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accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>登录</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 未登录编辑者的页面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%97%A8" aria-label="了解有关编辑的更多信息"><span>了解详情</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="来自此IP地址的编辑列表[y]" accesskey="y"><span>贡献</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="对于来自此IP地址编辑的讨论[n]" accesskey="n"><span>讨论</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">序言</div> </a> </li> <li id="toc-歷史" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#歷史"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>歷史</span> </div> </a> <ul id="toc-歷史-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-共振的類型" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#共振的類型"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>共振的類型</span> </div> </a> <ul id="toc-共振的類型-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-在太陽系的平均運動共振" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#在太陽系的平均運動共振"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>在太陽系的平均運動共振</span> </div> </a> <button aria-controls="toc-在太陽系的平均運動共振-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>开关在太陽系的平均運動共振子章节</span> </button> <ul id="toc-在太陽系的平均運動共振-sublist" class="vector-toc-list"> <li id="toc-拉普拉斯共振" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#拉普拉斯共振"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>拉普拉斯共振</span> </div> </a> <ul id="toc-拉普拉斯共振-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-冥族小天體的共振" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#冥族小天體的共振"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>冥族小天體的共振</span> </div> </a> <ul id="toc-冥族小天體的共振-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-系外行星的平均運動共振" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#系外行星的平均運動共振"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>系外行星的平均運動共振</span> </div> </a> <ul id="toc-系外行星的平均運動共振-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-符合'接近'比率的平均運動" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#符合'接近'比率的平均運動"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>符合'接近'比率的平均運動</span> </div> </a> <ul id="toc-符合'接近'比率的平均運動-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-相關條目" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#相關條目"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>相關條目</span> </div> </a> <ul id="toc-相關條目-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参考文献" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参考文献"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>参考文献</span> </div> </a> <button aria-controls="toc-参考文献-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>开关参考文献子章节</span> </button> <ul id="toc-参考文献-sublist" class="vector-toc-list"> <li id="toc-引用" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#引用"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>引用</span> </div> </a> <ul id="toc-引用-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-书目" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#书目"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>书目</span> </div> </a> <ul id="toc-书目-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-外部連結" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部連結"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>外部連結</span> </div> </a> <ul id="toc-外部連結-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="目录" 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="开关目录" > <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">开关目录</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">轨道共振</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="前往另一种语言写成的文章。47种语言可用" > <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-47" 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">47种语言</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/Baanresonansie" title="Baanresonansie – 南非荷兰语" lang="af" hreflang="af" data-title="Baanresonansie" data-language-autonym="Afrikaans" data-language-local-name="南非荷兰语" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Bahnresonanz" title="Bahnresonanz – 瑞士德语" lang="gsw" hreflang="gsw" data-title="Bahnresonanz" data-language-autonym="Alemannisch" data-language-local-name="瑞士德语" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B1%D9%86%D9%8A%D9%86_%D9%85%D8%AF%D8%A7%D8%B1%D9%8A" title="رنين مداري – 阿拉伯语" lang="ar" hreflang="ar" data-title="رنين مداري" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D1%80%D0%B1%D1%96%D1%82%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D1%80%D1%8D%D0%B7%D0%B0%D0%BD%D0%B0%D0%BD%D1%81" title="Арбітальны рэзананс – 白俄罗斯语" lang="be" hreflang="be" data-title="Арбітальны рэзананс" data-language-autonym="Беларуская" data-language-local-name="白俄罗斯语" 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%9E%D1%80%D0%B1%D0%B8%D1%82%D0%B0%D0%BB%D0%B5%D0%BD_%D1%80%D0%B5%D0%B7%D0%BE%D0%BD%D0%B0%D0%BD%D1%81" title="Орбитален резонанс – 保加利亚语" lang="bg" hreflang="bg" data-title="Орбитален резонанс" data-language-autonym="Български" data-language-local-name="保加利亚语" 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/Resson%C3%A0ncia_orbital" title="Ressonància orbital – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Ressonància