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class="vector-toc-numb">2</span> <span>Historical origins</span> </div> </a> <ul id="toc-Historical_origins-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Purpose" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Purpose"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Purpose</span> </div> </a> <ul id="toc-Purpose-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Limits" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Limits"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Limits</span> </div> </a> <ul id="toc-Limits-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notable_examples_of_use" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notable_examples_of_use"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Notable examples of use</span> </div> </a> <ul id="toc-Notable_examples_of_use-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">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-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">8</span> <span>References</span> </div> </a> <ul id="toc-References-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">9</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">Gravity assist</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 46 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-46" 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">46 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/Swaartekragslinger" title="Swaartekragslinger – Afrikaans" lang="af" hreflang="af" data-title="Swaartekragslinger" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B3%D8%A7%D8%B9%D8%AF%D8%A9_%D8%A7%D9%84%D8%AC%D8%A7%D8%B0%D8%A8%D9%8A%D8%A9" title="مساعدة الجاذبية – Arabic" lang="ar" hreflang="ar" data-title="مساعدة الجاذبية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Asistencia_gravitatoria" title="Asistencia gravitatoria – Asturian" lang="ast" hreflang="ast" data-title="Asistencia gravitatoria" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%93%D1%80%D0%B0%D0%B2%D1%96%D1%82%D0%B0%D1%86%D1%8B%D0%B9%D0%BD%D1%8B_%D0%BC%D0%B0%D0%BD%D0%B5%D1%9E%D1%80" title="Гравітацыйны манеўр – Belarusian" lang="be" hreflang="be" data-title="Гравітацыйны манеўр" 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%93%D1%80%D0%B0%D0%B2%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B5%D0%BD_%D0%BC%D0%B0%D0%BD%D1%8C%D0%BE%D0%B2%D1%8A%D1%80" title="Гравитационен маньовър – Bulgarian" lang="bg" hreflang="bg" data-title="Гравитационен маньовър" 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/Assist%C3%A8ncia_gravitat%C3%B2ria" title="Assistència gravitatòria – Catalan" lang="ca" hreflang="ca" data-title="Assistència gravitatòria" 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/Gravita%C4%8Dn%C3%AD_man%C3%A9vr" title="Gravitační manévr – Czech" lang="cs" hreflang="cs" data-title="Gravitační manévr" 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/Gravitationel_slynge" title="Gravitationel slynge – Danish" lang="da" hreflang="da" data-title="Gravitationel slynge" 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/Swing-by" title="Swing-by – German" lang="de" hreflang="de" data-title="Swing-by" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Asistencia_gravitatoria" title="Asistencia gravitatoria – Spanish" lang="es" hreflang="es" data-title="Asistencia gravitatoria" 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/Grabitatearen_laguntza" title="Grabitatearen laguntza – Basque" lang="eu" hreflang="eu" data-title="Grabitatearen laguntza" 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/%DA%A9%D9%85%DA%A9_%DA%AF%D8%B1%D8%A7%D9%86%D8%B4%DB%8C" title="کمک گرانشی – Persian" lang="fa" hreflang="fa" data-title="کمک گرانشی" 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/Assistance_gravitationnelle" title="Assistance gravitationnelle – French" lang="fr" hreflang="fr" data-title="Assistance gravitationnelle" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Swiertekr%C3%AAftslinger" title="Swiertekrêftslinger – Western Frisian" lang="fy" hreflang="fy" data-title="Swiertekrêftslinger" data-language-autonym="Frysk" data-language-local-name="Western Frisian" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Cabhair_imtharraingthe" title="Cabhair imtharraingthe – Irish" lang="ga" hreflang="ga" data-title="Cabhair imtharraingthe" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Asistencia_gravitacional" title="Asistencia gravitacional – Galician" lang="gl" hreflang="gl" data-title="Asistencia gravitacional" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%8A%A4%EC%9C%99%EB%B0%94%EC%9D%B4" title="스윙바이 – Korean" lang="ko" hreflang="ko" data-title="스윙바이" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Gravitacijska_pra%C4%87ka" title="Gravitacijska praćka – Croatian" lang="hr" hreflang="hr" data-title="Gravitacijska praćka" 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/Bantuan_gravitasi" title="Bantuan gravitasi – Indonesian" lang="id" hreflang="id" data-title="Bantuan gravitasi" 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/Fionda_gravitazionale" title="Fionda gravitazionale – Italian" lang="it" hreflang="it" data-title="Fionda gravitazionale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A7%D7%9C%D7%A2%D7%AA_%D7%9B%D7%91%D7%99%D7%93%D7%AA%D7%99%D7%AA" title="מקלעת כבידתית – Hebrew" lang="he" hreflang="he" data-title="מקלעת כבידתית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%92%E1%83%A0%E1%83%90%E1%83%95%E1%83%98%E1%83%A2%E1%83%90%E1%83%AA%E1%83%98%E1%83%A3%E1%83%9A%E1%83%98_%E1%83%9B%E1%83%90%E1%83%9C%E1%83%94%E1%83%95%E1%83%A0%E1%83%98" title="გრავიტაციული მანევრი – Georgian" lang="ka" hreflang="ka" data-title="გრავიტაციული მანევრი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Gravit%C4%81cijas_manevrs" title="Gravitācijas manevrs – Latvian" lang="lv" hreflang="lv" data-title="Gravitācijas manevrs" 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/Swing-by" title="Swing-by – Luxembourgish" lang="lb" hreflang="lb" data-title="Swing-by" 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/Hintaman%C5%91ver" title="Hintamanőver – Hungarian" lang="hu" hreflang="hu" data-title="Hintamanőver" 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%93%D1%80%D0%B0%D0%B2%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D1%81%D0%BA%D0%B8_%D0%BC%D0%B0%D0%BD%D0%B5%D0%B2%D0%B0%D1%80" title="Гравитациски маневар – Macedonian" lang="mk" hreflang="mk" data-title="Гравитациски маневар" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Zwaartekrachtsslinger" title="Zwaartekrachtsslinger – Dutch" lang="nl" hreflang="nl" data-title="Zwaartekrachtsslinger" 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/%E3%82%B9%E3%82%A4%E3%83%B3%E3%82%B0%E3%83%90%E3%82%A4" title="スイングバイ – Japanese" lang="ja" hreflang="ja" data-title="スイングバイ" 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/Gravitasjonsslynge" title="Gravitasjonsslynge – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Gravitasjonsslynge" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Asysta_grawitacyjna" title="Asysta grawitacyjna – Polish" lang="pl" hreflang="pl" data-title="Asysta grawitacyjna" 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/Gravidade_assistida" title="Gravidade assistida – Portuguese" lang="pt" hreflang="pt" data-title="Gravidade assistida" 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/Asisten%C8%9B%C4%83_gravita%C8%9Bional%C4%83" title="Asistență gravitațională – Romanian" lang="ro" hreflang="ro" data-title="Asistență gravitațională" 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%93%D1%80%D0%B0%D0%B2%D0%B8%D1%82%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%BD%D1%8B%D0%B9_%D0%BC%D0%B0%D0%BD%D1%91%D0%B2%D1%80" title="Гравитационный манёвр – Russian" lang="ru" hreflang="ru" data-title="Гравитационный манёвр" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Asistimi_gravitacional" title="Asistimi gravitacional – Albanian" lang="sq" hreflang="sq" data-title="Asistimi gravitacional" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Gravity_assist" title="Gravity assist – Simple English" lang="en-simple" hreflang="en-simple" data-title="Gravity assist" 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/Gravita%C4%8Dn%C3%BD_man%C3%A9ver" title="Gravitačný manéver – Slovak" lang="sk" hreflang="sk" data-title="Gravitačný manéver" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Gravitacioni_manuvar" title="Gravitacioni manuvar – Serbian" lang="sr" hreflang="sr" data-title="Gravitacioni manuvar" 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-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Painovoimalinko" title="Painovoimalinko – Finnish" lang="fi" hreflang="fi" data-title="Painovoimalinko" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Gravitationsslunga" title="Gravitationsslunga – Swedish" lang="sv" hreflang="sv" data-title="Gravitationsslunga" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/Gravitatsi%C3%A4_man%C3%B6vr%C4%B1" title="Gravitatsiä manövrı – Tatar" lang="tt" hreflang="tt" data-title="Gravitatsiä manövrı" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/K%C3%BCtle_%C3%A7ekimsel_sapan" title="Kütle çekimsel sapan – Turkish" lang="tr" hreflang="tr" data-title="Kütle çekimsel sapan" 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%93%D1%80%D0%B0%D0%B2%D1%96%D1%82%D0%B0%D1%86%D1%96%D0%B9%D0%BD%D0%B8%D0%B9_%D0%BC%D0%B0%D0%BD%D0%B5%D0%B2%D1%80" title="Гравітаційний маневр – Ukrainian" lang="uk" hreflang="uk" data-title="Гравітаційний маневр" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AB%D9%82%D9%84%DB%8C_%D9%85%D8%AF%D8%AF" title="ثقلی مدد – Urdu" lang="ur" hreflang="ur" data-title="ثقلی مدد" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%E1%BB%97_tr%E1%BB%A3_h%E1%BA%A5p_d%E1%BA%ABn" title="Hỗ trợ hấp dẫn – Vietnamese" lang="vi" hreflang="vi" data-title="Hỗ trợ hấp dẫn" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%87%8D%E5%8A%9B%E5%8A%A9%E6%8E%A8" title="重力助推 – Cantonese" lang="yue" hreflang="yue" data-title="重力助推" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%87%8D%E5%8A%9B%E5%8A%A9%E6%8E%A8" title="重力助推 – Chinese" lang="zh" hreflang="zh" data-title="重力助推" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q223776#sitelinks-wikipedia" title="Edit interlanguage links" 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.mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle">Astrodynamics</th></tr><tr><td class="sidebar-image" style="padding-bottom:0.85em;"><span typeof="mw:File"><a href="/wiki/File:Orbit_mechanics_icon.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Orbit_mechanics_icon.svg/60px-Orbit_mechanics_icon.svg.png" decoding="async" width="60" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Orbit_mechanics_icon.svg/90px-Orbit_mechanics_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Orbit_mechanics_icon.svg/120px-Orbit_mechanics_icon.