_{\text{a}}}{r_{\text{p}}}}={\frac {\,a\,(1+e)\,}{\,a\,(1-e)\,}}={\frac {1+e}{1-e}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mspace width="thinmathspace" /> <mi>a</mi> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>e</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mrow> <mrow> <mspace width="thinmathspace" /> <mi>a</mi> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>e</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>e</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mi>e</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {r_{\text{a}}}{r_{\text{p}}}}={\frac {\,a\,(1+e)\,}{\,a\,(1-e)\,}}={\frac {1+e}{1-e}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0ec5bdd553feeb2d29b07d606d519f52e6b285b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:25.273ex; height:6.509ex;" alt="{\displaystyle {\frac {r_{\text{a}}}{r_{\text{p}}}}={\frac {\,a\,(1+e)\,}{\,a\,(1-e)\,}}={\frac {1+e}{1-e}}}"></span> </p><p>For Earth, orbital eccentricity <span class="texhtml"><i>e</i> ≈ <span class="nowrap"><span data-sort-value="6998167100000000000♠"></span>0.016<span style="margin-left:.25em;">71</span></span></span>, <a href="/wiki/Apoapsis" class="mw-redirect" title="Apoapsis">apoapsis</a> is aphelion and <a href="/wiki/Periapsis" class="mw-redirect" title="Periapsis">periapsis</a> is perihelion, relative to the Sun. </p><p>For Earth's annual orbit path, the ratio of longest radius (<span class="texhtml mvar" style="font-style:italic;">r</span><sub>a</sub>) / shortest radius (<span class="texhtml mvar" style="font-style:italic;">r</span><sub>p</sub>) is <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 {\frac {\,r_{\text{a}}\,}{r_{\text{p}}}}={\frac {\,1+e\,}{1-e}}{\text{ ≈ 1.03399 .}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mspace width="thinmathspace" /> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <mspace width="thinmathspace" /> </mrow> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mspace width="thinmathspace" /> <mn>1</mn> <mo>+</mo> <mi>e</mi> <mspace width="thinmathspace" /> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mi>e</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext> ≈ 1.03399 .</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\,r_{\text{a}}\,}{r_{\text{p}}}}={\frac {\,1+e\,}{1-e}}{\text{ ≈ 1.03399 .}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45d2675f3cdb73aa94bd207d988042e29460411a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.327ex; height:5.843ex;" alt="{\displaystyle {\frac {\,r_{\text{a}}\,}{r_{\text{p}}}}={\frac {\,1+e\,}{1-e}}{\text{ ≈ 1.03399 .}}}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Orbital_eccentricity&action=edit&section=4" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Eccentricity_rocky_planets.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Eccentricity_rocky_planets.jpg/500px-Eccentricity_rocky_planets.jpg" decoding="async" width="500" height="261" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/9/98/Eccentricity_rocky_planets.jpg 1.5x" data-file-width="650" data-file-height="339" /></a><figcaption>Plot of the changing orbital eccentricities of <a href="/wiki/Mercury_(planet)" title="Mercury (planet)">Mercury</a>, <a href="/wiki/Venus" title="Venus">Venus</a>, <a href="/wiki/Earth" title="Earth">Earth</a> and <a href="/wiki/Mars" title="Mars">Mars</a> over the next 50 000 years. The arrows indicate the different scales used, as the eccentricities of Mercury and Mars are much greater than those of Venus and Earth. The 0 point on x-axis in this plot is the year 2007.</figcaption></figure> <table class="wikitable floatright"> <caption>Eccentricities of Solar System bodies </caption> <tbody><tr> <th>Object</th> <th>Eccentricity </th></tr> <tr> <td><a href="/wiki/Triton_(moon)" title="Triton (moon)">Triton</a></td> <td><span style="white-space:nowrap">0.000<span style="margin-left:0.25em">02</span></span> </td></tr> <tr> <td><a href="/wiki/Venus" title="Venus">Venus</a></td> <td><span style="white-space:nowrap">0.006<span style="margin-left:0.25em">8</span></span> </td></tr> <tr> <td><a href="/wiki/Neptune" title="Neptune">Neptune</a></td> <td><span style="white-space:nowrap">0.008<span style="margin-left:0.25em">6</span></span> </td></tr> <tr> <td><a href="/wiki/Earth" title="Earth">Earth</a></td> <td><span style="white-space:nowrap">0.016<span style="margin-left:0.25em">7</span></span> </td></tr> <tr> <td><a href="/wiki/Titan_(moon)" title="Titan (moon)">Titan</a></td> <td><span style="white-space:nowrap">0.028<span style="margin-left:0.25em">8</span></span> </td></tr> <tr> <td><a href="/wiki/Uranus" title="Uranus">Uranus</a></td> <td><span style="white-space:nowrap">0.047<span style="margin-left:0.25em">2</span></span> </td></tr> <tr> <td><a href="/wiki/Jupiter" title="Jupiter">Jupiter</a></td> <td><span style="white-space:nowrap">0.048<span style="margin-left:0.25em">4</span></span> </td></tr> <tr> <td><a href="/wiki/Saturn" title="Saturn">Saturn</a></td> <td><span style="white-space:nowrap">0.054<span style="margin-left:0.25em">1</span></span> </td></tr> <tr> <td><a href="/wiki/Moon" title="Moon">Luna (Moon)</a></td> <td><span style="white-space:nowrap">0.054<span style="margin-left:0.25em">9</span></span> </td></tr> <tr> <td><a href="/wiki/1_Ceres" class="mw-redirect" title="1 Ceres">Ceres</a></td> <td><span style="white-space:nowrap">0.075<span style="margin-left:0.25em">8</span></span> </td></tr> <tr> <td><a href="/wiki/4_Vesta" title="4 