orbital" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" 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/Dr%C3%A1hov%C3%A1_rezonance" title="Dráhová rezonance – 捷克语" lang="cs" hreflang="cs" data-title="Dráhová rezonance" data-language-autonym="Čeština" data-language-local-name="捷克语" 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/Baneresonans" title="Baneresonans – 丹麦语" lang="da" hreflang="da" data-title="Baneresonans" data-language-autonym="Dansk" data-language-local-name="丹麦语" 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/Bahnresonanz" title="Bahnresonanz – 德语" lang="de" hreflang="de" data-title="Bahnresonanz" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Orbital_resonance" title="Orbital resonance – 英语" lang="en" hreflang="en" data-title="Orbital resonance" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Orbita_resonanco" title="Orbita resonanco – 世界语" lang="eo" hreflang="eo" data-title="Orbita resonanco" data-language-autonym="Esperanto" data-language-local-name="世界语" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Resonancia_orbital" title="Resonancia orbital – 西班牙语" lang="es" hreflang="es" data-title="Resonancia orbital" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D8%B2%D9%86%D8%A7%D9%86%D8%B3_%D9%85%D8%AF%D8%A7%D8%B1%DB%8C" title="رزنانس مداری – 波斯语" lang="fa" hreflang="fa" data-title="رزنانس مداری" data-language-autonym="فارسی" data-language-local-name="波斯语" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Keskiliikeresonanssi" title="Keskiliikeresonanssi – 芬兰语" lang="fi" hreflang="fi" data-title="Keskiliikeresonanssi" data-language-autonym="Suomi" data-language-local-name="芬兰语" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/R%C3%A9sonance_orbitale" title="Résonance orbitale – 法语" lang="fr" hreflang="fr" data-title="Résonance orbitale" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Resonancia_orbital" title="Resonancia orbital – 加利西亚语" lang="gl" hreflang="gl" data-title="Resonancia orbital" data-language-autonym="Galego" data-language-local-name="加利西亚语" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%94%D7%95%D7%93%D7%94_%D7%9E%D7%A1%D7%9C%D7%95%D7%9C%D7%99%D7%AA" title="תהודה מסלולית – 希伯来语" lang="he" hreflang="he" data-title="תהודה מסלולית" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A5%80%E0%A4%AF_%E0%A4%85%E0%A4%A8%E0%A5%81%E0%A4%A8%E0%A4%BE%E0%A4%A6" title="कक्षीय अनुनाद – 印地语" lang="hi" hreflang="hi" data-title="कक्षीय अनुनाद" data-language-autonym="हिन्दी" data-language-local-name="印地语" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Orbitalna_rezonancija" title="Orbitalna rezonancija – 克罗地亚语" lang="hr" hreflang="hr" data-title="Orbitalna rezonancija" data-language-autonym="Hrvatski" data-language-local-name="克罗地亚语" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%88%D6%82%D5%B2%D5%A5%D5%AE%D6%80%D5%A1%D5%B5%D5%AB%D5%B6_%D5%BC%D5%A5%D5%A6%D5%B8%D5%B6%D5%A1%D5%B6%D5%BD" title="Ուղեծրային ռեզոնանս – 亚美尼亚语" lang="hy" hreflang="hy" data-title="Ուղեծրային ռեզոնանս" data-language-autonym="Հայերեն" data-language-local-name="亚美尼亚语" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Resonansi_orbit" title="Resonansi orbit – 印度尼西亚语" lang="id" hreflang="id" data-title="Resonansi orbit" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" 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/Risonanza_orbitale" title="Risonanza orbitale – 意大利语" lang="it" hreflang="it" data-title="Risonanza orbitale" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%BB%8C%E9%81%93%E5%85%B1%E9%B3%B4" title="軌道共鳴 – 日语" lang="ja" hreflang="ja" data-title="軌道共鳴" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B6%A4%EB%8F%84_%EA%B3%B5%EB%AA%85" title="궤도 공명 – 韩语" lang="ko" hreflang="ko" data-title="궤도 공명" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Bunnresonanz" title="Bunnresonanz – 卢森堡语" lang="lb" hreflang="lb" data-title="Bunnresonanz" data-language-autonym="Lëtzebuergesch" data-language-local-name="卢森堡语" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Orbitinis_rezonansas" title="Orbitinis rezonansas – 立陶宛语" lang="lt" hreflang="lt" data-title="Orbitinis rezonansas" data-language-autonym="Lietuvių" data-language-local-name="立陶宛语" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Orbit%C4%81l%C4%81_rezonanse" title="Orbitālā rezonanse – 拉脱维亚语" lang="lv" hreflang="lv" data-title="Orbitālā rezonanse" data-language-autonym="Latviešu" data-language-local-name="拉脱维亚语" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9E%D1%80%D0%B1%D0%B8%D1%82%D0%B0%D0%BB%D0%BD%D0%B0_%D1%80%D0%B5%D0%B7%D0%BE%D0%BD%D0%B0%D0%BD%D1%86%D0%B0" title="Орбитална резонанца – 马其顿语" lang="mk" hreflang="mk" data-title="Орбитална резонанца" data-language-autonym="Македонски" data-language-local-name="马其顿语" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Bahnresonanz" title="Bahnresonanz – 低地德语" lang="nds" hreflang="nds" data-title="Bahnresonanz" data-language-autonym="Plattdüütsch" data-language-local-name="低地德语" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Baanresonantie" title="Baanresonantie – 荷兰语" lang="nl" hreflang="nl" data-title="Baanresonantie" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Baneresonans" title="Baneresonans – 书面挪威语" lang="nb" hreflang="nb" data-title="Baneresonans" data-language-autonym="Norsk