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span></td></tr><tr><th class="sidebar-heading" style="padding-bottom:0.55em;"> <div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Orbital_mechanics" title="Orbital mechanics"><span style="font-size:110%;">Orbital mechanics</span></a></div></th></tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/Orbital_elements" title="Orbital elements">Orbital elements</a></div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"> <ul><li><a href="/wiki/Apsis" title="Apsis">Apsis</a></li> <li><a href="/wiki/Argument_of_periapsis" title="Argument of periapsis">Argument of periapsis</a></li> <li><a href="/wiki/Orbital_eccentricity" title="Orbital eccentricity">Eccentricity</a></li> <li><a href="/wiki/Orbital_inclination" title="Orbital inclination">Inclination</a></li> <li><a href="/wiki/Mean_anomaly" title="Mean anomaly">Mean anomaly</a></li> <li><a href="/wiki/Orbital_node" title="Orbital node">Orbital nodes</a></li> <li><a href="/wiki/Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">Semi-major axis</a></li> <li><a href="/wiki/True_anomaly" title="True anomaly">True anomaly</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Types of <a href="/wiki/Two-body_problem" title="Two-body problem">two-body orbits</a> by <br />eccentricity</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"> <ul><li><a href="/wiki/Circular_orbit" title="Circular orbit">Circular orbit</a></li> <li><a href="/wiki/Elliptic_orbit" title="Elliptic orbit">Elliptic orbit</a></li></ul> <div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Transfer_orbit" title="Transfer orbit">Transfer orbit</a> <div class="hlist" style="font-size:90%"><ul><li>(<a href="/wiki/Hohmann_transfer_orbit" title="Hohmann transfer orbit">Hohmann transfer orbit</a></li><li><a href="/wiki/Bi-elliptic_transfer" title="Bi-elliptic transfer">Bi-elliptic transfer orbit</a>)</li></ul></div></div> <ul><li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Parabolic orbit</a></li> <li><a href="/wiki/Hyperbolic_trajectory" title="Hyperbolic trajectory">Hyperbolic orbit</a></li> <li><a href="/wiki/Radial_trajectory" title="Radial trajectory">Radial orbit</a></li> <li><a href="/wiki/Orbital_decay" title="Orbital decay">Decaying orbit</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Equations</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"> <ul><li><a href="/wiki/Dynamical_friction" title="Dynamical friction">Dynamical friction</a></li> <li><a href="/wiki/Escape_velocity" title="Escape velocity">Escape velocity</a></li> <li><a href="/wiki/Kepler%27s_equation" title="Kepler's equation">Kepler's equation</a></li> <li><a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws of planetary motion</a></li> <li><a href="/wiki/Orbital_period" title="Orbital period">Orbital period</a></li> <li><a href="/wiki/Orbital_speed" title="Orbital speed">Orbital velocity</a></li> <li><a href="/wiki/Surface_gravity" title="Surface gravity">Surface gravity</a></li> <li><a href="/wiki/Specific_orbital_energy" title="Specific orbital energy">Specific orbital energy</a></li> <li><a href="/wiki/Vis-viva_equation" title="Vis-viva equation">Vis-viva equation</a></li></ul></div></div></td> </tr><tr><th class="sidebar-heading" style="padding-bottom:0.55em;"> <div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Celestial_mechanics" title="Celestial mechanics"><span style="font-size:110%;">Celestial mechanics</span></a></div></th></tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Gravitational influences</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"> <ul><li><a href="/wiki/Barycenter" class="mw-redirect" title="Barycenter">Barycenter</a></li> <li><a href="/wiki/Hill_sphere" title="Hill sphere">Hill sphere</a></li> <li><a href="/wiki/Perturbation_(astronomy)" title="Perturbation (astronomy)">Perturbations</a></li> <li><a href="/wiki/Sphere_of_influence_(astrodynamics)" title="Sphere of influence (astrodynamics)">Sphere of influence</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><a href="/wiki/N-body_problem" title="N-body problem">N-body orbits</a></div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Lagrange_point" title="Lagrange point">Lagrangian points</a> <div class="hlist" style="font-size:90%"><ul><li>(<a href="/wiki/Halo_orbit" title="Halo orbit">Halo orbits</a>)</li></ul></div></div> <ul><li><a href="/wiki/Lissajous_orbit" title="Lissajous orbit">Lissajous orbits</a></li> <li><a href="/wiki/Lyapunov_stability" title="Lyapunov stability">Lyapunov orbits</a></li></ul></div></div></td> </tr><tr><th class="sidebar-heading" style="padding-bottom:0.55em;"> <div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Aerospace_engineering" title="Aerospace engineering"><span style="font-size:110%;">Engineering and efficiency</span></a></div></th></tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Preflight engineering</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"> <ul><li><a href="/wiki/Mass_ratio" title="Mass ratio">Mass ratio</a></li> <li><a href="/wiki/Payload_fraction" title="Payload fraction">Payload fraction</a></li> <li><a href="/wiki/Propellant_mass_fraction" title="Propellant mass fraction">Propellant mass fraction</a></li> <li><a href="/wiki/Tsiolkovsky_rocket_equation" title="Tsiolkovsky rocket equation">Tsiolkovsky rocket equation</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Efficiency measures</div><div class="sidebar-list-content mw-collapsible-content plainlist" style="padding-top:0;"> <ul><li><a class="mw-selflink selflink">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>A <b>gravity assist</b>, <b>gravity assist maneuver</b>, <b>swing-by</b>, or generally a <b>gravitational <a href="/wiki/Slingshot" title="Slingshot">slingshot</a></b> in <a href="/wiki/Orbital_mechanics" title="Orbital mechanics">orbital mechanics</a>, is a type of <a href="/wiki/Spaceflight" title="Spaceflight">spaceflight</a> <a href="/wiki/Flyby_(spaceflight)" title="Flyby (spaceflight)">flyby</a> which makes use of the relative movement (e.g. orbit around the <a href="/wiki/Sun" title="Sun">Sun</a>) and <a href="/wiki/Gravity" title="Gravity">gravity</a> of a <a href="/wiki/Planet" title="Planet">planet</a> or other <a href="/wiki/Astronomical_object" title="Astronomical object">astronomical object</a> to alter the <a href="/wiki/Course_(navigation)" title="Course (navigation)">path</a> and <a href="/wiki/Speed" title="Speed">speed</a> of a <a href="/wiki/Spacecraft" title="Spacecraft">spacecraft</a>, typically to save <a href="/wiki/Propellant" title="Propellant">propellant</a> and reduce expense. </p><p>Gravity assistance can be used to <a href="/wiki/Accelerate" class="mw-redirect" title="Accelerate">accelerate</a> a spacecraft, that is, to increase or decrease its speed or redirect its path. The "assist" is provided by the motion of the gravitating body as it pulls on the spacecraft.<sup id="cite_ref-basics-traject_1-0" class="reference"><a href="#cite_note-basics-traject-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Any gain or loss of <a href="/wiki/Kinetic_energy" title="Kinetic energy">kinetic energy</a> and <a href="/wiki/Linear_momentum" class="mw-redirect" title="Linear momentum">linear momentum</a> by a passing spacecraft is correspondingly lost or gained by the gravitational body, in accordance with <a href="/wiki/Newton%27s_laws_of_motion#Newton's_third_law" title="Newton's laws of motion">Newton's Third Law</a>. The gravity assist maneuver was first used in 1959 when the Soviet probe <a href="/wiki/Luna_3" title="Luna 3">Luna 3</a> photographed the far side of Earth's <a href="/wiki/Moon" title="Moon">Moon</a>, and it was used by interplanetary probes from <a href="/wiki/Mariner_10" title="Mariner 10">Mariner 10</a> onward, including the two <a href="/wiki/Voyager_program" title="Voyager program">Voyager</a> probes' notable <a href="/wiki/Planetary_flyby" title="Planetary flyby">flybys</a> of Jupiter and Saturn. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Explanation">Explanation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravity_assist&action=edit&section=1" title="Edit section: Explanation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:GravAssis.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/GravAssis.gif/220px-GravAssis.gif" decoding="async" width="220" height="236" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/GravAssis.gif/330px-GravAssis.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/c/c9/GravAssis.gif 2x" data-file-width="360" data-file-height="386" /></a><figcaption>Example encounter.<sup id="cite_ref-:0_2-0" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><br />In the planet's frame of reference, the space probe leaves with the exact same speed at which it had arrived. But when observed in the reference frame of the Solar System (fixed to the Sun), the benefit of this maneuver becomes apparent. Here it can be seen how the probe gains speed by tapping energy from the speed of the planet as it orbits the Sun. (If the trajectory is designed to pass in front of the planet instead of behind it, the gravity assist can be used as a braking maneuver rather than accelerating.) Because the mass of the probe is many orders of magnitude smaller than that of the planet, while the result on the probe is quite significant, the deceleration reaction experienced by the planet, according to <a href="/wiki/Newton%27s_third_law" class="mw-redirect" title="Newton's third law">Newton's third law</a>, is utterly imperceptible.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:GravPoss.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/GravPoss.gif/220px-GravPoss.gif" decoding="async" width="220" height="219" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/GravPoss.gif/330px-GravPoss.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/7/7e/GravPoss.gif 2x" data-file-width="432" data-file-height="431" /></a><figcaption>Possible outcomes of a gravity assist maneuver depending on the velocity vector and flyby position of the incoming spacecraft</figcaption></figure> <p>A gravity assist around a planet changes a spacecraft's <a href="/wiki/Velocity" title="Velocity">velocity</a> (relative to the <a href="/wiki/Sun" title="Sun">Sun</a>) by entering and leaving the gravitational sphere of influence of a planet. The sum of the kinetic energies of both bodies remains constant (see <a href="/wiki/Elastic_collision" title="Elastic collision">elastic collision</a>). A slingshot maneuver can therefore be used to change the spaceship's trajectory and speed relative to the Sun.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>A close terrestrial analogy is provided by a tennis ball bouncing off the front of a moving train. Imagine standing on a train platform, and throwing a ball at 30 km/h toward a train approaching at 50 km/h. The driver of the train sees the ball approaching at 80 km/h and then departing at 80 km/h after the ball bounces elastically off the front of the train. Because of the train's motion, however, that departure is at 130 km/h relative to the train platform; the ball has added twice the train's velocity to its own.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Translating this analogy into space: in the planet <a href="/wiki/Frame_of_reference" title="Frame of reference">reference frame</a>, the spaceship has a vertical velocity of <i>v</i> relative to the planet. After the slingshot occurs the spaceship is leaving on a course 90 degrees to that which it arrived on. It will still have a velocity of <i>v</i>, but in the horizontal direction.<sup id="cite_ref-:0_2-1" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In the Sun reference frame, the planet has a horizontal velocity of v, and by using the Pythagorean Theorem, the spaceship initially has a total velocity of <span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">2</span></span><i>v</i>. After the spaceship leaves the planet, it will have a velocity of <i>v + v =</i> 2<i>v</i>, gaining approximately 0.6<i>v</i>.<sup id="cite_ref-:0_2-2" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>This oversimplified example cannot be refined without additional details regarding the orbit, but if the spaceship travels in a path which forms a <a href="/wiki/Hyperbola" title="Hyperbola">hyperbola</a>, it can leave the planet in the opposite direction without firing its engine. This example is one of many trajectories and gains of speed the spaceship can experience. </p><p>This explanation might seem to violate the conservation of energy and momentum, apparently adding velocity to the spacecraft out of nothing, but the spacecraft's effects on the planet must also be taken into consideration to provide a complete picture of the mechanics involved. The linear momentum gained by the spaceship is equal in magnitude to that lost by the planet, so the spacecraft gains velocity and the planet loses velocity. However, the planet's enormous mass compared to the spacecraft makes the resulting change in its speed negligibly small even when compared to the <a href="/wiki/Perturbation_(astronomy)" title="Perturbation (astronomy)">orbital perturbations</a> planets undergo due to interactions with other celestial bodies on astronomically short timescales. For example, one <a href="/wiki/Metric_ton" class="mw-redirect" title="Metric ton">metric ton</a> is a typical mass for an interplanetary space probe whereas <a href="/wiki/Jupiter" title="Jupiter">Jupiter</a> <a href="/wiki/Orders_of_magnitude_(mass)" title="Orders of magnitude (mass)">has a mass</a> of almost 2 x 10<sup>24</sup> metric tons. Therefore, a one-ton spacecraft passing Jupiter will theoretically cause the planet to lose approximately 5 x 10<sup>−25</sup> km/s of orbital velocity for every km/s of velocity relative to the Sun gained by the spacecraft. For all practical purposes the effects on the planet can be ignored in the calculation.