Vesta">Vesta</a></td> <td><span style="white-space:nowrap">0.088<span style="margin-left:0.25em">7</span></span> </td></tr> <tr> <td><a href="/wiki/Mars" title="Mars">Mars</a></td> <td><span style="white-space:nowrap">0.093<span style="margin-left:0.25em">4</span></span> </td></tr> <tr> <td><a href="/wiki/10_Hygiea" title="10 Hygiea">10 Hygiea</a></td> <td><span style="white-space:nowrap">0.114<span style="margin-left:0.25em">6</span></span> </td></tr> <tr> <td><a href="/wiki/Makemake" title="Makemake">Makemake</a></td> <td><span style="white-space:nowrap">0.155<span style="margin-left:0.25em">9</span></span> </td></tr> <tr> <td><a href="/wiki/Haumea" title="Haumea">Haumea</a></td> <td><span style="white-space:nowrap">0.188<span style="margin-left:0.25em">7</span></span> </td></tr> <tr> <td><a href="/wiki/Mercury_(planet)" title="Mercury (planet)">Mercury</a></td> <td><span style="white-space:nowrap">0.205<span style="margin-left:0.25em">6</span></span> </td></tr> <tr> <td><a href="/wiki/2_Pallas" title="2 Pallas">2 Pallas</a></td> <td><span style="white-space:nowrap">0.231<span style="margin-left:0.25em">3</span></span> </td></tr> <tr> <td><a href="/wiki/Pluto" title="Pluto">Pluto</a></td> <td><span style="white-space:nowrap">0.248<span style="margin-left:0.25em">8</span></span> </td></tr> <tr> <td><a href="/wiki/3_Juno" title="3 Juno">3 Juno</a></td> <td><span style="white-space:nowrap">0.255<span style="margin-left:0.25em">5</span></span> </td></tr> <tr> <td><a href="/wiki/324_Bamberga" title="324 Bamberga">324 Bamberga</a></td> <td><span style="white-space:nowrap">0.340<span style="margin-left:0.25em">0</span></span> </td></tr> <tr> <td><a href="/wiki/Eris_(dwarf_planet)" title="Eris (dwarf planet)">Eris</a></td> <td><span style="white-space:nowrap">0.440<span style="margin-left:0.25em">7</span></span> </td></tr> <tr> <td><a href="/wiki/Nereid_(moon)" title="Nereid (moon)">Nereid</a></td> <td><span style="white-space:nowrap">0.750<span style="margin-left:0.25em">7</span></span> </td></tr> <tr> <td><a href="/wiki/90377_Sedna" class="mw-redirect" title="90377 Sedna">Sedna</a></td> <td><span style="white-space:nowrap">0.854<span style="margin-left:0.25em">9</span></span> </td></tr> <tr> <td><a href="/wiki/Halley%27s_Comet" title="Halley's Comet">Halley's Comet</a></td> <td><span style="white-space:nowrap">0.967<span style="margin-left:0.25em">1</span></span> </td></tr> <tr> <td><a href="/wiki/Comet_Hale-Bopp" class="mw-redirect" title="Comet Hale-Bopp">Comet Hale-Bopp</a></td> <td><span style="white-space:nowrap">0.995<span style="margin-left:0.25em">1</span></span> </td></tr> <tr> <td><a href="/wiki/Comet_Ikeya-Seki" class="mw-redirect" title="Comet Ikeya-Seki">Comet Ikeya-Seki</a></td> <td><span style="white-space:nowrap">0.999<span style="margin-left:0.25em">9</span></span> </td></tr> <tr> <td><a href="/wiki/Comet_McNaught" title="Comet McNaught">Comet McNaught</a></td> <td><span style="white-space:nowrap">1.000<span style="margin-left:0.25em">2</span></span><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/C/1980_E1" class="mw-redirect" title="C/1980 E1">C/1980 E1</a></td> <td>1.057 </td></tr> <tr> <td><a href="/wiki/%CA%BBOumuamua" title="ʻOumuamua">ʻOumuamua</a></td> <td>1.20<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/2I/Borisov" title="2I/Borisov">2I/Borisov</a></td> <td>3.5<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>c<span class="cite-bracket">]</span></a></sup> </td></tr></tbody></table> <p>The table lists the values for all planets and dwarf planets, and selected asteroids, comets, and moons. <a href="/wiki/Mercury_(planet)" title="Mercury (planet)">Mercury</a> has the greatest orbital eccentricity of any planet in the <a href="/wiki/Solar_System" title="Solar System">Solar System</a> (<i>e</i> = <span class="nowrap"><span data-sort-value="6999205600000000000♠"></span>0.2056</span>), followed by <a href="/wiki/Mars" title="Mars">Mars</a> of <span style="white-space:nowrap">0.093<span style="margin-left:0.25em">4</span></span>. Such eccentricity is sufficient for Mercury to receive twice as much <a href="/wiki/Solar_irradiation" class="mw-redirect" title="Solar irradiation">solar irradiation</a> at perihelion compared to aphelion. Before its demotion from <a href="/wiki/IAU_definition_of_planet" title="IAU definition of planet">planet status</a> in 2006, <a href="/wiki/Pluto" title="Pluto">Pluto</a> was considered to be the planet with the most eccentric orbit (<i>e</i> = <span class="nowrap"><span data-sort-value="6999248000000000000♠"></span>0.248</span>). Other <a href="/wiki/Trans-Neptunian_objects" class="mw-redirect" title="Trans-Neptunian objects">Trans-Neptunian objects</a> have significant eccentricity, notably the dwarf planet <a href="/wiki/Eris_(dwarf_planet)" title="Eris (dwarf planet)">Eris</a> (0.44). Even further out, <a href="/wiki/90377_Sedna" class="mw-redirect" title="90377 Sedna">Sedna</a> has an extremely-high eccentricity of <span class="nowrap"><span data-sort-value="6999855000000000000♠"></span>0.855</span> due to its estimated aphelion of 937 AU and perihelion of about 76 AU, possibly under influence of <a href="/wiki/Planet_9" class="mw-redirect" title="Planet 9">unknown object(s)</a>. </p><p>The eccentricity of <a href="/wiki/Earth%27s_orbit" title="Earth's orbit">Earth's orbit</a> is currently about <span style="white-space:nowrap">0.016<span style="margin-left:0.25em">7</span></span>; its orbit is nearly circular. <a href="/wiki/Neptune#Orbit" title="Neptune">Neptune's</a> and <a href="/wiki/Venus%27s_orbit" class="mw-redirect" title="Venus's orbit">Venus's</a> have even lower eccentricities of <span style="white-space:nowrap">0.008<span style="margin-left:0.25em">6</span></span> and <span style="white-space:nowrap">0.006<span style="margin-left:0.25em">8</span></span> respectively, the latter being the least orbital eccentricity of any planet in the Solar System. Over hundreds of thousands of years, the eccentricity of the Earth's orbit varies from nearly <span style="white-space:nowrap">0.003<span style="margin-left:0.25em">4</span></span> to almost 0.058 as a result of gravitational attractions among the planets.