bokmål" data-language-local-name="书面挪威语" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Resson%C3%A0ncia_orbitala" title="Ressonància orbitala – 奥克语" lang="oc" hreflang="oc" data-title="Ressonància orbitala" data-language-autonym="Occitan" data-language-local-name="奥克语" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Rezonans_orbitalny" title="Rezonans orbitalny – 波兰语" lang="pl" hreflang="pl" data-title="Rezonans orbitalny" data-language-autonym="Polski" data-language-local-name="波兰语" 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/Resson%C3%A2ncia_orbital" title="Ressonância orbital – 葡萄牙语" lang="pt" hreflang="pt" data-title="Ressonância orbital" data-language-autonym="Português" data-language-local-name="葡萄牙语" 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/Rezonan%C8%9B%C4%83_orbital%C4%83" title="Rezonanță orbitală – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Rezonanță orbitală" data-language-autonym="Română" data-language-local-name="罗马尼亚语" 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%9E%D1%80%D0%B1%D0%B8%D1%82%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D0%B9_%D1%80%D0%B5%D0%B7%D0%BE%D0%BD%D0%B0%D0%BD%D1%81" title="Орбитальный резонанс – 俄语" lang="ru" hreflang="ru" data-title="Орбитальный резонанс" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Orbital_resonance" title="Orbital resonance – Simple English" lang="en-simple" hreflang="en-simple" data-title="Orbital resonance" 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/Dr%C3%A1hov%C3%A1_rezonancia" title="Dráhová rezonancia – 斯洛伐克语" lang="sk" hreflang="sk" data-title="Dráhová rezonancia" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克语" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Orbitalna_resonanca" title="Orbitalna resonanca – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Orbitalna resonanca" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9E%D1%80%D0%B1%D0%B8%D1%82%D0%B0%D0%BB%D0%BD%D0%B5_%D1%80%D0%B5%D0%B7%D0%BE%D0%BD%D0%B0%D0%BD%D1%86%D0%B5" title="Орбиталне резонанце – 塞尔维亚语" lang="sr" hreflang="sr" data-title="Орбиталне резонанце" data-language-autonym="Српски / srpski" data-language-local-name="塞尔维亚语" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Banresonans" title="Banresonans – 瑞典语" lang="sv" hreflang="sv" data-title="Banresonans" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%AA%E0%B8%B1%E0%B9%88%E0%B8%99%E0%B8%9E%E0%B9%89%E0%B8%AD%E0%B8%87%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%A7%E0%B8%87%E0%B9%82%E0%B8%84%E0%B8%88%E0%B8%A3" title="การสั่นพ้องของวงโคจร – 泰语" lang="th" hreflang="th" data-title="การสั่นพ้องของวงโคจร" data-language-autonym="ไทย" data-language-local-name="泰语" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Y%C3%B6r%C3%BCngesel_rezonans" title="Yörüngesel rezonans – 土耳其语" lang="tr" hreflang="tr" data-title="Yörüngesel rezonans" data-language-autonym="Türkçe" data-language-local-name="土耳其语" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9E%D1%80%D0%B1%D0%B8%D1%82%D0%B0%D0%BB%D1%8C_%D1%80%D0%B5%D0%B7%D0%BE%D0%BD%D0%B0%D0%BD%D1%81" title="Орбиталь резонанс – 鞑靼语" lang="tt" hreflang="tt" data-title="Орбиталь резонанс" data-language-autonym="Татарча / tatarça" data-language-local-name="鞑靼语" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9E%D1%80%D0%B1%D1%96%D1%82%D0%B0%D0%BB%D1%8C%D0%BD%D0%B8%D0%B9_%D1%80%D0%B5%D0%B7%D0%BE%D0%BD%D0%B0%D0%BD%D1%81" title="Орбітальний резонанс – 乌克兰语" lang="uk" hreflang="uk" data-title="Орбітальний резонанс" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/C%E1%BB%99ng_h%C6%B0%E1%BB%9Fng_qu%E1%BB%B9_%C4%91%E1%BA%A1o" title="Cộng hưởng quỹ đạo – 越南语" lang="vi" hreflang="vi" data-title="Cộng hưởng quỹ đạo" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" 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/%E8%BB%8C%E9%81%93%E5%85%B1%E6%8C%AF" title="軌道共振 – 粤语" lang="yue" hreflang="yue" data-title="軌道共振" data-language-autonym="粵語" data-language-local-name="粤语" class="interlanguage-link-target"><span>粵語</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/Q271561#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div 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id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> <div id="mw-indicator-noteTA-ffd8db3e" class="mw-indicator"><div class="mw-parser-output"><span class="skin-invert" typeof="mw:File"><span title="本页使用了标题或全文手工转换"><img alt="本页使用了标题或全文手工转换" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/35px-Zh_conversion_icon_m.svg.png" decoding="async" width="35" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/53px-Zh_conversion_icon_m.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/70px-Zh_conversion_icon_m.svg.png 2x" data-file-width="32" data-file-height="20" /></span></span></div></div> </div> <div id="siteSub" class="noprint">维基百科，自由的百科全书</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">（重定向自<a href="/w/index.php?title=%E8%BB%8C%E9%81%93%E5%85%B1%E6%8C%AF&redirect=no" class="mw-redirect" title="軌道共振">軌道共振</a>）</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="zh" dir="ltr"><div id="noteTA-ffd8db3e" class="noteTA"><div class="noteTA-group"><div data-noteta-group-source="module" data-noteta-group="Astronomy"></div><div data-noteta-group-source="module" data-noteta-group="Physics"></div></div></div> <p><b>軌道共振</b>是<a href="/wiki/%E5%A4%A9%E9%AB%94%E5%8A%9B%E5%AD%B8" title="天體力學">天體力學</a>中的一種效應與現象，指當<a href="/wiki/%E8%BB%8C%E9%81%93" class="mw-disambig" title="軌道">軌道</a>上的天體於<a href="/wiki/%E8%BD%A8%E9%81%93%E5%91%A8%E6%9C%9F" title="轨道周期">週期</a>上有簡單（小數值）的<a href="/wiki/%E6%95%B4%E6%95%B8" class="mw-redirect" title="整數">整數</a>比時，定期施加的<a href="/wiki/%E5%BC%95%E5%8A%9B" title="引力">引力</a>影響到對方所產生的。