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Realistic portrayals of encounters in space require the consideration of three dimensions. The same principles apply as above except adding the planet's velocity to that of the spacecraft requires <a href="/wiki/Vector_addition" class="mw-redirect" title="Vector addition">vector addition</a> as shown below. </p> <figure class="mw-default-size mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/File:Grav_slingshot_diag.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Grav_slingshot_diag.svg/220px-Grav_slingshot_diag.svg.png" decoding="async" width="220" height="156" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Grav_slingshot_diag.svg/330px-Grav_slingshot_diag.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/Grav_slingshot_diag.svg/440px-Grav_slingshot_diag.svg.png 2x" data-file-width="1052" data-file-height="744" /></a><figcaption>Two-dimensional schematic of gravitational slingshot. The arrows show the direction in which the spacecraft is traveling before and after the encounter. The length of the arrows shows the spacecraft's speed.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Mdis_depart_anot.ogv/220px--Mdis_depart_anot.ogv.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="201" data-durationhint="12" data-mwtitle="Mdis_depart_anot.ogv" data-mwprovider="wikimediacommons" resource="/wiki/File:Mdis_depart_anot.ogv"><source src="//upload.wikimedia.org/wikipedia/commons/e/e0/Mdis_depart_anot.ogv" type="video/ogg; codecs="theora"" data-width="400" data-height="366" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e0/Mdis_depart_anot.ogv/Mdis_depart_anot.ogv.144p.mjpeg.mov" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="158" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e0/Mdis_depart_anot.ogv/Mdis_depart_anot.ogv.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="262" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e0/Mdis_depart_anot.ogv/Mdis_depart_anot.ogv.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="394" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/e/e0/Mdis_depart_anot.ogv/Mdis_depart_anot.ogv.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="394" data-height="360" /></video></span><figcaption>A view from MESSENGER as it uses Earth as a gravitational slingshot to decelerate to allow insertion into an orbit around Mercury</figcaption></figure> <p>Due to the <a href="/wiki/Reversibility_of_orbits" class="mw-redirect" title="Reversibility of orbits">reversibility of orbits</a>, gravitational slingshots can also be used to reduce the speed of a spacecraft. Both <a href="/wiki/Mariner_10" title="Mariner 10">Mariner 10</a> and <a href="/wiki/MESSENGER" title="MESSENGER">MESSENGER</a> performed this maneuver to reach <a href="/wiki/Mercury_(planet)" title="Mercury (planet)">Mercury</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2022)">citation needed</span></a></i>]</sup> </p><p>If more speed is needed than available from gravity assist alone, a rocket burn near the <a href="/wiki/Periapsis" class="mw-redirect" title="Periapsis">periapsis</a> (closest planetary approach) uses the least fuel. A given rocket burn always provides the same change in velocity (<a href="/wiki/%CE%94v" class="mw-redirect" title="Δv">Δv</a>), but the change in kinetic energy is proportional to the vehicle's velocity at the time of the burn. Therefore the maximum kinetic energy is obtained when the burn occurs at the vehicle's maximum velocity (periapsis). The <a href="/wiki/Oberth_effect" title="Oberth effect">Oberth effect</a> describes this technique in more detail. </p> <div class="mw-heading mw-heading2"><h2 id="Historical_origins">Historical origins</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravity_assist&action=edit&section=2" title="Edit section: Historical origins"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In his paper "To Those Who Will Be Reading in Order to Build" (<span title="Russian-language text"><span lang="ru">"Тем, кто будет читать, чтобы строить"</span></span>),<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> published in 1938 but dated 1918–1919,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Yuri_Kondratyuk" title="Yuri Kondratyuk">Yuri Kondratyuk</a> suggested that a spacecraft traveling between two planets could be accelerated at the beginning and end of its trajectory by using the gravity of the two planets' moons. The portion of his manuscript considering gravity-assists received no later development and was not published until the 1960s.<sup id="cite_ref-urlib.net_8-0" class="reference"><a href="#cite_note-urlib.net-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> In his 1925 paper "Problems of Flight by Jet Propulsion: Interplanetary Flights" (<span title="Russian-language text"><span lang="ru">"Проблема полета при помощи реактивных аппаратов: межпланетные полеты"</span></span>),<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Friedrich_Zander" title="Friedrich Zander">Friedrich Zander</a> showed a deep understanding of the physics behind the concept of gravity assist and its potential for the interplanetary exploration of the solar system.<sup id="cite_ref-urlib.net_8-1" class="reference"><a href="#cite_note-urlib.net-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Italian engineer <a href="/wiki/Gaetano_Crocco" title="Gaetano Crocco">Gaetano Crocco</a> was first to calculate an interplanetary journey considering multiple gravity-assists.<sup id="cite_ref-urlib.net_8-2" class="reference"><a href="#cite_note-urlib.net-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>The gravity assist maneuver was first used in 1959 when the Soviet probe <a href="/wiki/Luna_3" title="Luna 3">Luna 3</a> photographed the far side of the Moon. The maneuver relied on research performed under the direction of <a href="/wiki/Mstislav_Keldysh" title="Mstislav Keldysh">Mstislav Keldysh</a> at the <a href="/wiki/Keldysh_Institute_of_Applied_Mathematics" title="Keldysh Institute of Applied Mathematics">Keldysh Institute of Applied Mathematics</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>In 1961, <a href="/wiki/Michael_Minovitch" title="Michael Minovitch">Michael Minovitch</a>, <a href="/wiki/UCLA" class="mw-redirect" title="UCLA">UCLA</a> graduate student who worked at NASA's <a href="/wiki/Jet_Propulsion_Laboratory" title="Jet Propulsion Laboratory">Jet Propulsion Laboratory</a> (JPL), developed a gravity assist technique, that would later be used for the <a href="/wiki/Gary_Flandro" title="Gary Flandro">Gary Flandro</a>'s <a href="/wiki/Planetary_Grand_Tour" class="mw-redirect" title="Planetary Grand Tour">Planetary Grand Tour</a> idea.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>During the summer of 1964 at the NASA JPL, Gary Flandro was assigned the task of studying techniques for exploring the outer planets of the solar system. In this study he discovered the rare alignment of the outer planets (Jupiter, Saturn, Uranus, and Neptune) and conceived the Planetary Grand Tour multi-planet mission utilizing gravity assist to reduce mission duration from forty years to less than ten.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Purpose">Purpose</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravity_assist&action=edit&section=3" title="Edit section: Purpose"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Voyager_2_velocity_vs_distance_from_sun.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Voyager_2_velocity_vs_distance_from_sun.svg/220px-Voyager_2_velocity_vs_distance_from_sun.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Voyager_2_velocity_vs_distance_from_sun.svg/330px-Voyager_2_velocity_vs_distance_from_sun.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Voyager_2_velocity_vs_distance_from_sun.svg/440px-Voyager_2_velocity_vs_distance_from_sun.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>Plot of Voyager 2's heliocentric velocity against its distance from the Sun, illustrating the use of gravity assist to accelerate the spacecraft by Jupiter, Saturn and Uranus. To observe <a href="/wiki/Triton_(moon)" title="Triton (moon)">Triton</a>, Voyager 2 passed over Neptune's north pole resulting in an acceleration out of the plane of the ecliptic and reduced velocity away from the Sun.<sup id="cite_ref-basics-traject_1-1" class="reference"><a href="#cite_note-basics-traject-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>A spacecraft traveling from Earth to an inner planet will increase its relative speed because it is falling toward the Sun, and a spacecraft traveling from Earth to an outer planet will decrease its speed because it is leaving the vicinity of the Sun. </p><p>Although the orbital speed of an inner planet is greater than that of the Earth, a spacecraft traveling to an inner planet, even at the minimum speed needed to reach it, is still accelerated by the Sun's gravity to a speed notably greater than the orbital speed of that destination planet. If the spacecraft's purpose is only to fly by the inner planet, then there is typically no need to slow the spacecraft. However, if the spacecraft is to be inserted into <a href="/wiki/Orbit" title="Orbit">orbit</a> about that inner planet, then there must be some way to slow it down. </p><p>Similarly, while the orbital speed of an outer planet is less than that of the Earth, a spacecraft leaving the Earth at the minimum speed needed to travel to some outer planet is slowed by the Sun's gravity to a speed far less than the orbital speed of that outer planet. Therefore, there must be some way to accelerate the spacecraft when it reaches that outer planet if it is to enter orbit about it. </p><p><a href="/wiki/Rocket_engine" title="Rocket engine">Rocket engines</a> can certainly be used to increase and decrease the speed of the spacecraft. However, rocket thrust takes propellant, propellant has mass, and even a small change in velocity (known as Δ<i>v</i>, or "delta-<i>v</i>", the <a href="/wiki/Delta_(letter)" title="Delta (letter)">delta symbol</a> being used to represent a change and "v" signifying <a href="/wiki/Velocity" title="Velocity">velocity</a>) translates to a far larger requirement for propellant needed to escape Earth's <a href="/wiki/Gravity_well" class="mw-redirect" title="Gravity well">gravity well</a>. This is because not only must the primary-stage engines lift the extra propellant, they must also lift the extra propellant beyond that which is needed to lift <i>that</i> additional propellant. The liftoff mass requirement <a href="/wiki/Rocket_equation" class="mw-redirect" title="Rocket equation">increases exponentially</a> with an increase in the required delta-<i>v</i> of the spacecraft. </p><p>Because additional fuel is needed to lift fuel into space, space missions are designed with a tight propellant "budget", known as the "<a href="/wiki/Delta-v_budget" title="Delta-v budget">delta-v budget</a>". The delta-v budget is in effect the total propellant that will be available after leaving the earth, for speeding up, slowing down, stabilization against external buffeting (by particles or other external effects), or direction changes, if it cannot acquire more propellant. The entire mission must be planned within that capability. Therefore, methods of speed and direction change that do not require fuel to be burned are advantageous, because they allow extra maneuvering capability and course enhancement, without spending fuel from the limited amount which has been carried into space. Gravity assist maneuvers can greatly change the speed of a spacecraft without expending propellant, and can save significant amounts of propellant, so they are a very common technique to save fuel. </p> <div class="mw-heading mw-heading2"><h2 id="Limits">Limits</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravity_assist&action=edit&section=4" title="Edit section: Limits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Voyager_Path.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Voyager_Path.svg/220px-Voyager_Path.svg.png" decoding="async" width="220" height="183" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Voyager_Path.svg/330px-Voyager_Path.