<sup id="cite_ref-Berger1991_6-0" class="reference"><a href="#cite_note-Berger1991-6"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Moon" title="Moon">Luna</a>'s value is <span style="white-space:nowrap">0.054<span style="margin-left:0.25em">9</span></span>, the most eccentric of the large moons in the Solar System. The four <a href="/wiki/Galilean_moon" class="mw-redirect" title="Galilean moon">Galilean moons</a> (<a href="/wiki/Io_(moon)" title="Io (moon)">Io</a>, <a href="/wiki/Europa_(moon)" title="Europa (moon)">Europa</a>, <a href="/wiki/Ganymede_(moon)" title="Ganymede (moon)">Ganymede</a> and <a href="/wiki/Callisto_(moon)" title="Callisto (moon)">Callisto</a>) have their eccentricities of less than 0.01. <a href="/wiki/Neptune" title="Neptune">Neptune</a>'s largest moon <a href="/wiki/Triton_(moon)" title="Triton (moon)">Triton</a> has an eccentricity of <span class="nowrap"><span data-sort-value="6995160000000000000♠"></span>1.6<span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−5</sup></span> (<span style="white-space:nowrap">0.000<span style="margin-left:0.25em">016</span></span>),<sup id="cite_ref-Triton_7-0" class="reference"><a href="#cite_note-Triton-7"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> the smallest eccentricity of any known moon in the Solar System;<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. (September 2016)">citation needed</span></a></i>]</sup> its orbit is as close to a perfect circle as can be currently<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers#Chronological_items" title="Wikipedia:Manual of Style/Dates and numbers"><span title="The time period mentioned near this tag is ambiguous. (September 2016)">when?</span></a></i>]</sup> measured. Smaller moons, particularly <a href="/wiki/Irregular_moon" title="Irregular moon">irregular moons</a>, can have significant eccentricities, such as Neptune's third largest moon, <a href="/wiki/Nereid_(moon)" title="Nereid (moon)">Nereid</a>, of <span class="nowrap"><span data-sort-value="6999750000000000000♠"></span>0.75</span>. </p><p>Most of the Solar System's <a href="/wiki/Asteroid" title="Asteroid">asteroids</a> have orbital eccentricities between 0 and 0.35 with an average value of 0.17.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Their comparatively high eccentricities are probably due to under influence of <a href="/wiki/Jupiter" title="Jupiter">Jupiter</a> and to past collisions. </p><p><a href="/wiki/Comet" title="Comet">Comets</a> have very different values of eccentricities. <a href="/wiki/Periodic_comet" class="mw-redirect" title="Periodic comet">Periodic comets</a> have eccentricities mostly between 0.2 and 0.7,<sup id="cite_ref-Comets_9-0" class="reference"><a href="#cite_note-Comets-9"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> but some of them have highly eccentric elliptical orbits with eccentricities just below 1; for example, <a href="/wiki/Halley%27s_Comet" title="Halley's Comet">Halley's Comet</a> has a value of 0.967. Non-periodic comets follow near-<a href="/wiki/Parabolic_orbit" class="mw-redirect" title="Parabolic orbit">parabolic orbits</a> and thus have eccentricities even closer to 1. Examples include <a href="/wiki/Comet_Hale%E2%80%93Bopp" title="Comet Hale–Bopp">Comet Hale–Bopp</a> with a value of <span style="white-space:nowrap">0.995<span style="margin-left:0.25em">1</span></span>,<sup id="cite_ref-Hale-Bopp-jpl_10-0" class="reference"><a href="#cite_note-Hale-Bopp-jpl-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Comet_Ikeya-Seki" class="mw-redirect" title="Comet Ikeya-Seki">Comet Ikeya-Seki</a> with a value of <span style="white-space:nowrap">0.999<span style="margin-left:0.25em">9</span></span> and <a href="/wiki/Comet_McNaught" title="Comet McNaught">Comet McNaught</a> (C/2006 P1) with a value of <span style="white-space:nowrap">1.000<span style="margin-left:0.25em">019</span></span>.<sup id="cite_ref-McNaught-jpl_11-0" class="reference"><a href="#cite_note-McNaught-jpl-11"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> As first two's values are less than 1, their orbit are elliptical and they will return.<sup id="cite_ref-Hale-Bopp-jpl_10-1" class="reference"><a href="#cite_note-Hale-Bopp-jpl-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> McNaught has a <a href="/wiki/Hyperbolic_orbit" class="mw-redirect" title="Hyperbolic orbit">hyperbolic orbit</a> but within the influence of the planets,<sup id="cite_ref-McNaught-jpl_11-1" class="reference"><a href="#cite_note-McNaught-jpl-11"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> is still bound to the Sun with an orbital period of about 10<sup>5</sup> years.