軌道共振的物理原理在概念上類似於推動兒童盪的鞦韆，軌道和擺動的鞦韆之間有著一個<a href="/wiki/%E5%85%B1%E6%8C%AF" title="共振">自然頻率</a>，其它機制和“推”所做的動作週期性地重複施加，產生累積性的影響。軌道共振大大增加了相互之間引力影響的機構，即它們能夠改變或限制對方的軌道。在多數情況下，這會導致“不穩定”的互動，在其中的兩者互相交換<a href="/wiki/%E5%8B%95%E8%83%BD" class="mw-redirect" title="動能">動能</a>和轉移軌道，直到共振不再存在。在某些情況下，一個諧振系統可以穩定和自我糾正，所以這些天體仍維持著共振。例如，<a href="/wiki/%E6%9C%A8%E6%98%9F" title="木星">木星</a>衛星<a href="/wiki/%E6%9C%A8%E8%A1%9B%E4%B8%89" class="mw-redirect" title="木衛三">佳利美德</a>、<a href="/wiki/%E6%9C%A8%E8%A1%9B%E4%BA%8C" class="mw-redirect" title="木衛二">歐羅巴</a>、和<a href="/wiki/%E6%9C%A8%E8%A1%9B%E4%B8%80" class="mw-redirect" title="木衛一">埃歐</a>軌道的1:2:4共振，以及<a href="/wiki/%E5%86%A5%E7%8E%8B%E6%98%9F" title="冥王星">冥王星</a>和<a href="/wiki/%E6%B5%B7%E7%8E%8B%E6%98%9F" title="海王星">海王星</a>之間的2:3共振。<a href="/wiki/%E5%9C%9F%E6%98%9F" title="土星">土星</a>內側衛星的不穩定共振造成<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0" title="土星環">土星環</a>中間的空隙。1:1的共振（有著相似軌道半徑的天體）在特殊的情況下，造成<a href="/wiki/%E5%A4%AA%E9%99%BD%E7%B3%BB" class="mw-redirect" title="太陽系">太陽系</a>大天體將共享軌道的小天體彈射出去；這是<a href="/wiki/%E6%B8%85%E9%99%A4%E9%84%B0%E8%BF%91%E7%9A%84%E5%B0%8F%E5%A4%A9%E9%AB%94" title="清除鄰近的小天體">清除鄰居</a>最廣泛應用的機制，而此一效果也應用在目前的<a href="/wiki/%E8%A1%8C%E6%98%9F%E5%AE%9A%E7%BE%A9" title="行星定義">行星定義</a>中。 </p><p>除了拉普拉斯共振圖（見下文）中指出，在這篇文章中的共振比率應被解釋為在相同的時間間隔內完成<b>軌道數的比例</b>，而不是作為<b>公轉週期比</b>（其中將會呈反比關係）。上面2:3的比例意味著冥王星完成兩次完整公轉的同時，海王星要完成三次完整的公轉。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="歷史"><span id=".E6.AD.B7.E5.8F.B2"></span>歷史</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&action=edit&section=1" title="编辑章节：歷史"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>自17世紀發現<a href="/wiki/%E7%89%9B%E9%A0%93%E8%90%AC%E6%9C%89%E5%BC%95%E5%8A%9B%E5%AE%9A%E5%BE%8B" class="mw-redirect" title="牛頓萬有引力定律">牛頓萬有引力定律</a>以來，從<a href="/wiki/%E7%9A%AE%E8%80%B6%E7%88%BE-%E8%A5%BF%E8%92%99%C2%B7%E6%8B%89%E6%99%AE%E6%8B%89%E6%96%AF" class="mw-redirect" title="皮耶爾-西蒙·拉普拉斯">拉普拉斯</a>開始，就有許多數學家全神貫注<a href="/wiki/%E5%A4%AA%E9%98%B3%E7%B3%BB%E7%A8%B3%E5%AE%9A%E6%80%A7%E9%97%AE%E9%A2%98" title="太阳系稳定性问题">太陽系的穩定性</a>。<a href="/wiki/%E5%A4%9A%E4%BD%93%E9%97%AE%E9%A2%98" title="多体问题">二體問題近似解</a>的穩定軌道忽略其它天體的影響。在<a href="/wiki/%E5%A4%AA%E9%99%BD%E7%B3%BB" class="mw-redirect" title="太陽系">太陽系</a>中添加其它天體的交互作用對穩定性造成的影響很小，但是首先不知道在很長的週期中添加會造成何種軌道參數的改變和不同的配置，或是其它一些穩定的影響是否能維持行星軌道的配置。 </p><p>拉普拉斯是最先找到解釋<a href="/wiki/%E4%BC%BD%E5%88%A9%E7%95%A5%E8%A1%9B%E6%98%9F" title="伽利略衛星">伽利略衛星</a>奇異舞蹈（見下文）答案的人。持平而論，自當時迄今以來，在這個領域的研究是非常活躍的，但是仍有許多待解決的問題（例如，在巨大行星的環，環中的小衛星和微粒的交互作用如何維繫環）。 </p> <div class="mw-heading mw-heading2"><h2 id="共振的類型"><span id=".E5.85.B1.E6.8C.AF.E7.9A.84.E9.A1.9E.E5.9E.8B"></span>共振的類型</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&action=edit&section=2" title="编辑章节：共振的類型"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:TheKuiperBelt_75AU_All.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/TheKuiperBelt_75AU_All.svg/300px-TheKuiperBelt_75AU_All.svg.png" decoding="async" width="300" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/86/TheKuiperBelt_75AU_All.svg/450px-TheKuiperBelt_75AU_All.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/86/TheKuiperBelt_75AU_All.svg/600px-TheKuiperBelt_75AU_All.svg.png 2x" data-file-width="800" data-file-height="400" /></a><figcaption>對照於那些<a href="/wiki/%E5%82%B3%E7%B5%B1%E5%8F%A4%E6%9F%8F%E5%B8%B6%E5%A4%A9%E9%AB%94" title="傳統古柏帶天體">QB1</a>（藍色）和非共振（或不知道是否共振）的<a href="/wiki/%E9%9B%A2%E6%95%A3%E7%9B%A4" title="離散盤">離散盤</a>天體（灰色），<a href="/wiki/%E5%85%B1%E6%8C%AF%E6%B5%B7%E7%8E%8B%E6%98%9F%E5%A4%96%E5%A4%A9%E9%AB%94" title="共振海王星外天體">共振海王星外天體</a>（紅色）的<a href="/wiki/%E5%8D%8A%E9%95%B7%E8%BB%B8" title="半長軸">半長軸</a>聚集在與<a href="/wiki/%E6%B5%B7%E7%8E%8B%E6%98%9F" title="海王星">海王星</a>的低整數共振（接近頂端的垂直紅色條）。</figcaption></figure> <p>通常，軌道共振可能 </p> <ul><li>涉及一個或任何組合的軌道參數（例如，<a href="/wiki/%E9%9B%A2%E5%BF%83%E7%8E%87" title="離心率">離心率</a>相對於<a href="/wiki/%E5%8D%8A%E9%95%B7%E8%BB%B8" title="半長軸">半長軸</a>，或軌道傾角）。</li> <li>從短期的任何時間尺度來看，在10<sup>4</sup>至10<sup>6</sup>年的<a href="/wiki/%E9%95%B7%E6%9C%9F%E8%AE%8A%E5%8C%96" title="長期變化">長期</a>測量都有其<a href="/wiki/%E9%80%9A%E7%BA%A6%E6%80%A7_(%E5%A4%A9%E6%96%87%E5%AD%A6)" title="通约性 (天文学)">通約性</a>。</li> <li>導致即使長期穩定運行的軌道，也有可能造成不穩定性。</li></ul> <p><b><a href="/w/index.php?title=%E5%B9%B3%E5%9D%87%E9%81%8B%E5%8B%95%E8%BB%8C%E9%81%93%E5%85%B1%E6%8C%AF&action=edit&redlink=1" class="new" title="平均運動軌道共振（页面不存在）">平均運動軌道共振</a></b>發生在兩個天體的<a href="/wiki/%E8%BB%8C%E9%81%93" class="mw-disambig" title="軌道">公轉</a>週期，其中一個的週期是對方的簡單整數比。依據詳細的資料，這可以使軌道穩定，也可以使軌道被摧毀。當這兩個天體在這種同步的運動中沒有密切接觸時，可能會出現<i>穩定</i>。例如： </p> <ul><li>無論與<a href="/wiki/%E6%B5%B7%E7%8E%8B%E6%98%9F" title="海王星">海王星</a>多麼接近，<a href="/wiki/%E5%86%A5%E7%8E%8B%E6%98%9F" title="冥王星">冥王星</a>和<a href="/wiki/%E5%86%A5%E6%97%8F%E5%B0%8F%E5%A4%A9%E9%AB%94" title="冥族小天體">冥族小天體</a>的軌道都是穩定的，因為它們與海王星是3:2的共振。