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/Voyager_Path.svg/440px-Voyager_Path.svg.png 2x" data-file-width="794" data-file-height="660" /></a><figcaption>The trajectories that enabled NASA's twin Voyager spacecraft to tour the four giant planets and achieve velocity to escape the Solar System</figcaption></figure> <p>The main practical limit to the use of a gravity assist maneuver is that planets and other large masses are seldom in the right places to enable a voyage to a particular destination. For example, the <a href="/wiki/Voyager_1" title="Voyager 1">Voyager</a> missions which started in the late 1970s were made possible by the "<a href="/wiki/Planetary_Grand_Tour" class="mw-redirect" title="Planetary Grand Tour">Grand Tour</a>" alignment of Jupiter, Saturn, Uranus and Neptune. A similar alignment will not occur again until the middle of the 22nd century. That is an extreme case, but even for less ambitious missions there are years when the planets are scattered in unsuitable parts of their orbits.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2022)">citation needed</span></a></i>]</sup> </p><p>Another limitation is the atmosphere, if any, of the available planet. The closer the spacecraft can approach, the faster its <a href="/wiki/Periapsis" class="mw-redirect" title="Periapsis">periapsis</a> speed as gravity accelerates the spacecraft, allowing for more kinetic energy to be gained from a rocket burn. However, if a spacecraft gets too deep into the atmosphere, the energy lost to drag can exceed that gained from the planet's gravity. On the other hand, the atmosphere can be used to accomplish <a href="/wiki/Aerobraking" title="Aerobraking">aerobraking</a>. There have also been theoretical proposals to use <a href="/wiki/Lift_(force)" title="Lift (force)">aerodynamic lift</a> as the spacecraft flies through the atmosphere. This maneuver, called an <a href="/wiki/Aerogravity_assist" title="Aerogravity assist">aerogravity assist</a>, could bend the trajectory through a larger angle than gravity alone, and hence increase the gain in energy.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2022)">citation needed</span></a></i>]</sup> </p><p>Even in the case of an airless body, there is a limit to how close a spacecraft may approach. The magnitude of the achievable change in velocity depends on the spacecraft's approach velocity and the planet's escape velocity at the point of closest approach (limited by either the surface or the atmosphere.)<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2022)">citation needed</span></a></i>]</sup> </p><p>Interplanetary slingshots using the Sun itself are not possible because the Sun is at rest relative to the Solar System as a whole. However, thrusting when near the Sun has the same effect as the powered slingshot described as the <a href="/wiki/Oberth_effect" title="Oberth effect">Oberth effect</a>. This has the potential to magnify a spacecraft's thrusting power enormously, but is limited by the spacecraft's ability to resist the heat.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2022)">citation needed</span></a></i>]</sup> </p><p>A <a href="/wiki/Rotating_black_hole" title="Rotating black hole">rotating black hole</a> might provide additional assistance, if its spin axis is aligned the right way. <a href="/wiki/General_relativity" title="General relativity">General relativity</a> predicts that a large spinning mass produces <a href="/wiki/Frame-dragging" title="Frame-dragging">frame-dragging</a>—close to the object, space itself is dragged around in the direction of the spin. Any ordinary rotating object produces this effect. Although attempts to measure frame dragging about the Sun have produced no clear evidence, experiments performed by <a href="/wiki/Gravity_Probe_B" title="Gravity Probe B">Gravity Probe B</a> have detected frame-dragging effects caused by Earth.<sup id="cite_ref-PRL_17-0" class="reference"><a href="#cite_note-PRL-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> General relativity predicts that a spinning black hole is surrounded by a region of space, called the <a href="/wiki/Ergosphere" title="Ergosphere">ergosphere</a>, within which standing still (with respect to the black hole's spin) is impossible, because space itself is dragged at the speed of light in the same direction as the black hole's spin. The <a href="/wiki/Penrose_process" title="Penrose process">Penrose process</a> may offer a way to gain energy from the ergosphere, although it would require the spaceship to dump some "ballast" into the black hole, and the spaceship would have had to expend energy to carry the "ballast" to the black hole.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2022)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Notable_examples_of_use">Notable examples of use</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravity_assist&action=edit&section=5" title="Edit section: Notable examples of use"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dt><i>Luna 3</i></dt></dl> <p>The gravity assist maneuver was first attempted in 1959 for <a href="/wiki/Luna_3" title="Luna 3">Luna 3</a>, to photograph the far side of the Moon.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> The satellite did not gain speed, but its orbit was changed in a way that allowed successful transmission of the photos.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><i>Pioneer 10</i></dt></dl> <p>NASA's <i><a href="/wiki/Pioneer_10" title="Pioneer 10">Pioneer 10</a></i> is a space probe launched in 1972 that completed the first mission to the planet <a href="/wiki/Jupiter" title="Jupiter">Jupiter</a>.<sup id="cite_ref-PionOdys_20-0" class="reference"><a href="#cite_note-PionOdys-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Thereafter, <i>Pioneer 10</i> became the <a href="/wiki/List_of_artificial_objects_leaving_the_Solar_System" title="List of artificial objects leaving the Solar System">first of five artificial objects</a> to achieve the <a href="/wiki/Escape_velocity" title="Escape velocity">escape velocity</a> needed to <a href="/wiki/Solar_System#Farthest_regions" title="Solar System">leave the Solar System</a>. In December 1973, <i>Pioneer 10</i> spacecraft was the first one to use the gravitational slingshot effect to reach escape velocity to leave Solar System.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><i>Pioneer 11</i></dt></dl> <p><a href="/wiki/Pioneer_11" title="Pioneer 11">Pioneer 11</a> was launched by NASA in 1973, to study the <a href="/wiki/Asteroid_belt" title="Asteroid belt">asteroid belt</a>, the environment around <a href="/wiki/Jupiter" title="Jupiter">Jupiter</a> and <a href="/wiki/Saturn" title="Saturn">Saturn</a>, <a href="/wiki/Solar_wind" title="Solar wind">solar winds</a>, and <a href="/wiki/Cosmic_ray" title="Cosmic ray">cosmic rays</a>.<sup id="cite_ref-PionOdys_20-1" class="reference"><a href="#cite_note-PionOdys-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> It was the first probe to <a href="/wiki/Exploration_of_Saturn" title="Exploration of Saturn">encounter Saturn</a>, the second to fly through the <a href="/wiki/Asteroid_belt#Exploration" title="Asteroid belt">asteroid belt</a>, and the second to fly <a href="/wiki/Exploration_of_Jupiter" title="Exploration of Jupiter">by Jupiter</a>. To get to Saturn, the spacecraft got a gravity assist on Jupiter.<sup id="cite_ref-InDepth_23-0" class="reference"><a href="#cite_note-InDepth-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><i>Mariner 10</i></dt></dl> <p>The <a href="/wiki/Mariner_10" title="Mariner 10">Mariner 10</a> probe was the first spacecraft to use the gravitational slingshot effect to reach another planet, passing by Venus on 5 February 1974 on its way to becoming the first spacecraft to explore <a href="/wiki/Mercury_(planet)" title="Mercury (planet)">Mercury</a>.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><i>Voyager 1</i></dt></dl> <p><i><a href="/wiki/Voyager_1" title="Voyager 1">Voyager 1</a></i> was launched by NASA on September 5, 1977. It gained the energy to escape the Sun's gravity by performing slingshot maneuvers around Jupiter and Saturn.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> Having operated for 47 years, 2 months and 20 days as of November 25, 2024 <a href="/wiki/Coordinated_Universal_Time" title="Coordinated Universal Time">UTC</a> <span class="plainlinks" style="font-size:85%;">[<a class="external text" href="https://en.wikipedia.org/w/index.php?title=Gravity_assist&action=purge">refresh</a>]</span>, the spacecraft still communicates with the <a href="/wiki/Deep_Space_Network" class="mw-redirect" title="Deep Space Network">Deep Space Network</a> to receive routine commands and to transmit data to Earth. Real-time distance and velocity data is provided<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> by NASA and JPL. At a distance of 152.2 <a href="/wiki/Astronomical_unit" title="Astronomical unit">AU</a> (22.8 <a href="/wiki/1000000000_(number)" class="mw-redirect" title="1000000000 (number)">billion</a> <a href="/wiki/Kilometre" title="Kilometre">km</a>; 14.1 billion <a href="/wiki/Mile" title="Mile">mi</a>) from Earth as of January 12, 2020,<sup id="cite_ref-voyager_29-0" class="reference"><a href="#cite_note-voyager-29"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> it is the most distant human-made object from Earth.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><i>Voyager 2</i></dt></dl> <p><i><a href="/wiki/Voyager_2" title="Voyager 2">Voyager 2</a></i> was launched by NASA on August 20, 1977, to study the <a href="/wiki/Outer_planets" class="mw-redirect" title="Outer planets">outer planets</a>. Its trajectory took longer to reach <a href="/wiki/Jupiter" title="Jupiter">Jupiter</a> and <a href="/wiki/Saturn" title="Saturn">Saturn</a> than its twin spacecraft but enabled further encounters with <a href="/wiki/Uranus" title="Uranus">Uranus</a> and <a href="/wiki/Neptune" title="Neptune">Neptune</a>.<sup id="cite_ref-ESBS_31-0" class="reference"><a href="#cite_note-ESBS-31"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><i>Galileo</i></dt></dl> <p>The <i><a href="/wiki/Galileo_(spacecraft)" title="Galileo (spacecraft)">Galileo</a></i> spacecraft was launched by <a href="/wiki/NASA" title="NASA">NASA</a> in 1989 and on its route to <a href="/wiki/Jupiter" title="Jupiter">Jupiter</a> got three gravity assists, one from Venus (February 10, 1990), and two from Earth (December 8, 1990 and December 8, 1992). Spacecraft reached Jupiter in December 1995. Gravity assists also allowed <i>Galileo</i> to flyby two asteroids, <a href="/wiki/243_Ida" title="243 Ida">243 Ida</a> and <a href="/wiki/951_Gaspra" title="951 Gaspra">951 Gaspra</a>.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><i>Ulysses</i></dt></dl> <p>In 1990, NASA launched the <a href="/wiki/European_Space_Agency" title="European Space Agency">ESA</a> spacecraft <i><a href="/wiki/Ulysses_(spacecraft)" title="Ulysses (spacecraft)">Ulysses</a></i> to study the <a href="/wiki/Geographical_pole" title="Geographical pole">polar</a> regions of the Sun. All the planets orbit approximately in a plane aligned with the equator of the Sun. Thus, to enter an orbit passing over the poles of the Sun, the spacecraft would have to eliminate the speed it inherited from the Earth's orbit around the Sun and gain the speed needed to orbit the Sun in the pole-to-pole plane. It was achieved by a gravity assist from Jupiter on February 8, 1992.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><i>MESSENGER</i></dt></dl> <p>The <a href="/wiki/MESSENGER" title="MESSENGER">MESSENGER</a> mission (launched in August 2004) made extensive use of gravity assists to slow its speed before orbiting Mercury. The MESSENGER mission included one flyby of Earth, two flybys of Venus, and three flybys of Mercury before finally arriving at Mercury in March 2011 with a velocity low enough to permit orbit insertion with available fuel. Although the flybys were primarily orbital maneuvers, each provided an opportunity for significant scientific observations.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><i>Cassini</i></dt></dl> <p>The <a href="/wiki/Cassini%E2%80%93Huygens" title="Cassini–Huygens"><i>Cassini–Huygens</i> spacecraft</a> was launched from Earth on 15 October 1997, followed by gravity assist flybys of Venus (26 April 1998 and 21 June 1999), Earth (18 August 1999), and Jupiter (30 December 2000). Transit to Saturn took 6.7 years, the spacecraft arrived at 1 July 2004.