<sup id="cite_ref-Perth_12-0" class="reference"><a href="#cite_note-Perth-12"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> <a href="/wiki/C/1980_E1" class="mw-redirect" title="C/1980 E1">Comet C/1980 E1</a> has the largest eccentricity of any known hyperbolic comet of solar origin with an eccentricity of 1.057,<sup id="cite_ref-C/1980E1-jpl_13-0" class="reference"><a href="#cite_note-C/1980E1-jpl-13"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> and will eventually leave the Solar System. </p><p><a href="/wiki/%CA%BBOumuamua" title="ʻOumuamua">ʻOumuamua</a> is the first <a href="/wiki/Interstellar_object" title="Interstellar object">interstellar object</a> to be found passing through the Solar System. Its orbital eccentricity of 1.20 indicates that ʻOumuamua has never been gravitationally bound to the Sun. It was discovered 0.2 AU (<span style="white-space:nowrap">30<span style="margin-left:0.25em">000</span><span style="margin-left:0.25em">000</span></span> km; <span style="white-space:nowrap">19<span style="margin-left:0.25em">000</span><span style="margin-left:0.25em">000</span></span> mi) from Earth and is roughly 200 meters in diameter. It has an interstellar speed (velocity at infinity) of 26.33 km/s (<span style="white-space:nowrap">58<span style="margin-left:0.25em">900</span></span> mph). </p> <div class="mw-heading mw-heading2"><h2 id="Mean_average">Mean average</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Orbital_eccentricity&action=edit&section=5" title="Edit section: Mean average"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The mean eccentricity of an object is the average eccentricity as a result of <a href="/wiki/Perturbation_(astronomy)" title="Perturbation (astronomy)">perturbations</a> over a given time period. Neptune currently has an instant (current <a href="/wiki/Epoch_(astronomy)" title="Epoch (astronomy)">epoch</a>) eccentricity of <span style="white-space:nowrap">0.011<span style="margin-left:0.25em">3</span></span>,<sup id="cite_ref-nssdc-Neptune_14-0" class="reference"><a href="#cite_note-nssdc-Neptune-14"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> but from 1800 to 2050 has a mean eccentricity of <span class="nowrap"><span data-sort-value="6997859000000000000♠"></span>0.008<span style="margin-left:.25em;">59</span></span>.<sup id="cite_ref-ssd-mean_15-0" class="reference"><a href="#cite_note-ssd-mean-15"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Climatic_effect">Climatic effect</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Orbital_eccentricity&action=edit&section=6" title="Edit section: Climatic effect"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Orbital mechanics require that the duration of the seasons be proportional to the area of Earth's orbit swept between the <a href="/wiki/Solstices" class="mw-redirect" title="Solstices">solstices</a> and <a href="/wiki/Equinoxes" class="mw-redirect" title="Equinoxes">equinoxes</a>, so when the orbital eccentricity is extreme, the seasons that occur on the far side of the orbit (<a href="/wiki/Aphelion" class="mw-redirect" title="Aphelion">aphelion</a>) can be substantially longer in duration. Northern hemisphere autumn and winter occur at closest approach (<a href="/wiki/Perihelion" class="mw-redirect" title="Perihelion">perihelion</a>), when Earth is moving at its maximum velocity—while the opposite occurs in the southern hemisphere. As a result, in the northern hemisphere, autumn and winter are slightly shorter than spring and summer—but in global terms this is balanced with them being longer below the equator. In 2006, the northern hemisphere summer was 4.66 days longer than winter, and spring was 2.9 days longer than autumn due to orbital eccentricity.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Apsidal_precession" title="Apsidal precession">Apsidal precession</a> also slowly changes the place in Earth's orbit where the solstices and equinoxes occur. This is a slow change in the orbit of Earth, not the axis of rotation, which is referred to as <a href="/wiki/Axial_precession" title="Axial precession">axial precession</a>. The climatic effects of this change are part of the <a href="/wiki/Milankovitch_cycles" title="Milankovitch cycles">Milankovitch cycles</a>. Over the next <span style="white-space:nowrap">10<span style="margin-left:0.25em">000</span></span> years, the northern hemisphere winters will become gradually longer and summers will become shorter. Any cooling effect in one hemisphere is balanced by warming in the other, and any overall change will be counteracted by the fact that the eccentricity of Earth's orbit will be almost halved.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> This will reduce the mean orbital radius and raise temperatures in both hemispheres closer to the mid-interglacial peak. </p> <div class="mw-heading mw-heading2"><h2 id="Exoplanets">Exoplanets</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Orbital_eccentricity&action=edit&section=7" title="Edit section: Exoplanets"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Of the many <a href="/wiki/Exoplanet" title="Exoplanet">exoplanets</a> discovered, most have a higher orbital eccentricity than planets in the Solar System. Exoplanets found with low orbital eccentricity (near-circular orbits) are very close to their star and are <a href="/wiki/Tidally-locked" class="mw-redirect" title="Tidally-locked">tidally-locked</a> to the star. All eight planets in the Solar System have near-circular orbits. The exoplanets discovered show that the Solar System, with its unusually-low eccentricity, is rare and unique.