共振可以確保當它們接近近日點和海王星的軌道時，海王星是在相當遠的距離之外（平均有它的軌道距離的四分之一）。其它沒有共振的近海王星天體（數量更多）會被海王星強大的<a href="/wiki/%E6%94%9D%E5%8B%95" title="攝動">攝動</a>從這個區域逐出。還有規模較小，但是很明確有著1:1共振的<a href="/wiki/%E5%85%B1%E6%8C%AF%E6%B5%B7%E7%8E%8B%E6%98%9F%E5%A4%96%E5%A4%A9%E9%AB%94" title="共振海王星外天體">共振海王星外天體</a>（<a href="/wiki/%E6%B5%B7%E7%8E%8B%E6%98%9F%E7%89%B9%E6%B4%9B%E4%BC%8A" title="海王星特洛伊">海王星特洛伊</a>）、<a href="/wiki/%E5%85%B1%E6%8C%AF%E6%B5%B7%E7%8E%8B%E6%98%9F%E5%A4%96%E5%A4%A9%E9%AB%94#已知的群體" title="共振海王星外天體">3:5</a>（週期約275年）、<a href="/wiki/%E5%85%B1%E6%8C%AF%E6%B5%B7%E7%8E%8B%E6%98%9F%E5%A4%96%E5%A4%A9%E9%AB%94#已知的群體" title="共振海王星外天體">4:7</a>（週期約290年）、<a href="/wiki/%E5%85%B1%E6%8C%AF%E6%B5%B7%E7%8E%8B%E6%98%9F%E5%A4%96%E5%A4%A9%E9%AB%94#已知的群體" title="共振海王星外天體">1:2</a>（週期約330年）、和<a href="/wiki/%E5%85%B1%E6%8C%AF%E6%B5%B7%E7%8E%8B%E6%98%9F%E5%A4%96%E5%A4%A9%E9%AB%94#已知的群體" title="共振海王星外天體">2:5</a>（週期約410年），除此之外，在海王星之外還有其它的。</li> <li>在距離太陽3.5AU以內的<a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F%E5%B8%B6" class="mw-redirect" title="小行星帶">小行星帶</a>，有與<a href="/wiki/%E6%9C%A8%E6%98%9F" title="木星">木星</a>有著3:2、4:3、和1:1的族群分布著（特別是<a href="/wiki/%E5%B8%8C%E5%B0%94%E8%BE%BE%E6%97%8F" title="希尔达族">希爾達族</a>、<a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F279" title="小行星279">（279）圖勒</a>、和<a href="/wiki/%E7%89%B9%E6%B4%9B%E4%BC%8A%E5%A4%A9%E4%BD%93" title="特洛伊天体">特洛伊天體</a>）。</li></ul> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Kirkwood_Gaps.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Kirkwood_Gaps.svg/300px-Kirkwood_Gaps.svg.png" decoding="async" width="300" height="232" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Kirkwood_Gaps.svg/450px-Kirkwood_Gaps.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Kirkwood_Gaps.svg/600px-Kirkwood_Gaps.svg.png 2x" data-file-width="792" data-file-height="612" /></a><figcaption><a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F" title="小行星">小行星</a>軌道<a href="/wiki/%E5%8D%8A%E9%95%B7%E8%BB%B8" title="半長軸">半長軸</a>的分布圖，顯示出因為與<a href="/wiki/%E6%9C%A8%E6%98%9F" title="木星">木星</a>共振造成不穩定的<a href="/wiki/%E6%9F%AF%E5%85%8B%E4%BC%8D%E5%BE%B7%E7%A9%BA%E9%9A%99" title="柯克伍德空隙">柯克伍德空隙</a>。</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:PIA10452_-_Saturn_A_ring_spiral_density_waves.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/PIA10452_-_Saturn_A_ring_spiral_density_waves.jpg/300px-PIA10452_-_Saturn_A_ring_spiral_density_waves.jpg" decoding="async" width="300" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/PIA10452_-_Saturn_A_ring_spiral_density_waves.jpg/450px-PIA10452_-_Saturn_A_ring_spiral_density_waves.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/PIA10452_-_Saturn_A_ring_spiral_density_waves.jpg/600px-PIA10452_-_Saturn_A_ring_spiral_density_waves.jpg 2x" data-file-width="1014" data-file-height="1014" /></a><figcaption>在<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0#A環" title="土星環">土星環</a>的<a href="/wiki/%E5%AF%86%E5%BA%A6%E6%B3%A2%E7%90%86%E8%AE%BA" title="密度波理论">螺旋密度波</a>是<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%9A%84%E8%A1%9B%E6%98%9F#牧羊人衛星" class="mw-redirect" title="土星的衛星">環內的衛星</a>所激起的共振。這些波從土星（左上方）向外傳播，位於中心正下方最大的波與<a href="/wiki/%E5%9C%9F%E8%A1%9B%E5%8D%81" class="mw-redirect" title="土衛十">土衛十</a>有著6:5的共振。</figcaption></figure> <p>軌道共振也可以摧毀一個穩定的軌道。對小天體而言，不穩定實際上是更有可能的。例如： </p> <ul><li>在距離太陽3.5AU以內的<a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F%E5%B8%B6" class="mw-redirect" title="小行星帶">小行星帶</a>，與<a href="/wiki/%E6%9C%A8%E6%98%9F" title="木星">木星</a>的主要平均運動軌道共振落在小行星位置分布的<i>空隙</i>，<a href="/wiki/%E6%9F%AF%E5%85%8B%E4%BC%8D%E5%BE%B7%E7%A9%BA%E9%9A%99" title="柯克伍德空隙">柯克伍德空隙</a>（最顯著的是在3:1、5:2、7:3、和2:1的共振）。在這些位置上的<a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F" title="小行星">小行星</a>因為反覆的受到<a href="/wiki/%E6%9C%A8%E6%98%9F" title="木星">木星</a>的攝動，幾乎已經完全被拋空了。然而，還是有少數的小行星目前暫時在或接近這些共振的位置。例如，<a href="/wiki/%E8%89%BE%E7%90%B3%E9%81%94%E6%97%8F" title="艾琳達族">艾琳達族</a>就為位於或接近3:1共振，而它們的軌道離心率在與木星的交互作用下持續的在增加，直到最終它們會與內側的行星密切接觸，然後將它們從共振軌道彈射出去。</li> <li>在<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0" title="土星環">土星環</a>內，<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0#卡西尼縫" title="土星環">卡西尼縫</a>是<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0#B環" title="土星環"> B環</a>和外側的<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0#A環" title="土星環"> A環</a>之間的空隙，與<a href="/wiki/%E5%9C%9F%E5%8D%AB%E4%B8%80" title="土卫一">米瑪斯</a>有著2:1的共振（更特別的是<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0#卡西尼縫" title="土星環">卡西尼縫</a>內側邊緣<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0#惠更斯縫" title="土星環">惠更斯縫</a>的位置。）。</li> <li>在土星環，<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0#恩克環縫" title="土星環">恩克環縫</a>和<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0#凱勒環縫" title="土星環">基勒環縫</a>是與置身在A環內的<a href="/wiki/%E5%9C%9F%E5%8D%AB%E5%8D%81%E5%85%AB" title="土卫十八">潘</a>和<a href="/wiki/%E5%9C%9F%E5%8D%AB%E4%B8%89%E5%8D%81%E4%BA%94" title="土卫三十五">達佛涅斯</a>1:1共振清空微粒形成的。A環的外側是由<a href="/wiki/%E5%9C%9F%E8%A1%9B%E5%8D%81" class="mw-redirect" title="土衛十">土衛十</a>有著7:6的不穩定共振維繫著。</li></ul> <p>大多數天體中的共振軌道都有著相同的方向，然而有少數是<a href="/wiki/%E9%A0%86%E8%A1%8C%E5%92%8C%E9%80%86%E8%A1%8C" title="順行和逆行">逆行</a>的，<a href="/wiki/%E9%81%94%E6%91%A9%E5%85%8B%E5%9E%8B%E5%B0%8F%E8%A1%8C%E6%98%9F" class="mw-redirect" title="達摩克型小行星">達摩克型小行星</a>是被土星或木星捕獲，並被發現暫時處在<b>平均運動軌道共振</b>上的小行星<sup id="cite_ref-Morais_2013_1-0" class="reference"><a href="#cite_note-Morais_2013-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>。