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> Its trajectory was called "the Most Complex Gravity-Assist Trajectory Flown to Date" in 2019.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237032888/mw-parser-output/.tmulti"><div class="thumb tmulti tnone center"><div class="thumbinner multiimageinner" style="width:991px;max-width:991px"><div class="trow"><div class="tsingle" style="width:293px;max-width:293px"><div class="thumbimage" style="height:181px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Cassini_interplanet_trajectory.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Cassini_interplanet_trajectory.svg/291px-Cassini_interplanet_trajectory.svg.png" decoding="async" width="291" height="182" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Cassini_interplanet_trajectory.svg/437px-Cassini_interplanet_trajectory.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Cassini_interplanet_trajectory.svg/582px-Cassini_interplanet_trajectory.svg.png 2x" data-file-width="444" data-file-height="277" /></a></span></div><div class="thumbcaption text-align-center"><i>Cassini</i> interplanetary trajectory</div></div><div class="tsingle" style="width:244px;max-width:244px"><div class="thumbimage" style="height:181px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Animation_of_Cassini_trajectory.gif" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Animation_of_Cassini_trajectory.gif/242px-Animation_of_Cassini_trajectory.gif" decoding="async" width="242" height="182" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Animation_of_Cassini_trajectory.gif/363px-Animation_of_Cassini_trajectory.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Animation_of_Cassini_trajectory.gif/484px-Animation_of_Cassini_trajectory.gif 2x" data-file-width="560" data-file-height="420" /></a></span></div><div class="thumbcaption text-align-center">Animation of <i>Cassini</i><span class="nowrap" style="padding-left:0.1em;">'s</span> trajectory from 15 October 1997 to 4 May 2008 <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:magenta; color:black;"> </span> <i>Cassini–Huygens</i></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> <a href="/wiki/Jupiter" title="Jupiter">Jupiter</a></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> <a href="/wiki/Saturn" title="Saturn">Saturn</a></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:Royalblue; color:white;"> </span> <a href="/wiki/Earth" title="Earth">Earth</a></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> <a href="/wiki/Venus" title="Venus">Venus</a></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: OrangeRed; color:black;"> </span>  <a href="/wiki/Mars" title="Mars">Mars</a></span></div></div><div class="tsingle" style="width:448px;max-width:448px"><div class="thumbimage" style="height:181px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Cassini%27s_speed_related_to_Sun.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Cassini%27s_speed_related_to_Sun.png/446px-Cassini%27s_speed_related_to_Sun.png" decoding="async" width="446" height="182" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Cassini%27s_speed_related_to_Sun.png/669px-Cassini%27s_speed_related_to_Sun.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/Cassini%27s_speed_related_to_Sun.png/892px-Cassini%27s_speed_related_to_Sun.png 2x" data-file-width="1968" data-file-height="802" /></a></span></div><div class="thumbcaption text-align-center"><i>Cassini</i><span class="nowrap" style="padding-left:0.1em;">'s</span> speed relative to the Sun. Gravity assists form peaks to the left, while periodic variations on the right are caused by the spacecraft's orbit around Saturn.</div></div></div></div></div> <p>After entering orbit around Saturn, the <i>Cassini</i> spacecraft used multiple <a href="/wiki/Titan_(moon)" title="Titan (moon)">Titan</a> gravity assists to achieve significant changes in the inclination of its orbit as well so that instead of staying nearly in the equatorial plane, the spacecraft's flight path was inclined well out of the plane of the rings.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> A typical Titan encounter changed the spacecraft's velocity by 0.75 km/s, and the spacecraft made 127 Titan encounters. These encounters enabled an orbital tour with a wide range of periapsis and apoapsis distances, various alignments of the orbit with respect to the Sun, and orbital inclinations from 0° to 74°. The multiple flybys of Titan also allowed Cassini to flyby other moons, such as <a href="/wiki/Rhea_(moon)" title="Rhea (moon)">Rhea</a> and <a href="/wiki/Enceladus_(moon)" class="mw-redirect" title="Enceladus (moon)">Enceladus</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2022)">citation needed</span></a></i>]</sup> </p> <dl><dt><i>Rosetta</i></dt></dl> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Animation_of_Rosetta_trajectory.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Animation_of_Rosetta_trajectory.gif/220px-Animation_of_Rosetta_trajectory.gif" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Animation_of_Rosetta_trajectory.gif/330px-Animation_of_Rosetta_trajectory.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Animation_of_Rosetta_trajectory.gif/440px-Animation_of_Rosetta_trajectory.gif 2x" data-file-width="560" data-file-height="420" /></a><figcaption>Animation of <i>Rosetta</i><span class="nowrap" style="padding-left:0.1em;">'s</span> trajectory from 2 March 2004 to 9 September 2016 <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:magenta; color:black;"> </span> <i>Rosetta</i></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> <a href="/wiki/67P/Churyumov%E2%80%93Gerasimenko" title="67P/Churyumov–Gerasimenko">67P/C-G</a></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:Royalblue; color:white;"> </span> <a href="/wiki/Earth" title="Earth">Earth</a></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:maroon; color:white;"> </span> <a href="/wiki/Mars" title="Mars">Mars</a></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> <a href="/wiki/21_Lutetia" title="21 Lutetia">21 Lutetia</a> </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> <a href="/wiki/2867_%C5%A0teins" title="2867 Šteins">2867 Šteins</a></span></figcaption></figure> <p>The <i><a href="/wiki/Rosetta_(spacecraft)" title="Rosetta (spacecraft)">Rosetta</a></i> probe, launched in March 2004, used four gravity assist maneuvers (including one just 250 km from the surface of Mars, and three assists from Earth) to accelerate throughout the inner Solar System. That enabled it to flyby the asteroids <a href="/wiki/21_Lutetia" title="21 Lutetia">21 Lutetia</a> and <a href="/wiki/2867_%C5%A0teins" title="2867 Šteins">2867 Šteins</a> as well as eventually match the velocity of the <a href="/wiki/67P/Churyumov%E2%80%93Gerasimenko" title="67P/Churyumov–Gerasimenko">67P/Churyumov–Gerasimenko</a> comet at the rendezvous point in August 2014.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><i>New Horizons</i></dt></dl> <p><i><a href="/wiki/New_Horizons_(spacecraft)" class="mw-redirect" title="New Horizons (spacecraft)">New Horizons</a></i> was launched by NASA in 2006, and reached <a href="/wiki/Pluto" title="Pluto">Pluto</a> in 2015. In 2007 it performed a gravity assist on Jupiter.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><i>Juno</i></dt></dl> <p>The <a href="/wiki/Juno_(spacecraft)" title="Juno (spacecraft)">Juno spacecraft</a> was launched on August 5, 2011 (UTC). The trajectory used a gravity assist speed boost from Earth, accomplished by an Earth flyby in October 2013, two years after its launch on August 5, 2011.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> In that way <i>Juno</i> changed its orbit (and speed) toward its final goal, <a href="/wiki/Jupiter" title="Jupiter">Jupiter</a>, after only five years. </p> <dl><dt>Parker Solar Probe</dt></dl> <p>The <a href="/wiki/Parker_Solar_Probe" title="Parker Solar Probe">Parker Solar Probe</a>, launched by NASA in 2018, has seven planned Venus gravity assists. Each gravity assist brings the Parker Solar Probe progressively closer to the Sun. As of 2022, the spacecraft has performed five of its seven assists. The Parker Solar Probe's mission will make the closest approach to the Sun by any space mission.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p> <dl><dt>Solar Orbiter</dt></dl> <p><a href="/wiki/Solar_Orbiter" title="Solar Orbiter">Solar Orbiter</a> was launched by ESA in 2020. In its initial cruise phase, which lasts until November 2021, Solar Orbiter performed two gravity-assist manoeuvres around Venus and one around Earth to alter the spacecraft's trajectory, guiding it towards the innermost regions of the Solar System. The first close solar pass will take place on 26 March 2022 at around a third of Earth's distance from the Sun.<sup id="cite_ref-NASA_50-0" class="reference"><a href="#cite_note-NASA-50"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><i>BepiColombo</i></dt></dl> <p><a href="/wiki/BepiColombo" title="BepiColombo">BepiColombo</a> is a joint mission of the <a href="/wiki/European_Space_Agency" title="European Space Agency">European Space Agency</a> (ESA) and the <a href="/wiki/JAXA" title="JAXA">Japan Aerospace Exploration Agency</a> (JAXA) to the planet <a href="/wiki/Mercury_(planet)" title="Mercury (planet)">Mercury</a>. It was launched on 20 October 2018. It will use the gravity assist technique with <a href="/wiki/Earth" title="Earth">Earth</a> once, with <a href="/wiki/Venus" title="Venus">Venus</a> twice, and six times with <a href="/wiki/Mercury_(planet)" title="Mercury (planet)">Mercury</a>. It will arrive in 2025. BepiColombo is named after <a href="/wiki/Giuseppe_Colombo" title="Giuseppe Colombo">Giuseppe (Bepi) Colombo</a> who was a pioneer thinker with this way of maneuvers.<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> </p> <dl><dt><i>Lucy</i></dt></dl> <p><i><a href="/wiki/Lucy_(spacecraft)" title="Lucy (spacecraft)">Lucy</a></i> was launched by NASA on 16 October 2021. It gained one gravity assist from Earth on the 16th of October, 2022,<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> and after a flyby of the main-belt asteroid <a href="/wiki/152830_Dinkinesh" title="152830 Dinkinesh">152830 Dinkinesh</a> it will gain another in 2024.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> In 2025, it will fly by the inner main-belt asteroid <a href="/wiki/52246_Donaldjohanson" title="52246 Donaldjohanson">52246 Donaldjohanson</a>.<sup id="cite_ref-round_1_54-0" class="reference"><a href="#cite_note-round_1-54"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> In 2027, it will arrive at the <a href="/wiki/Lagrange_point#L4_and_L5" title="Lagrange point">L<sub>4</sub></a> Trojan cloud (the <a href="/wiki/Greek_camp" class="mw-redirect" title="Greek camp">Greek camp</a> of asteroids that orbits about 60° ahead of Jupiter), where it will fly by four Trojans, <a href="/wiki/3548_Eurybates" title="3548 Eurybates">3548 Eurybates</a> (with its satellite), <a href="/wiki/15094_Polymele" title="15094 Polymele">15094 Polymele</a>, <a href="/wiki/11351_Leucus" title="11351 Leucus">11351 Leucus</a>, and <a href="/wiki/21900_Orus" title="21900 Orus">21900 Orus</a>.<sup id="cite_ref-NYT-20170106_55-0" class="reference"><a href="#cite_note-NYT-20170106-55"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> After these flybys, <i>Lucy</i> will return to Earth in 2031 for another gravity assist toward the <a href="/wiki/Lagrange_point#L4_and_L5" title="Lagrange point">L<sub>5</sub></a> Trojan cloud (the <a href="/wiki/Trojan_camp" class="mw-redirect" title="Trojan camp">Trojan camp</a> which trails about 60° behind Jupiter), where it will visit the <a href="/wiki/Binary_asteroid" title="Binary asteroid">binary</a> Trojan <a href="/wiki/617_Patroclus" title="617 Patroclus">617 Patroclus</a> with its <a href="/wiki/Minor-planet_moon" title="Minor-planet moon">satellite</a> <a href="/wiki/617_Patroclus" title="617 Patroclus">Menoetius</a> in 2033. </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=Gravity_assist&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/28px-RocketSunIcon.