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> One theory attributes this low eccentricity to the high number of planets in the Solar System; another suggests it arose because of its unique asteroid belts. A few other <a href="/wiki/List_of_multiplanetary_systems" title="List of multiplanetary systems">multiplanetary systems</a> have been found, but none resemble the Solar System. The Solar System has unique <a href="/wiki/Planetesimal" title="Planetesimal">planetesimal</a> systems, which led the planets to have near-circular orbits. Solar planetesimal systems include the <a href="/wiki/Asteroid_belt" title="Asteroid belt">asteroid belt</a>, <a href="/wiki/Hilda_family" title="Hilda family">Hilda family</a>, <a href="/wiki/Kuiper_belt" title="Kuiper belt">Kuiper belt</a>, <a href="/wiki/Hills_cloud" title="Hills cloud">Hills cloud</a>, and the <a href="/wiki/Oort_cloud" title="Oort cloud">Oort cloud</a>. The exoplanet systems discovered have either no planetesimal systems or a very large one. Low eccentricity is needed for habitability, especially advanced life.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> High multiplicity planet systems are much more likely to have habitable exoplanets.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Grand_tack_hypothesis" title="Grand tack hypothesis">grand tack hypothesis</a> of the Solar System also helps understand its near-circular orbits and other unique features.<sup id="cite_ref-Zubritsky_2011_23-0" class="reference"><a href="#cite_note-Zubritsky_2011-23"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Sanders_2011_24-0" class="reference"><a href="#cite_note-Sanders_2011-24"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Choi_2015_25-0" class="reference"><a href="#cite_note-Choi_2015-25"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Davidsson_2014_26-0" class="reference"><a href="#cite_note-Davidsson_2014-26"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Raymond_2013_27-0" class="reference"><a href="#cite_note-Raymond_2013-27"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-O'Brien_2014_28-0" class="reference"><a href="#cite_note-O'Brien_2014-28"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </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_eccentricity&action=edit&section=8" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Equation_of_time" title="Equation of time">Equation of time</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Footnotes">Footnotes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Orbital_eccentricity&action=edit&section=9" title="Edit section: Footnotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">While its orbit is hyperbolic, it is however still bound to the Sun due to the influence of planets</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">ʻOumuamua was never bound to the Sun, so its orbit is hyperbolic: <span class="nowrap"><span class="texhtml mvar" style="font-style:italic;">e</span> ≈ 1.20 > 1</span> </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">C/2019 Q4 (Borisov) was never bound to the Sun, so its orbit is hyperbolic: <span class="nowrap"><span class="texhtml mvar" style="font-style:italic;">e</span> ≈ 3.5 > 1</span> </span> </li> </ol></div></div> <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_eccentricity&action=edit&section=10" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-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="CITEREFAbraham2008" class="citation book cs1">Abraham, Ralph (2008). <i>Foundations of mechanics</i>. Jerrold E. Marsden (2nd ed.). Providence, R.I.: AMS Chelsea Pub./American Mathematical Society. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8218-4438-0" title="Special:BookSources/978-0-8218-4438-0"><bdi>978-0-8218-4438-0</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/191847156">191847156</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Foundations+of+mechanics&rft.place=Providence%2C+R.I.&rft.edition=2nd&rft.pub=AMS+Chelsea+Pub.%2FAmerican+Mathematical+Society&rft.date=2008&rft_id=info%3Aoclcnum%2F191847156&rft.isbn=978-0-8218-4438-0&rft.aulast=Abraham&rft.aufirst=Ralph&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></span> </li> <li id="cite_note-BateEtAl-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-BateEtAl_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-BateEtAl_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-BateEtAl_2-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-BateEtAl_2-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBateMuellerWhiteSaylor2020" class="citation book cs1">Bate, Roger R.; Mueller, Donald D.; White, Jerry E.; Saylor, William W. (2020). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UEC9DwAAQBAJ"><i>Fundamentals of Astrodynamics</i></a>. <a href="/wiki/Courier_Dover" class="mw-redirect" title="Courier Dover">Courier Dover</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-49704-4" title="Special:BookSources/978-0-486-49704-4"><bdi>978-0-486-49704-4</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">4 March</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Astrodynamics&rft.pub=Courier+Dover&rft.date=2020&rft.isbn=978-0-486-49704-4&rft.aulast=Bate&rft.aufirst=Roger+R.&rft.au=Mueller%2C+Donald+D.&rft.au=White%2C+Jerry+E.&rft.au=Saylor%2C+William+W.