這種軌道的交互作用比軌道在同一方向的機制的交互作用為弱<sup id="cite_ref-Morais_2013_1-1" class="reference"><a href="#cite_note-Morais_2013-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>。 </p><p><b><a href="/wiki/%E6%8B%89%E6%99%AE%E6%8B%89%E6%96%AF%E5%85%B1%E6%8C%AF" class="mw-redirect" title="拉普拉斯共振">拉普拉斯共振</a></b>發生在三個或更多天體的軌道週期之間有著簡單整數比的系統上。例如，木星的<a href="/wiki/%E6%9C%A8%E8%A1%9B%E4%B8%89" class="mw-redirect" title="木衛三">佳利美德</a>、<a href="/wiki/%E6%9C%A8%E8%A1%9B%E4%BA%8C" class="mw-redirect" title="木衛二">歐羅巴</a>、和<a href="/wiki/%E6%9C%A8%E8%A1%9B%E4%B8%80" class="mw-redirect" title="木衛一">埃歐</a>軌道的1:2:4軌道共振。<a href="/wiki/%E7%B3%BB%E5%A4%96%E8%A1%8C%E6%98%9F" class="mw-redirect" title="系外行星">系外行星</a><a href="/wiki/%E6%A0%BC%E5%88%A9%E6%BE%A4876" title="格利澤876">格利澤876</a> e、b、和c，也有1:2:4的軌道共振<sup id="cite_ref-rivera2010_2-0" class="reference"><a href="#cite_note-rivera2010-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>。 </p><p><b><a href="/wiki/%E6%9E%97%E9%81%94%E5%8D%9A%E5%85%B1%E6%8C%AF" title="林達博共振">林達博共振</a></b>導出<a href="/wiki/%E5%AF%86%E5%BA%A6%E6%B3%A2%E7%90%86%E8%AE%BA" title="密度波理论">螺旋密度波</a>不僅適用在<a href="/wiki/%E6%98%9F%E7%B3%BB" title="星系">星系</a>（恆星是受螺旋臂本身的<a href="/wiki/%E8%B0%90%E6%8C%AF" class="mw-redirect" title="谐振">力</a>支配的），也適用於<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0" title="土星環">土星環</a>（環中的微粒是受到<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%9A%84%E8%A1%9B%E6%98%9F" class="mw-redirect" title="土星的衛星">土星衛星</a>的力支配）。 </p><p><b><a href="/wiki/%E9%95%B7%E6%9C%9F%E5%85%B1%E6%8C%AF" title="長期共振">長期共振</a></b>發生於兩個軌道的<a href="/wiki/%E6%AD%B2%E5%B7%AE_(%E5%A4%A9%E6%96%87)" class="mw-redirect" title="歲差 (天文)">進動</a>同步時（通常是<a href="/wiki/%E6%8B%B1%E9%BB%9E" title="拱點">近日點</a>或<a href="/wiki/%E5%8D%87%E4%BA%A4%E9%BB%9E" class="mw-redirect" title="升交點">升交點</a>）。一顆小天體在與大許多的天體（例如<a href="/wiki/%E8%A1%8C%E6%98%9F" title="行星">行星</a>）長期共振下，將有與大天體相同的速率。長時間（100萬年或更長）的長期共振會改變小天體的<a href="/wiki/%E8%BB%8C%E9%81%93%E9%9B%A2%E5%BF%83%E7%8E%87" title="軌道離心率">軌道離心率</a>和<a href="/wiki/%E8%BB%8C%E9%81%93%E5%82%BE%E8%A7%92" title="軌道傾角">軌道傾角</a>。 </p><p>幾個明顯的長期共振例子，包括土星都是。土星自轉軸的進動和海王星自轉軸的進動之間有著共振（兩者的周期都長達187萬年），已經確定與土星巨大的<a href="/wiki/%E8%BD%89%E8%BB%B8%E5%82%BE%E8%A7%92" title="轉軸傾角">轉軸傾角</a>（26.7°）可能有著相同的來源<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><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><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>。最初，土星的傾角大概是比角接近木星（3.1°）。古柏帶逐漸的枯竭使海王星的進動減少；最終，兩著的頻率匹配，而土星的軸向進動進入到自旋－軌道共振，導致土星的傾角增加（海王星軌道的角動量是土星自轉的10<sup>4</sup>倍，因此主導著互動的關係。）。 </p><p><a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F" title="小行星">小行星</a>和<a href="/wiki/%E5%9C%9F%E6%98%9F" title="土星">土星</a>之間的<a href="/wiki/%E9%95%B7%E6%9C%9F%E5%85%B1%E6%8C%AF#ν6共振" title="長期共振">拱點長期共振</a>（<i>ν<sub>6</sub></i> = <i>g -g<sub>6</sub></i>）協助塑造出了小行星帶。接近它的小行星，離心率會緩慢的增加，直到它們成為<a href="/wiki/%E7%81%AB%E6%98%9F%E8%BB%8C%E9%81%93%E7%A9%BF%E8%B6%8A%E5%B0%8F%E8%A1%8C%E6%98%9F" title="火星軌道穿越小行星">接近火星</a>的小行星。此時，它們會因為與<a href="/wiki/%E7%81%AB%E6%98%9F" title="火星">火星</a>遭遇而從<a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F%E5%B8%B6" class="mw-redirect" title="小行星帶">小行星帶</a>彈出。這種共振形成小行星帶內部和側面邊界的距離大約是2<a href="/wiki/%E5%A4%A9%E6%96%87%E5%96%AE%E4%BD%8D" title="天文單位">AU</a>和約20°的<a href="/wiki/%E8%BB%8C%E9%81%93%E5%82%BE%E8%A7%92" title="軌道傾角">軌道傾角</a>。 </p><p>數值模擬認為<a href="/wiki/%E6%B0%B4%E6%98%9F" title="水星">水星</a>和<a href="/wiki/%E6%9C%A8%E6%98%9F" title="木星">木星</a>（<i>g<sub>1</sub>=g<sub>5</sub></i>）之間的拱點長期共振，最終有可能增加水星的離心率，並且可能在今後的數億年破壞內太陽系<sup id="cite_ref-Laskar2008_6-0" class="reference"><a href="#cite_note-Laskar2008-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Laskar2009_7-0" class="reference"><a href="#cite_note-Laskar2009-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>。 </p><p>在<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0" title="土星環">土星環</a><a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0#C環" title="土星環">C環</a>內的<a href="/wiki/%E5%9C%9F%E6%98%9F%E7%92%B0#可倫坡縫和泰坦小環" title="土星環">泰坦小環</a>代表著另一種形式的共振，在其中的一個軌道的<a href="/wiki/%E9%80%B2%E5%8B%95#行星軌道進動" title="進動">拱點進動</a>率完全符合另一個的公轉速度。這個偏心小環外側的末端永遠朝向土星最大的衛星<a href="/wiki/%E5%9C%9F%E8%A1%9B%E5%85%AD" class="mw-redirect" title="土衛六">泰坦</a>。 </p><p><b><a href="/wiki/%E5%8F%A4%E5%9C%A8%E6%A9%9F%E5%88%B6" title="古在機制">古在共振</a></b>發生在對軌道傾角和離心率<a href="/wiki/%E6%91%84%E5%8A%A8%E7%90%86%E8%AE%BA" title="摄动理论">攝動</a>的同步振盪（增加離心率而同時漸少傾角，反之亦然）。這種共振僅適用於高軌道傾角的天體；因此，這種軌道往往是不穩定的，因為越來越大的離心率會導致<a href="/wiki/%E6%8B%B1%E9%BB%9E" title="拱點">近心點</a>變小，因而造成碰撞或被<a href="/wiki/%E6%BD%AE%E6%B1%90%E5%8A%9B" title="潮汐力">潮汐力</a>破壞（對於大衛星）。 </p><p>涉及軌道離心率另一種類型的例子是木衛三和木衛四的離心率，即使有著相對的相位，依然有181年的共通變化週期<sup id="cite_ref-Musotto2002_8-0" class="reference"><a href="#cite_note-Musotto2002-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="在太陽系的平均運動共振"><span id=".E5.9C.A8.E5.A4.AA.E9.99.BD.E7.B3.BB.E7.9A.84.E5.B9.B3.E5.9D.87.E9.81.8B.E5.8B.95.E5.85.B1.E6.8C.AF"></span>在太陽系的平均運動共振</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&action=edit&section=3" title="编辑章节：在太陽系的平均運動共振"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Haumea.