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/42px-RocketSunIcon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/RocketSunIcon.svg/56px-RocketSunIcon.svg.png 2x" data-file-width="128" data-file-height="128" /></span></span></span><span class="portalbox-link"><a href="/wiki/Portal:Spaceflight" title="Portal:Spaceflight">Spaceflight portal</a></span></li></ul> <ul><li><a href="/wiki/3753_Cruithne" title="3753 Cruithne">3753 Cruithne</a>, an asteroid which periodically has gravitational slingshot encounters with Earth</li> <li><a href="/wiki/Delta-v_budget" title="Delta-v budget">Delta-<i>v</i> budget</a></li> <li><a href="/wiki/Low-energy_transfer" title="Low-energy transfer">Low-energy transfer</a>, a type of gravitational assist where a spacecraft is gravitationally snagged into orbit by a celestial body. This method is usually executed in the Earth-Moon system.</li> <li><a href="/wiki/Dynamical_friction" title="Dynamical friction">Dynamical friction</a></li> <li><a href="/wiki/Flyby_anomaly" title="Flyby anomaly">Flyby anomaly</a>, an anomalous delta-<i>v</i> increase during gravity assists</li> <li><a href="/wiki/Gravitational_keyhole" title="Gravitational keyhole">Gravitational keyhole</a></li> <li><a href="/wiki/Interplanetary_Transport_Network" title="Interplanetary Transport Network">Interplanetary Transport Network</a></li> <li><a href="/wiki/N-body_problem" title="N-body problem"><i>n</i>-body problem</a></li> <li><a href="/wiki/Oberth_effect" title="Oberth effect">Oberth effect</a>, applying thrust near closest approach in a gravity well</li> <li><i><a href="/wiki/Pioneer_H" title="Pioneer H">Pioneer H</a></i>, first Out-Of-The-Ecliptic mission (OOE) proposed, for Jupiter and solar (Sun) observations</li> <li><a href="/wiki/STEREO" title="STEREO">STEREO</a>, a gravity-assisted mission which used Earth's Moon to eject two spacecraft from Earth's orbit into <a href="/wiki/Heliocentric" class="mw-redirect" title="Heliocentric">heliocentric</a> orbit</li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Gravity_assist&action=edit&section=7" title="Edit section: Notes"><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-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">In 1938, when Kondratyuk submitted his manuscript "To whoever will read in order to build" for publication, he dated the manuscript 1918–1919, although it was apparent that the manuscript had been revised at various times. See page 49 of NASA Technical Translation F-9285 (1 November 1965).</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=Gravity_assist&action=edit&section=8" 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-basics-traject-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-basics-traject_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-basics-traject_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://solarsystem.nasa.gov/basics/chapter4-1">"Section 1: Environment, Chapter 4: Trajectories"</a>. Basics of Space Flight. NASA<span class="reference-accessdate">. Retrieved <span class="nowrap">21 July</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Section+1%3A+Environment%2C+Chapter+4%3A+Trajectories&rft.series=Basics+of+Space+Flight&rft.pub=NASA&rft_id=https%3A%2F%2Fsolarsystem.nasa.gov%2Fbasics%2Fchapter4-1&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravity+assist" class="Z3988"></span></span> </li> <li id="cite_note-:0-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_2-2"><sup><i><b>c</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="http://www.planetary.org/blogs/guest-blogs/2013/20130926-gravity-assist.html">"Gravity assist"</a>. The Planetary Society<span class="reference-accessdate">. Retrieved <span class="nowrap">1 January</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Gravity+assist&rft.pub=The+Planetary+Society&rft_id=http%3A%2F%2Fwww.planetary.org%2Fblogs%2Fguest-blogs%2F2013%2F20130926-gravity-assist.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravity+assist" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><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.esa.int/Science_Exploration/Space_Science/Exploring_space/Let_gravity_assist_you">"Let gravity assist you ..."</a> <i>ESA</i><span class="reference-accessdate">. Retrieved <span class="nowrap">8 March</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=ESA&rft.atitle=Let+gravity+assist+you+...&rft_id=https%3A%2F%2Fwww.esa.int%2FScience_Exploration%2FSpace_Science%2FExploring_space%2FLet_gravity_assist_you&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravity+assist" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://solarsystem.nasa.gov/basics/primer/">"A Gravity Assist Primer"</a>. Basics of Space Flight. NASA<span class="reference-accessdate">. Retrieved <span class="nowrap">21 July</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+Gravity+Assist+Primer&rft.series=Basics+of+Space+Flight&rft.pub=NASA&rft_id=https%3A%2F%2Fsolarsystem.nasa.gov%2Fbasics%2Fprimer%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravity+assist" class="Z3988"></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohnson2003" class="citation report cs1">Johnson, R. C. (January 2003). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200801071531/http://maths.dur.ac.uk/~dma0rcj/Psling/sling.pdf">The Slingshot Effect</a> <span class="cs1-format">(PDF)</span> (Report). Durham University. Archived from <a rel="nofollow" class="external text" href="http://maths.dur.ac.uk/~dma0rcj/Psling/sling.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2020-08-01<span class="reference-accessdate">. Retrieved <span class="nowrap">2018-07-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=The+Slingshot+Effect&rft.pub=Durham+University&rft.date=2003-01&rft.aulast=Johnson&rft.aufirst=R.+C.&rft_id=http%3A%2F%2Fmaths.dur.ac.uk%2F~dma0rcj%2FPsling%2Fsling.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravity+assist" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Kondratyuk's paper is included in the book: Mel'kumov, T. M., ed., <i>Pionery Raketnoy Tekhniki</i> [Pioneers of Rocketry: Selected Papers] (Moscow, U.S.S.R.: Institute for the History of Natural Science and Technology, Academy of Sciences of the USSR, 1964). An English translation of Kondratyuk's paper was made by NASA. See: NASA Technical Translation F-9285, pages 15–56 (1 November 1965).</span> </li> <li id="cite_note-urlib.net-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-urlib.net_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-urlib.net_8-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-urlib.net_8-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNegriPrado2020" class="citation journal cs1">Negri, Rodolfo Batista; Prado, Antônio Fernando Bertachini de Alme (14 July 2020). <a rel="nofollow" class="external text" href="http://urlib.net/8JMKD3MGP3W34R/42T4NAH">"A historical review of the theory of gravity-assists in the pre-spaceflight era"</a>. <i>Journal of the Brazilian Society of Mechanical Sciences and Engineering</i>. <b>42</b> (8). <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs40430-020-02489-x">10.1007/s40430-020-02489-x</a></span>. <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:220510617">220510617</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+the+Brazilian+Society+of+Mechanical+Sciences+and+Engineering&rft.atitle=A+historical+review+of+the+theory+of+gravity-assists+in+the+pre-spaceflight+era&rft.volume=42&rft.issue=8&rft.date=2020-07-14&rft_id=info%3Adoi%2F10.1007%2Fs40430-020-02489-x&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A220510617%23id-name%3DS2CID&rft.aulast=Negri&rft.aufirst=Rodolfo+Batista&rft.au=Prado%2C+Ant%C3%B4nio+Fernando+Bertachini+de+Alme&rft_id=http%3A%2F%2Furlib.net%2F8JMKD3MGP3W34R%2F42T4NAH&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravity+assist" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Zander's 1925 paper, "Problems of Flight by Jet Propulsion: Interplanetary Flights" was translated by NASA. See NASA Technical Translation F-147 (1964); specifically, Section 7: Flight Around a Planet's Satellite for Accelerating or Decelerating Spaceship, pages 290–292.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEneevAkim" class="citation web cs1 cs1-prop-foreign-lang-source">Eneev, T.; Akim, E. <a rel="nofollow" class="external text" href="http://www.keldysh.ru/events/fly">"Mstislav Keldysh. Mechanics of the Space Flight"</a> (in Russian). 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Retrieved <span class="nowrap">21 July</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+Gravity+Assist+Primer&rft.series=Basics+of+Space+Flight&rft.pub=NASA&rft_id=https%3A%2F%2Fsolarsystem.nasa.gov%2Fbasics%2Fprimer%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravity+assist" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</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://voyager.jpl.nasa.gov/mission/status/">"Voyager - Mission Status"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Voyager+-+Mission+Status&rft_id=https%3A%2F%2Fvoyager.jpl.nasa.gov%2Fmission%2Fstatus%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravity+assist" class="Z3988"></span></span> </li> <li id="cite_note-voyager-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-voyager_29-0">^</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://voyager.jpl.nasa.gov/mission/status/">"Voyager – Mission Status"</a>. <i><a href="/wiki/Jet_Propulsion_Laboratory" title="Jet Propulsion Laboratory">Jet Propulsion Laboratory</a></i>. <a href="/wiki/National_Aeronautics_and_Space_Administration" class="mw-redirect" title="National Aeronautics and Space Administration">National Aeronautics and Space Administration</a><span class="reference-accessdate">. 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Retrieved <span class="nowrap">September 4,</span> 2015</span>. <q>Despite the name change, Voyager remained in many ways the Grand Tour concept, though certainly not the Grand Tour (TOPS) spacecraft. <i>Voyager 2</i> was launched on August 20, 1977, followed by <i>Voyager 1</i> on September 5, 1977. The decision to reverse the order of launch had to do with keeping open the possibility of carrying out the Grand Tour mission to Uranus, Neptune, and beyond. <i>Voyager 2</i>, if boosted by the maximum performance from the Titan-Centaur, could just barely catch the old Grand Tour trajectory and encounter Uranus. Two weeks later, <i>Voyager 1</i> would leave on an easier and much faster trajectory, visiting Jupiter and Saturn only. <i>Voyager 1</i> would arrive at Jupiter four months ahead of Voyager 2, then arrive at Saturn nine months earlier. Hence, the second spacecraft launched was <i>Voyager 1</i>, not <i>Voyager 2</i>. 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Retrieved <span class="nowrap">29 March</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=nasa.gov&rft.atitle=NASA+Awards+Launch+Services+Contract+for+Lucy+Mission&rft.date=2019-01-31&rft_id=https%3A%2F%2Fwww.nasa.gov%2Fpress-release%2Fnasa-awards-launch-services-contract-for-lucy-mission&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravity+assist" class="Z3988"></span> <span class="noviewer" typeof="mw:File"><span><img alt="Public Domain" src="//upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/12px-PD-icon.svg.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/18px-PD-icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/24px-PD-icon.svg.png 2x" data-file-width="196" data-file-height="196" /></span></span> This article incorporates text from this source, which is in the <a href="/wiki/Public_domain" title="Public domain">public domain</a>.</span> </li> <li id="cite_note-round_1-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-round_1_54-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDreierLakdawalla2015" class="citation news cs1">Dreier, Casey; Lakdawalla, Emily (30 September 2015). <a rel="nofollow" class="external text" href="http://www.planetary.org/blogs/casey-dreier/2015/09301336-discovery-downselect.html">"NASA announces five Discovery proposals selected for further study"</a>. The Planetary Society.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=NASA+announces+five+Discovery+proposals+selected+for+further+study&rft.date=2015-09-30&rft.aulast=Dreier&rft.aufirst=Casey&rft.au=Lakdawalla%2C+Emily&rft_id=http%3A%2F%2Fwww.planetary.org%2Fblogs%2Fcasey-dreier%2F2015%2F09301336-discovery-downselect.