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DUEC9DwAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></span> </li> <li id="cite_note-Berger1991-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Berger1991_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFA._BergerM.F._Loutre1991" class="citation web cs1">A. Berger & M.F. Loutre (1991). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180106070653/http://www.museum.state.il.us/exhibits/ice_ages/eccentricity_graph.html">"Graph of the eccentricity of the Earth's orbit"</a>. Illinois State Museum (Insolation values for the climate of the last 10 million years). Archived from <a rel="nofollow" class="external text" href="http://www.museum.state.il.us/exhibits/ice_ages/eccentricity_graph.html">the original</a> on 6 January 2018.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Graph+of+the+eccentricity+of+the+Earth%27s+orbit&rft.pub=Illinois+State+Museum+%28Insolation+values+for+the+climate+of+the+last+10+million+years%29&rft.date=1991&rft.au=A.+Berger&rft.au=M.F.+Loutre&rft_id=http%3A%2F%2Fwww.museum.state.il.us%2Fexhibits%2Fice_ages%2Feccentricity_graph.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></span> </li> <li id="cite_note-Triton-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Triton_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavid_R._Williams2008" class="citation web cs1">David R. Williams (22 January 2008). <a rel="nofollow" class="external text" href="https://nssdc.gsfc.nasa.gov/planetary/factsheet/neptuniansatfact.html">"Neptunian Satellite Fact Sheet"</a>. NASA.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Neptunian+Satellite+Fact+Sheet&rft.pub=NASA&rft.date=2008-01-22&rft.au=David+R.+Williams&rft_id=http%3A%2F%2Fnssdc.gsfc.nasa.gov%2Fplanetary%2Ffactsheet%2Fneptuniansatfact.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></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"><a rel="nofollow" class="external text" href="http://filer.case.edu/sjr16/advanced/asteroid.html">Asteroids</a><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070304161718/http://filer.case.edu/sjr16/advanced/asteroid.html">Archived</a> 4 March 2007 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-Comets-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Comets_9-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLewis2012" class="citation book cs1">Lewis, John (2 December 2012). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=35uwarLgVLsC&pg=PA281"><i>Physics and Chemistry of the Solar System</i></a>. Academic Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780323145848" title="Special:BookSources/9780323145848"><bdi>9780323145848</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+and+Chemistry+of+the+Solar+System&rft.pub=Academic+Press&rft.date=2012-12-02&rft.isbn=9780323145848&rft.aulast=Lewis&rft.aufirst=John&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D35uwarLgVLsC%26pg%3DPA281&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></span> </li> <li id="cite_note-Hale-Bopp-jpl-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-Hale-Bopp-jpl_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Hale-Bopp-jpl_10-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=Hale-Bopp">"JPL Small-Body Database Browser: C/1995 O1 (Hale-Bopp)"</a> (2007-10-22 last obs)<span class="reference-accessdate">. Retrieved <span class="nowrap">5 December</span> 2008</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=JPL+Small-Body+Database+Browser%3A+C%2F1995+O1+%28Hale-Bopp%29&rft_id=http%3A%2F%2Fssd.jpl.nasa.gov%2Fsbdb.cgi%3Fsstr%3DHale-Bopp&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></span> </li> <li id="cite_note-McNaught-jpl-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-McNaught-jpl_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-McNaught-jpl_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=C/2006+P1">"JPL Small-Body Database Browser: C/2006 P1 (McNaught)"</a> (2007-07-11 last obs)<span class="reference-accessdate">. Retrieved <span class="nowrap">17 December</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=JPL+Small-Body+Database+Browser%3A+C%2F2006+P1+%28McNaught%29&rft_id=http%3A%2F%2Fssd.jpl.nasa.gov%2Fsbdb.cgi%3Fsstr%3DC%2F2006%2BP1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></span> </li> <li id="cite_note-Perth-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-Perth_12-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110218054618/http://www.perthobservatory.wa.gov.au/information/comet_mcnaught_info.html">"Comet C/2006 P1 (McNaught) – facts and figures"</a>. Perth Observatory in Australia. 22 January 2007. Archived from <a rel="nofollow" class="external text" href="http://www.perthobservatory.wa.gov.au/information/comet_mcnaught_info.html">the original</a> on 18 February 2011.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Comet+C%2F2006+P1+%28McNaught%29+%E2%80%93+facts+and+figures&rft.pub=Perth+Observatory+in+Australia&rft.date=2007-01-22&rft_id=http%3A%2F%2Fwww.perthobservatory.wa.gov.au%2Finformation%2Fcomet_mcnaught_info.