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Haumea.GIF/300px-Haumea.GIF" decoding="async" width="300" height="261" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Haumea.GIF/450px-Haumea.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/3/3e/Haumea.GIF 2x" data-file-width="590" data-file-height="514" /></a><figcaption>描繪在<a href="/w/index.php?title=%E6%97%8B%E8%BD%89%E6%A1%86%E6%9E%B6&action=edit&redlink=1" class="new" title="旋轉框架（页面不存在）">旋轉框架</a>中，被推測與<a href="/wiki/%E6%B5%B7%E7%8E%8B%E6%98%9F" title="海王星">海王星</a>有著7:12共振的<a href="/wiki/%E5%A6%8A%E7%A5%9E%E6%98%9F" title="妊神星">妊神星</a>，圖中的海王星（右下方的藍色小點）被固定不動。妊神星變化著的軌道，對正於海王星會定期的反轉（<a href="/wiki/%E5%A4%A9%E7%A7%A4%E5%8B%95" class="mw-redirect" title="天秤動">天秤動</a>），保持著共振。</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Galilean_moon_Laplace_resonance_animation.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/8/83/Galilean_moon_Laplace_resonance_animation.gif" decoding="async" width="365" height="245" class="mw-file-element" data-file-width="365" data-file-height="245" /></a><figcaption>由三顆<a href="/wiki/%E4%BC%BD%E5%88%A9%E7%95%A5%E8%A1%9B%E6%98%9F" title="伽利略衛星">伽利略衛星</a>展示的拉普拉斯共振。圖中的比率是公轉的週期比。</figcaption></figure> <p>在<a href="/wiki/%E5%A4%AA%E9%99%BD%E7%B3%BB" class="mw-redirect" title="太陽系">太陽系</a>內只有少數的平均運動共振，包括行星、<a href="/wiki/%E7%9F%AE%E8%A1%8C%E6%98%9F" title="矮行星">矮行星</a>或大的<a href="/wiki/%E5%A4%A9%E7%84%B6%E8%A1%9B%E6%98%9F" class="mw-redirect" title="天然衛星">天然衛星</a>是已經知道的（在<a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F" title="小行星">小行星</a>、<a href="/wiki/%E8%A1%8C%E6%98%9F%E7%92%B0" class="mw-redirect" title="行星環">行星環</a>、<a href="/wiki/%E5%85%A7%E8%A1%9B%E6%98%9F" title="內衛星">小衛星</a>和更小的<a href="/wiki/%E5%8F%A4%E6%9F%8F%E5%B8%B6" class="mw-redirect" title="古柏帶">古柏帶</a>天體，和許多<a href="/wiki/%E7%9F%AE%E8%A1%8C%E6%98%9F%E5%80%99%E9%81%B8%E8%80%85%E5%88%97%E8%A1%A8" title="矮行星候選者列表">可能的矮行星</a>還會有更多）： </p> <ul><li>2:4 <a href="/wiki/%E5%9C%9F%E5%8D%AB%E4%B8%89" title="土卫三">土衛三特提斯</a>–<a href="/wiki/%E5%9C%9F%E5%8D%AB%E4%B8%80" title="土卫一">土衛一彌瑪斯</a></li> <li>2:3 <a href="/wiki/%E5%86%A5%E7%8E%8B%E6%98%9F" title="冥王星">冥王星</a>–<a href="/wiki/%E6%B5%B7%E7%8E%8B%E6%98%9F" title="海王星">海王星</a></li> <li>1:2 <a href="/wiki/%E5%9C%9F%E5%8D%AB%E5%9B%9B" title="土卫四">土衛四狄俄涅</a>–<a href="/wiki/%E5%9C%9F%E5%8D%AB%E4%BA%8C" title="土卫二">土衛二恩克拉多斯</a></li> <li>3:4 <a href="/wiki/%E5%9C%9F%E5%8D%AB%E4%B8%83" title="土卫七">土衛七許珀里翁</a>–<a href="/wiki/%E5%9C%9F%E5%8D%AB%E5%85%AD" title="土卫六">土衛六泰坦</a></li> <li>1:2:4 <a href="/wiki/%E6%9C%A8%E8%A1%9B%E4%B8%89" class="mw-redirect" title="木衛三">木衛三蓋尼米德</a>–<a href="/wiki/%E6%9C%A8%E8%A1%9B%E4%BA%8C" class="mw-redirect" title="木衛二">木衛二歐羅巴</a>–<a href="/wiki/%E6%9C%A8%E8%A1%9B%E4%B8%80" class="mw-redirect" title="木衛一">木衛一伊俄</a></li></ul> <p>此外，<a href="/wiki/%E5%A6%8A%E7%A5%9E%E6%98%9F" title="妊神星">妊神星</a>被認為是與海王星有著7:12的共振<sup id="cite_ref-Brown_2007_9-0" class="reference"><a href="#cite_note-Brown_2007-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Ragozzine_10-0" class="reference"><a href="#cite_note-Ragozzine-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>，<a href="/wiki/%E9%AC%A9%E7%A5%9E%E6%98%9F" class="mw-redirect" title="鬩神星">鬩神星</a>和<a href="/wiki/%E9%B8%9F%E7%A5%9E%E6%98%9F" title="鸟神星">鳥神星</a>與海王星分別有5:17和6:11的共振<sup id="cite_ref-10th_Planet_11-0" class="reference"><a href="#cite_note-10th_Planet-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>。 </p><p>週期之間<i>簡單的整數比</i>之後，很方便和簡化的隱藏了許多更複雜的關係： </p> <ul><li><a href="/wiki/%E5%90%88_(%E5%A4%A9%E9%AB%94%E4%BD%8D%E7%BD%AE)" title="合 (天體位置)">合</a>的點可以定義在附近振盪的共振均衡點（<a href="/wiki/%E5%A4%A9%E7%A7%A4%E5%8B%95" class="mw-redirect" title="天秤動">天秤動</a>）。</li> <li>在非零<a href="/wiki/%E9%9B%A2%E5%BF%83%E7%8E%87" title="離心率">離心率</a>的場合，<a href="/wiki/%E8%BB%8C%E9%81%93%E4%BA%A4%E9%BB%9E" title="軌道交點">交點</a>或<a href="/wiki/%E6%8B%B1%E9%BB%9E" title="拱點">近日點</a>可以漂移（共振的關聯，短週期，不是長期進動）。giv</li></ul> <p>參考稍後的插圖，考慮埃歐-歐羅巴著名的1:2共振。如果軌道週期在這種的關係，<a href="/wiki/%E5%B9%B3%E5%9D%87%E8%BF%90%E5%8A%A8" title="平均运动">平均運動</a><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddf4a520ae4c1cdb7467e78a29509510ea61a08f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.782ex; height:1.676ex;" alt="{\displaystyle n\,\!}"></span>(週期的倒數，通常表示為度/每天）將滿足下式： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{\rm {Io}}-2\cdot n_{\rm {Eu}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">I</mi> <mi mathvariant="normal">o</mi> </mrow> </mrow> </msub> <mo>−</mo> <mn>2</mn> <mo>⋅</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{\rm {Io}}-2\cdot n_{\rm {Eu}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c2401b24937a5d727cc7034be71fbb532dec9c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.646ex; height:2.509ex;" alt="{\displaystyle n_{\rm {Io}}-2\cdot n_{\rm {Eu}}=0}"></span></dd></dl> <p>代入資料（來自維基百科）將可以得到−0.7395° /日，於零有著極大不同的值！ </p><p>實際上，共振是完美的，但它也涉及<a href="/w/index.php?title=%E8%BF%91%E6%9C%A8%E9%BB%9E&action=edit&redlink=1" class="new" title="近木點（页面不存在）">近木點</a>（軌道上最接近木星的點）的進動，<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ω</mi> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {\omega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acf8369d9915a384686bd5947a0e43c46bccd982" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:2.176ex;" alt="{\displaystyle {\dot {\omega }}}"></span>。