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravity+assist" class="Z3988"></span></span> </li> <li id="cite_note-NYT-20170106-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-NYT-20170106_55-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChang2017" class="citation news cs1">Chang, Kenneth (6 January 2017). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2017/01/06/science/nasa-psyche-asteroid.html">"A Metal Ball the Size of Massachusetts That NASA Wants to Explore"</a>. <i>The New York Times</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=A+Metal+Ball+the+Size+of+Massachusetts+That+NASA+Wants+to+Explore&rft.date=2017-01-06&rft.aulast=Chang&rft.aufirst=Kenneth&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2017%2F01%2F06%2Fscience%2Fnasa-psyche-asteroid.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravity+assist" class="Z3988"></span></span> </li> </ol></div></div> <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=Gravity_assist&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/Special:Search/gravity_assist" class="extiw" title="wiktionary:Special:Search/gravity assist">gravity assist</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://solarsystem.nasa.gov/basics/primer/">Basics of Space Flight: A Gravity Assist Primer</a> at NASA.gov</li> <li><a rel="nofollow" class="external text" href="http://www.phy6.org/stargaze/Stostars.htm">Spaceflight and Spacecraft: Gravity Assist</a>, discussion at Phy6.org</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.mathpages.com/home/kmath114/kmath114.htm">"Gravitational Slingshot"</a>. <i>MathPages.com</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathPages.com&rft.atitle=Gravitational+Slingshot&rft_id=http%3A%2F%2Fwww.mathpages.com%2Fhome%2Fkmath114%2Fkmath114.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGravity+assist" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://hyperphysics.phy-astr.gsu.edu/hbase/doubal.html">Double-ball drop experiment</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="Spacecraft_propulsion" style="padding:3px"><table class="nowraplinks 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:Spacecraft_propulsion" title="Template:Spacecraft propulsion"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Spacecraft_propulsion" title="Template talk:Spacecraft propulsion"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Spacecraft_propulsion" title="Special:EditPage/Template:Spacecraft propulsion"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Spacecraft_propulsion" style="font-size:114%;margin:0 4em"><a href="/wiki/Spacecraft_propulsion" title="Spacecraft propulsion">Spacecraft propulsion</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Rocket" title="Rocket">Rocket</a></li> <li><a href="/wiki/Rocket_engine" title="Rocket engine">Rocket engine</a> <ul><li><a href="/wiki/Reaction_engine" title="Reaction engine">Reaction engine</a></li> <li><a href="/wiki/Reaction_mass" class="mw-redirect" title="Reaction mass">Reaction mass</a></li></ul></li> <li><a href="/wiki/Thrust" title="Thrust">Thrust</a> <ul><li><a href="/wiki/Specific_impulse" title="Specific impulse">Specific impulse</a></li> <li><a href="/wiki/Delta-v" title="Delta-v">Delta-v</a></li></ul></li> <li><a href="/wiki/Multistage_rocket" title="Multistage rocket">Staging</a></li> <li><a href="/wiki/Rocket_equation" class="mw-redirect" title="Rocket equation">Rocket equation</a></li> <li><a href="/wiki/Thermal_rocket" title="Thermal rocket">Thermal rocket</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Physical propulsion</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cold_gas_thruster" title="Cold gas thruster">Cold gas thruster</a></li> <li><a href="/wiki/Water_rocket" title="Water rocket">Water rocket</a></li> <li><a href="/wiki/Steam_rocket" title="Steam rocket">Steam rocket</a></li> <li><a href="/wiki/Solar_sail" title="Solar sail">Solar sail</a> <ul><li><a href="/wiki/Diffractive_solar_sail" title="Diffractive solar sail">Diffractive</a></li></ul></li> <li><a href="/wiki/Electric_sail" title="Electric sail">Electric sail</a></li> <li><a href="/wiki/Magnetic_sail" title="Magnetic sail">Magnetic sail</a></li> <li><a href="/wiki/Solar_thermal_rocket" title="Solar thermal rocket">Solar thermal rocket</a></li> <li><a href="/wiki/Photon_rocket" title="Photon rocket">Photon rocket</a></li> <li><a href="/wiki/World_Is_Not_Enough_(spacecraft_propulsion)" title="World Is Not Enough (spacecraft propulsion)">WINE</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Chemical propulsion</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" 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:1%">State</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/Liquid-propellant_rocket" title="Liquid-propellant rocket">Liquid-propellant rocket</a></li> <li><a href="/wiki/Solid-propellant_rocket" title="Solid-propellant rocket">Solid-propellant rocket</a></li> <li><a href="/wiki/Hybrid-propellant_rocket" title="Hybrid-propellant rocket">Hybrid-propellant rocket</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Propellants</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/Liquid_rocket_propellant" title="Liquid rocket propellant">Liquid propellant</a> <ul><li><a href="/wiki/Cryogenic_rocket_engine" title="Cryogenic rocket engine">Cryogenic</a></li> <li><a href="/wiki/Hypergolic_propellant" title="Hypergolic propellant">Hypergolic</a></li></ul></li> <li><a href="/wiki/Monopropellant_rocket" title="Monopropellant rocket">Monopropellant</a></li> <li><a href="/wiki/Bipropellant_rocket" class="mw-redirect" title="Bipropellant rocket">Bipropellant</a></li> <li><a href="/wiki/Tripropellant_rocket" title="Tripropellant rocket">Tripropellant</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Power cycles</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/Staged_combustion_cycle" title="Staged combustion cycle">Staged combustion cycle</a></li> <li><a href="/wiki/Expander_cycle" title="Expander cycle">Expander cycle</a></li> <li><a href="/wiki/Gas-generator_cycle" title="Gas-generator cycle">Gas-generator cycle</a></li> <li><a href="/wiki/Combustion_tap-off_cycle" title="Combustion tap-off cycle">Tap-off cycle</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Intake mechanisms</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/Pressure-fed_engine" title="Pressure-fed engine">Pressure-fed engine</a></li> <li><a href="/wiki/Pump-fed_engine" class="mw-redirect" title="Pump-fed engine">Pump-fed engine</a></li> <li><a href="/wiki/Electric-pump-fed_engine" title="Electric-pump-fed engine">Electric-pump-fed engine</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/Spacecraft_electric_propulsion" title="Spacecraft electric propulsion">Electrical propulsion</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" 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:1%">Electrostatic</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/Colloid_thruster" title="Colloid thruster">Colloid thruster</a></li> <li><a href="/wiki/Ion_thruster" title="Ion thruster">Ion thruster</a> <ul><li><a href="/wiki/Gridded_ion_thruster" title="Gridded ion thruster">Gridded</a></li> <li><a href="/wiki/Hall-effect_thruster" title="Hall-effect thruster">Hall-effect thruster</a></li> <li><a href="/wiki/Field-emission_electric_propulsion" title="Field-emission electric propulsion">Field-emission electric propulsion</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Electromagnetic</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/Pulsed_inductive_thruster" title="Pulsed inductive thruster">Pulsed inductive thruster</a></li> <li><a href="/wiki/Magnetoplasmadynamic_thruster" title="Magnetoplasmadynamic thruster">Magnetoplasmadynamic thruster</a></li> <li><a href="/wiki/Electrodeless_plasma_thruster" title="Electrodeless plasma thruster">Electrodeless plasma thruster</a></li> <li><a href="/wiki/Plasma_magnet" title="Plasma magnet">Plasma magnet</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Electrothermal</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/Pulsed_plasma_thruster" title="Pulsed plasma thruster">Pulsed plasma thruster</a></li> <li><a href="/wiki/Vacuum_arc_thruster" title="Vacuum arc thruster">Vacuum arc thruster</a></li> <li><a href="/wiki/Helicon_double-layer_thruster" title="Helicon double-layer thruster">Helicon double-layer thruster</a></li> <li><a href="/wiki/Arcjet_rocket" title="Arcjet rocket">Arcjet rocket</a></li> <li><a href="/wiki/Resistojet_rocket" title="Resistojet rocket">Resistojet rocket</a></li> <li><a href="/wiki/Microwave_electrothermal_thruster" title="Microwave electrothermal thruster">Microwave electrothermal thruster</a></li> <li><a href="/wiki/Variable_Specific_Impulse_Magnetoplasma_Rocket" title="Variable Specific Impulse Magnetoplasma Rocket">VASIMR</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</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/Atmosphere-breathing_electric_propulsion" title="Atmosphere-breathing electric propulsion">Atmosphere-breathing electric propulsion</a></li> <li><a href="/wiki/High_Power_Electric_Propulsion" title="High Power Electric Propulsion">High Power Electric Propulsion</a></li> <li><a href="/wiki/MagBeam" title="MagBeam">MagBeam</a></li> <li><a href="/wiki/Mass_driver" title="Mass driver">Mass driver</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/Nuclear_propulsion#Spacecraft" title="Nuclear propulsion">Nuclear propulsion</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" 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:1%">Closed system</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0;evenodd:swap"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Direct_Fusion_Drive" title="Direct Fusion Drive">Direct Fusion Drive</a></li> <li><a href="/wiki/Nuclear_electric_rocket" title="Nuclear electric rocket">Nuclear electric rocket</a></li> <li><a href="/wiki/Nuclear_thermal_rocket" title="Nuclear thermal rocket">Nuclear thermal rocket</a> <ul><li><a href="/wiki/Radioisotope_rocket" title="Radioisotope rocket">Radioisotope</a></li> <li><a href="/wiki/Nuclear_salt-water_rocket" title="Nuclear salt-water rocket">Salt-water</a></li> <li><a href="/wiki/Gas_core_reactor_rocket" title="Gas core reactor rocket">Gas core</a></li> <li><a href="/wiki/Nuclear_lightbulb" title="Nuclear lightbulb">"Lightbulb"</a></li></ul></li> <li><a href="/wiki/Nuclear_photonic_rocket" title="Nuclear photonic rocket">Nuclear photonic rocket</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Open system</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/Nuclear_pulse_propulsion" title="Nuclear pulse propulsion">Nuclear pulse propulsion</a> <ul><li><a href="/wiki/Antimatter-catalyzed_nuclear_pulse_propulsion" title="Antimatter-catalyzed nuclear pulse propulsion">Antimatter-catalyzed</a></li></ul></li> <li><a href="/wiki/Pulsed_nuclear_thermal_rocket" title="Pulsed nuclear thermal rocket">Pulsed nuclear thermal rocket‎</a></li> <li><a href="/wiki/Fusion_rocket" title="Fusion rocket">Fusion rocket</a> <ul><li><a href="/wiki/Bussard_ramjet" title="Bussard ramjet">Bussard ramjet</a></li></ul></li> <li><a href="/wiki/Fission-fragment_rocket" title="Fission-fragment rocket">Fission-fragment rocket</a> <ul><li><a href="/wiki/Fission_sail" title="Fission sail">Fission sail</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">External power</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Beam-powered_propulsion" title="Beam-powered propulsion">Beam-powered propulsion</a></li> <li><a href="/wiki/Space_tether" title="Space tether">Tethers</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related concepts</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Orbital_mechanics" title="Orbital mechanics">Orbital mechanics</a></li> <li><a href="/wiki/Orbital_maneuver" title="Orbital maneuver">Orbital maneuver</a></li> <li><a class="mw-selflink selflink">Gravity assist</a></li> <li><a href="/wiki/Aerogravity_assist" title="Aerogravity assist">Aerogravity assist</a></li> <li><a href="/wiki/Oberth_effect" title="Oberth effect">Oberth effect</a></li> <li><a href="/wiki/Space_launch" title="Space launch">Space launch</a></li> <li><a href="/wiki/Non-rocket_spacelaunch" title="Non-rocket spacelaunch">Non-rocket spacelaunch</a></li> <li><a href="/wiki/Aerobraking" title="Aerobraking">Aerobraking</a></li> <li><a href="/wiki/Aerocapture" title="Aerocapture">Aerocapture</a></li> <li><a href="/wiki/Atmospheric_entry" title="Atmospheric entry">Atmospheric entry</a></li> <li><a