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></span> </li> <li id="cite_note-C/1980E1-jpl-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-C/1980E1-jpl_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=1980E1">"JPL Small-Body Database Browser: C/1980 E1 (Bowell)"</a> (1986-12-02 last obs)<span class="reference-accessdate">. Retrieved <span class="nowrap">22 March</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=JPL+Small-Body+Database+Browser%3A+C%2F1980+E1+%28Bowell%29&rft_id=http%3A%2F%2Fssd.jpl.nasa.gov%2Fsbdb.cgi%3Fsstr%3D1980E1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></span> </li> <li id="cite_note-nssdc-Neptune-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-nssdc-Neptune_14-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilliams2007" class="citation web cs1">Williams, David R. (29 November 2007). <a rel="nofollow" class="external text" href="https://nssdc.gsfc.nasa.gov/planetary/factsheet/neptunefact.html">"Neptune Fact Sheet"</a>. 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Retrieved <span class="nowrap">17 December</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Keplerian+elements+for+1800+A.D.+to+2050+A.D.&rft.pub=JPL+Solar+System+Dynamics&rft_id=http%3A%2F%2Fssd.jpl.nasa.gov%2Ftxt%2Fp_elem_t1.txt&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">Data from <a rel="nofollow" class="external text" href="http://aa.usno.navy.mil/data/docs/EarthSeasons.php">United States Naval Observatory</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20071013000301/http://aa.usno.navy.mil/data/docs/EarthSeasons.php">Archived</a> 13 October 2007 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBerger_A.Loutre_M.F.Mélice_J.L.2006" class="citation journal cs1">Berger A.; Loutre M.F.; Mélice J.L. (2006). <a rel="nofollow" class="external text" href="https://www.clim-past-discuss.net/2/519/2006/cpd-2-519-2006.pdf">"Equatorial insolation: from precession harmonics to eccentricity frequencies"</a> <span class="cs1-format">(PDF)</span>. <i>Clim. 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"Water delivery and giant impacts in the 'Grand Tack' scenario". <i>Icarus</i>. <b>239</b>: 74–84. <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/1407.3290">1407.3290</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/2014Icar..239...74O">2014Icar..239...74O</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.icarus.2014.05.009">10.1016/j.icarus.2014.05.009</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:51737711">51737711</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Icarus&rft.atitle=Water+delivery+and+giant+impacts+in+the+%27Grand+Tack%27+scenario&rft.volume=239&rft.pages=74-84&rft.date=2014&rft_id=info%3Aarxiv%2F1407.3290&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A51737711%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.icarus.2014.05.009&rft_id=info%3Abibcode%2F2014Icar..239...74O&rft.aulast=O%27Brien&rft.aufirst=David+P.&rft.au=Walsh%2C+Kevin+J.&rft.au=Morbidelli%2C+Alessandro&rft.au=Raymond%2C+Sean+N.&rft.au=Mandell%2C+Avi+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLoebBatistaSloan2016" class="citation journal cs1">Loeb, Abraham; Batista, Rafael; Sloan, David (August 2016). "Relative Likelihood for Life as a Function of Cosmic Time". <i>Journal of Cosmology and Astroparticle Physics</i>. <b>2016</b> (8): 040. <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/1606.08448">1606.08448</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/2016JCAP...08..040L">2016JCAP...08..040L</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F1475-7516%2F2016%2F08%2F040">10.1088/1475-7516/2016/08/040</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:118489638">118489638</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Cosmology+and+Astroparticle+Physics&rft.atitle=Relative+Likelihood+for+Life+as+a+Function+of+Cosmic+Time&rft.volume=2016&rft.issue=8&rft.pages=040&rft.date=2016-08&rft_id=info%3Aarxiv%2F1606.08448&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A118489638%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F1475-7516%2F2016%2F08%2F040&rft_id=info%3Abibcode%2F2016JCAP...08..040L&rft.aulast=Loeb&rft.aufirst=Abraham&rft.au=Batista%2C+Rafael&rft.au=Sloan%2C+David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.cfa.harvard.edu/news/2016–17">"Is Earthly Life Premature from a Cosmic Perspective?"</a>. Harvard-Smithsonian Center for Astrophysics. 1 August 2016.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Is+Earthly+Life+Premature+from+a+Cosmic+Perspective%3F&rft.pub=Harvard-Smithsonian+Center+for+Astrophysics&rft.date=2016-08-01&rft_id=https%3A%2F%2Fwww.cfa.harvard.edu%2Fnews%2F2016%E2%80%9317&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></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=Orbital_eccentricity&action=edit&section=11" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPrussingConway1993" class="citation book cs1">Prussing, John E.; Conway, Bruce A. (1993). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/orbitalmechanics00prus"><i>Orbital Mechanics</i></a></span>. New York: Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-19-507834-9" title="Special:BookSources/0-19-507834-9"><bdi>0-19-507834-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Orbital+Mechanics&rft.place=New+York&rft.pub=Oxford+University+Press&rft.date=1993&rft.isbn=0-19-507834-9&rft.aulast=Prussing&rft.aufirst=John+E.&rft.au=Conway%2C+Bruce+A.