href="/wiki/Reactionless_drive" title="Reactionless drive">Reactionless drive</a></li> <li><a href="/wiki/Field_propulsion" title="Field propulsion">Field propulsion</a> <ul><li><a href="/wiki/Warp_drive" title="Warp drive">Warp drive</a></li> <li><a href="/wiki/Alcubierre_drive" title="Alcubierre drive">Alcubierre drive</a></li></ul></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Symbol_portal_class.svg" class="mw-file-description" title="Portal"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /></a></span><b><a href="/wiki/Portal:Spaceflight" title="Portal:Spaceflight">Spaceflight portal</a></b></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Gravitational_orbits" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Orbits" title="Template:Orbits"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Orbits" title="Template talk:Orbits"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Orbits" title="Special:EditPage/Template:Orbits"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Gravitational_orbits" style="font-size:114%;margin:0 4em">Gravitational <a href="/wiki/Orbit" title="Orbit">orbits</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_orbits" title="List of orbits">Types</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Box_orbit" title="Box orbit">Box</a></li> <li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Capture</a></li> <li><a href="/wiki/Circular_orbit" title="Circular orbit">Circular</a></li> <li><a href="/wiki/Elliptic_orbit" title="Elliptic orbit">Elliptical</a> / <a href="/wiki/Highly_elliptical_orbit" title="Highly elliptical orbit">Highly elliptical</a></li> <li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Escape</a></li> <li><a href="/wiki/Horseshoe_orbit" title="Horseshoe orbit">Horseshoe</a></li> <li><a href="/wiki/Hyperbolic_trajectory" title="Hyperbolic trajectory">Hyperbolic trajectory</a></li> <li><a href="/wiki/Inclined_orbit" title="Inclined orbit">Inclined</a> / <a href="/wiki/Non-inclined_orbit" class="mw-redirect" title="Non-inclined orbit">Non-inclined</a></li> <li><a href="/wiki/Kepler_orbit" title="Kepler orbit">Kepler</a></li> <li><a href="/wiki/Lagrange_point" title="Lagrange point">Lagrange point</a></li> <li><a href="/wiki/Osculating_orbit" title="Osculating orbit">Osculating</a></li> <li><a href="/wiki/Parabolic_trajectory" title="Parabolic trajectory">Parabolic trajectory</a></li> <li><a href="/wiki/Parking_orbit" title="Parking orbit">Parking</a></li> <li><a href="/wiki/Retrograde_and_prograde_motion" title="Retrograde and prograde motion">Prograde / Retrograde</a></li> <li><a href="/wiki/Synchronous_orbit" title="Synchronous orbit">Synchronous</a> <ul><li><a href="/wiki/Semi-synchronous_orbit" title="Semi-synchronous orbit">semi</a></li> <li><a href="/wiki/Subsynchronous_orbit" title="Subsynchronous orbit">sub</a></li></ul></li> <li><a href="/wiki/Hohmann_transfer_orbit" title="Hohmann transfer orbit">Transfer orbit</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em"><a href="/wiki/Geocentric_orbit" title="Geocentric orbit">Geocentric</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Geosynchronous_orbit" title="Geosynchronous orbit">Geosynchronous</a> <ul><li><a href="/wiki/Geostationary_orbit" title="Geostationary orbit">Geostationary</a></li> <li><a href="/wiki/Geostationary_transfer_orbit" title="Geostationary transfer orbit">Geostationary transfer</a></li></ul></li> <li><a href="/wiki/Graveyard_orbit" title="Graveyard orbit">Graveyard</a></li> <li><a href="/wiki/High_Earth_orbit" title="High Earth orbit">High Earth</a></li> <li><a href="/wiki/Low_Earth_orbit" title="Low Earth orbit">Low Earth</a></li> <li><a href="/wiki/Medium_Earth_orbit" title="Medium Earth orbit">Medium Earth</a></li> <li><a href="/wiki/Molniya_orbit" title="Molniya orbit">Molniya</a></li> <li><a href="/wiki/Near-equatorial_orbit" title="Near-equatorial orbit">Near-equatorial</a></li> <li><a href="/wiki/Orbit_of_the_Moon" title="Orbit of the Moon">Orbit of the Moon</a></li> <li><a href="/wiki/Polar_orbit" title="Polar orbit">Polar</a></li> <li><a href="/wiki/Sun-synchronous_orbit" title="Sun-synchronous orbit">Sun-synchronous</a></li> <li><a href="/wiki/Transatmospheric_orbit" title="Transatmospheric orbit">Transatmospheric</a></li> <li><a href="/wiki/Tundra_orbit" title="Tundra orbit">Tundra</a></li> <li><a href="/wiki/Very_low_Earth_orbit" title="Very low Earth orbit">Very low Earth</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">About<br />other points</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li>Mars <ul><li><a href="/wiki/Areocentric_orbit" title="Areocentric orbit">Areocentric</a></li> <li><a href="/wiki/Areosynchronous_orbit" title="Areosynchronous orbit">Areosynchronous</a></li> <li><a href="/wiki/Areostationary_orbit" title="Areostationary orbit">Areostationary</a></li></ul></li> <li>Lagrange points <ul><li><a href="/wiki/Distant_retrograde_orbit" title="Distant retrograde orbit">Distant retrograde</a></li> <li><a href="/wiki/Halo_orbit" title="Halo orbit">Halo</a></li> <li><a href="/wiki/Lissajous_orbit" title="Lissajous orbit">Lissajous</a></li> <li><a href="/wiki/Libration_point_orbit" title="Libration point orbit">Libration</a></li></ul></li> <li><a href="/wiki/Lunar_orbit" title="Lunar orbit">Lunar</a></li> <li>Sun <ul><li><a href="/wiki/Heliocentric_orbit" title="Heliocentric orbit">Heliocentric</a> <ul><li><a href="/wiki/Earth%27s_orbit" title="Earth's orbit">Earth's orbit</a></li></ul></li> <li><a href="/wiki/Mars_cycler" title="Mars cycler">Mars cycler</a></li> <li><a href="/wiki/Sun-synchronous_orbit" title="Sun-synchronous orbit">Heliosynchronous</a></li></ul></li> <li>Other <ul><li><a href="/wiki/Lunar_cycler" title="Lunar cycler">Lunar cycler</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Orbital_elements" title="Orbital elements">Parameters</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6em"><div class="hlist"><ul><li>Shape</li><li>Size</li></ul></div></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">e</span>  <a href="/wiki/Orbital_eccentricity" title="Orbital eccentricity">Eccentricity</a></li> <li><span class="texhtml mvar" style="font-style:italic;">a</span>  <a href="/wiki/Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">Semi-major axis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">b</span>  <a href="/wiki/Semi-major_and_semi-minor_axes" title="Semi-major and semi-minor axes">Semi-minor axis</a></li> <li><span class="texhtml mvar" style="font-style:italic;">Q</span>, <span class="texhtml mvar" style="font-style:italic;">q</span>  <a href="/wiki/Apsis" title="Apsis">Apsides</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6em">Orientation</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><span class="texhtml mvar" style="font-style:italic;">i</span>  <a 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 class="mw-selflink selflink">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> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Voyager_program" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align: center;"><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:Voyager_program" title="Template:Voyager program"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Voyager_program" title="Template talk:Voyager program"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Voyager_program" title="Special:EditPage/Template:Voyager program"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Voyager_program" style="font-size:114%;margin:0 4em"><a href="/wiki/Voyager_program" title="Voyager program">Voyager program</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Spacecraft</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Voyager_1" title="Voyager 1">Voyager 1</a></i></li> <li><i><a href="/wiki/Voyager_2" title="Voyager 2">Voyager 2</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Components</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/MHW-RTG" title="MHW-RTG">MHW-RTG</a></li> <li><a href="/wiki/Cosmic_Ray_Subsystem" title="Cosmic Ray Subsystem">Cosmic Ray Subsystem</a> (CRS)</li> <li><a href="/wiki/Infrared_interferometer_spectrometer_and_radiometer" title="Infrared interferometer spectrometer and radiometer">Infrared interferometer spectrometer and radiometer</a> (IRIS)</li> <li><a href="/wiki/Plasma_Wave_Subsystem" title="Plasma Wave Subsystem">Plasma Wave Subsystem</a> (PWS)</li> <li><a href="/wiki/Voyager_Golden_Record" title="Voyager Golden Record">Voyager Golden Record</a> (<a href="/wiki/Contents_of_the_Voyager_Golden_Record" title="Contents of the Voyager Golden Record">contents</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Images</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Pale_Blue_Dot" title="Pale Blue Dot">Pale Blue Dot</a></i></li> <li><a href="/wiki/Family_Portrait_(Voyager)" title="Family Portrait (Voyager)"><i>Family Portrait</i></a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Voyager team</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Stamatios_Krimigis" title="Stamatios Krimigis">Stamatios Krimigis</a></li> <li><a href="/wiki/Carolyn_Porco" title="Carolyn Porco">Carolyn Porco</a></li> <li><a href="/wiki/Raymond_Heacock" title="Raymond Heacock">Raymond Heacock</a></li> <li><a href="/wiki/Jim_Blinn" title="Jim Blinn">Jim Blinn</a></li> <li><a href="/wiki/Larry_Soderblom" title="Larry Soderblom">Larry Soderblom</a></li> <li><a href="/wiki/Edward_C._Stone" title="Edward C. Stone">Edward C. Stone</a></li> <li><a href="/wiki/Timothy_Ferris" title="Timothy Ferris">Timothy Ferris</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Gravity assist</a></li> <li><a href="/wiki/Radioisotope_thermoelectric_generator" title="Radioisotope thermoelectric generator">Radioisotope thermoelectric generator</a></li> <li><a href="/wiki/Specific_orbital_energy#Voyager_1" title="Specific orbital energy">Specific orbital energy of <i>Voyager 1</i></a></li> <li><a href="/wiki/Titan_IIIE" title="Titan IIIE">Titan IIIE</a></li> <li><a href="/wiki/Grand_Tour_program" title="Grand Tour program">Grand Tour program</a></li> <li><a href="/wiki/Rings_of_Jupiter" title="Rings of Jupiter">Rings of Jupiter</a></li> <li><a href="/wiki/NASA_Deep_Space_Network" title="NASA Deep Space Network">NASA Deep Space Network</a></li> <li><a href="/wiki/Frank_Drake" title="Frank Drake">Frank Drake</a></li> <li><a href="/wiki/Carl_Sagan" title="Carl Sagan">Carl Sagan</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Observation<br />targets</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" 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:1%"><a href="/wiki/Exploration_of_Jupiter#Voyager_program_(1979)" title="Exploration of Jupiter">Exploration of Jupiter</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>and its moon <a href="/wiki/Exploration_of_Io#Voyager_era:_1979–1995" title="Exploration of Io">Io</a> <ul><li>with volcanos <a href="/wiki/Masubi_(volcano)#Observations_by_Voyager_1" title="Masubi (volcano)">Masubi</a></li> <li><a href="/wiki/Pele_(volcano)" title="Pele (volcano)">Pele</a></li> <li><a href="/wiki/Prometheus_(volcano)" title="Prometheus (volcano)">Prometheus</a></li> <li><a href="/wiki/Surt_(volcano)" title="Surt (volcano)">Surt</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Exploration_of_Saturn#Voyager" title="Exploration of Saturn">Exploration of Saturn</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>and its moon <a href="/wiki/Enceladus#Exploration" title="Enceladus">Enceladus</a> <ul><li>with craters <a href="/wiki/Dunyazad_(crater)" title="Dunyazad (crater)">Dunyazad</a></li> <li><a href="/wiki/Shahrazad_(crater)" title="Shahrazad (crater)">Shahrazad</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Exploration_of_Uranus#Voyager_2" title="Exploration of Uranus">Exploration of Uranus</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>and its <a href="/wiki/Rings_of_Uranus#Exploration" title="Rings of Uranus">rings</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Exploration_of_Neptune#Voyager_2" title="Exploration of Neptune">Exploration of Neptune</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>and its moon <a href="/wiki/Triton_(moon)#Observation_and_exploration" title="Triton (moon)">Triton</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Popular culture</th><td class="navbox-list-with-group navbox-list navbox-even hlist" 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