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Forbitalmechanics00prus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOrbital+eccentricity" class="Z3988"></span></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=Orbital_eccentricity&action=edit&section=12" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://scienceworld.wolfram.com/physics/Eccentricity.html">World of Physics: Eccentricity</a></li> <li><a rel="nofollow" class="external text" href="http://www.ncdc.noaa.gov/paleo/forcing.html">The NOAA page on Climate Forcing Data</a> includes (calculated) data from <a rel="nofollow" class="external text" href="ftp://ftp.ncdc.noaa.gov/pub/data/paleo/insolation/">Berger (1978), Berger and Loutre (1991)</a><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged April 2020">permanent dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup>. <a rel="nofollow" class="external text" href="http://www.imcce.fr/Equipes/ASD/insola/earth/earth.html">Laskar et al. (2004)</a> on Earth orbital variations, Includes eccentricity over the last 50 million years and for the coming 20 million years.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060210012245/http://www.astrobiology.ucla.edu/OTHER/SSO/">The orbital simulations by Varadi, Ghil and Runnegar (2003)</a> provides series for Earth orbital eccentricity and orbital inclination.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20170424171326/http://www.walter-fendt.de/ph14e/keplerlaw2.htm">Kepler's Second law's simulation</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output 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 class="mw-selflink selflink">Eccentricity</a></li> <li><span class="texhtml mvar" style="font-style:italic;">a</span>  <a href="/wiki/Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">Semi-major axis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">b</span>  <a href="/wiki/Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">Semi-minor axis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">Q</span>, <span class="texhtml mvar" style="font-style:italic;">q</span>  <a href="/wiki/Apsis" title="Apsis">Apsides</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">Orientation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">i</span>  <a href="/wiki/Orbital_inclination" title="Orbital inclination">Inclination</a></li> <li><span class="texhtml mvar" style="font-style:italic;">Ω</span>  <a href="/wiki/Longitude_of_the_ascending_node" title="Longitude of the ascending node">Longitude of the ascending node</a></li> <li><span class="texhtml mvar" style="font-style:italic;">ω</span>  <a href="/wiki/Argument_of_periapsis" title="Argument of periapsis">Argument of periapsis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">ϖ</span>  <a href="/wiki/Longitude_of_the_periapsis" class="mw-redirect" title="Longitude of the periapsis">Longitude of the periapsis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">Position</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">M</span>  <a href="/wiki/Mean_anomaly" title="Mean anomaly">Mean anomaly</a></li> <li><span class="texhtml mvar" style="font-style:italic;">ν</span>, <span class="texhtml mvar" style="font-style:italic;">θ</span>, <span class="texhtml mvar" style="font-style:italic;">f</span>  <a href="/wiki/True_anomaly" title="True anomaly">True anomaly</a></li> <li><span class="texhtml mvar" style="font-style:italic;">E</span>  <a href="/wiki/Eccentric_anomaly" title="Eccentric anomaly">Eccentric anomaly</a></li> <li><span class="texhtml mvar" style="font-style:italic;">L</span>  <a href="/wiki/Mean_longitude" title="Mean longitude">Mean longitude</a></li> <li><span class="texhtml mvar" style="font-style:italic;">l</span>  <a href="/wiki/True_longitude" title="True longitude">True longitude</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">Variation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">T</span>  <a href="/wiki/Orbital_period" title="Orbital period">Orbital period</a></li> <li><span class="texhtml mvar" style="font-style:italic;">n</span>  <a href="/wiki/Mean_motion" title="Mean motion">Mean motion</a></li> <li><span class="texhtml mvar" style="font-style:italic;">v</span>  <a href="/wiki/Orbital_speed" title="Orbital speed">Orbital speed</a></li> <li><span class="texhtml"><i>t</i><sub>0</sub></span>  <a 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" srcset="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/23px-Symbol_list_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/31px-Symbol_list_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/List_of_orbits" title="List of orbits">List of orbits</a></li></ul> </div></td></tr></tbody></table></div> <style data-mw-deduplicate="TemplateStyles:r1130092004">.mw-parser-output .portal-bar{font-size:88%;font-weight:bold;display:flex;justify-content:center;align-items:baseline}.mw-parser-output .portal-bar-bordered{padding:0 2em;background-color:#fdfdfd;border:1px solid #a2a9b1;clear:both;margin:1em auto 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 .portal-bar-content-related{margin:0;list-style:none}.mw-parser-output .portal-bar-item{display:inline-block;margin:0.15em 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.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"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/17px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png" decoding="async" width="17" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/26px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg/34px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg.png 2x" data-file-width="530" data-file-height="600" /></a></span> </span><a href="/wiki/Portal:Physics" title="Portal:Physics">Physics</a></li><li class="portal-bar-item"><span class="nowrap"><span typeof="mw:File"><span><img alt="" 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" 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