正確的方程式（拉普拉斯方程式的一部分）是： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{\rm {Io}}-2\cdot n_{\rm {Eu}}+{\dot {\omega }}_{\rm {Io}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">I</mi> <mi mathvariant="normal">o</mi> </mrow> </mrow> </msub> <mo>−</mo> <mn>2</mn> <mo>⋅</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ω</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">I</mi> <mi mathvariant="normal">o</mi> </mrow> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{\rm {Io}}-2\cdot n_{\rm {Eu}}+{\dot {\omega }}_{\rm {Io}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5ec6d54875cc71e289939f48deaa4621146c51d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.58ex; height:2.509ex;" alt="{\displaystyle n_{\rm {Io}}-2\cdot n_{\rm {Eu}}+{\dot {\omega }}_{\rm {Io}}=0}"></span></dd></dl> <p>換言之，在考慮到近木點的進動，埃歐的平均運動確實是歐羅巴的兩倍。一位者設定在漂移的近木點上的觀測者，將看見衛星距角在同一個地點伸展。除了<a href="/wiki/%E5%9C%9F%E5%8D%AB%E4%B8%89" title="土卫三">土衛三特提斯</a>–<a href="/wiki/%E5%9C%9F%E5%8D%AB%E4%B8%80" title="土卫一">土衛一彌瑪斯</a>，列在上面的其它對都滿足相同類型的方程式。在這種情況下，共振滿足方程式 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 4\cdot n_{\rm {Te}}-2\cdot n_{\rm {Mi}}-{\dot {\Omega }}_{\rm {Te}}-{\dot {\Omega }}_{\rm {Mi}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> <mo>⋅</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>−</mo> <mn>2</mn> <mo>⋅</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">i</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="normal">Ω</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="normal">Ω</mi> <mo>˙</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">M</mi> <mi mathvariant="normal">i</mi> </mrow> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4\cdot n_{\rm {Te}}-2\cdot n_{\rm {Mi}}-{\dot {\Omega }}_{\rm {Te}}-{\dot {\Omega }}_{\rm {Mi}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e4ebcb07836873c52c0f0590fd7a4b0d13cdda3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:33.301ex; height:3.176ex;" alt="{\displaystyle 4\cdot n_{\rm {Te}}-2\cdot n_{\rm {Mi}}-{\dot {\Omega }}_{\rm {Te}}-{\dot {\Omega }}_{\rm {Mi}}=0}"></span></dd></dl> <p>天秤動的會合點將會圍繞在這兩顆衛星<a href="/wiki/%E8%BB%8C%E9%81%93%E4%BA%A4%E9%BB%9E" title="軌道交點">交點</a>的中間點上。 </p> <div class="mw-heading mw-heading3"><h3 id="拉普拉斯共振"><span id=".E6.8B.89.E6.99.AE.E6.8B.89.E6.96.AF.E5.85.B1.E6.8C.AF"></span>拉普拉斯共振</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&action=edit&section=4" title="编辑章节：拉普拉斯共振"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:TheLaplaceResonance2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/TheLaplaceResonance2.png/300px-TheLaplaceResonance2.png" decoding="async" width="300" height="105" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/TheLaplaceResonance2.png/450px-TheLaplaceResonance2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/0/05/TheLaplaceResonance2.png 2x" data-file-width="470" data-file-height="165" /></a><figcaption>埃歐、歐羅巴、佳利美德共振的圖解。從中心向外依序為埃歐（黃色）、歐羅巴（灰色）和佳利美德（黑色）。</figcaption></figure> <p>最著名的共振涉及埃歐－歐羅巴－佳利美德，包括下面鎖定衛星<i>軌道相位</i>的關係： </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Phi _{L}=\lambda _{\rm {Io}}-3\cdot \lambda _{\rm {Eu}}+2\cdot \lambda _{\rm {Ga}}=180^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">I</mi> <mi mathvariant="normal">o</mi> </mrow> </mrow> </msub> <mo>−</mo> <mn>3</mn> <mo>⋅</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msub> <mo>+</mo> <mn>2</mn> <mo>⋅</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">G</mi> <mi mathvariant="normal">a</mi> </mrow> </mrow> </msub> <mo>=</mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi _{L}=\lambda _{\rm {Io}}-3\cdot \lambda _{\rm {Eu}}+2\cdot \lambda _{\rm {Ga}}=180^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52bdf5d416c5209a28f2f93b28feccc84e773e6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:35.455ex; height:2.676ex;" alt="{\displaystyle \Phi _{L}=\lambda _{\rm {Io}}-3\cdot \lambda _{\rm {Eu}}+2\cdot \lambda _{\rm {Ga}}=180^{\circ }}"></span></dd></dl> <p>此處<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span>是衛星的<a href="/w/index.php?title=%E5%B9%B3%E5%9D%87%E7%B6%93%E5%BA%A6&action=edit&redlink=1" class="new" title="平均經度（页面不存在）">平均經度</a>。這種關係使得三重的合是不可能的。圖解說明了衛星埃歐在1、2、和3個週期後的位置。（在<a href="/wiki/%E6%A0%BC%E5%88%A9%E6%BE%A4876" title="格利澤876">格利澤876</a>的系統，相較之下，是最外層行星的運行軌道和每一顆行星合的三重關係<sup id="cite_ref-rivera2010_2-1" class="reference"><a href="#cite_note-rivera2010-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>。） </p> <div class="mw-heading mw-heading3"><h3 id="冥族小天體的共振"><span id=".E5.86.A5.E6.97.8F.E5.B0.8F.E5.A4.A9.E9.AB.94.E7.9A.84.E5.85.B1.E6.8C.AF"></span>冥族小天體的共振</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&action=edit&section=5" title="编辑章节：冥族小天體的共振"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>矮行星<a href="/wiki/%E5%86%A5%E7%8E%8B%E6%98%9F" title="冥王星">冥王星</a>被困在與<a href="/wiki/%E6%B5%B7%E7%8E%8B%E6%98%9F" title="海王星">海王星</a>有著共振軌道的圈套中，他的共振包括： </p> <ul><li>平均運動2:3的共振</li> <li><a href="/wiki/%E8%BF%91%E6%97%A5%E9%BB%9E" class="mw-redirect" title="近日點">近日點</a>的共振（大約90°的<a href="/wiki/%E5%A4%A9%E7%A7%A4%E5%8B%95" class="mw-redirect" title="天秤動">天秤動</a>），維持近日點在<a href="/wiki/%E9%BB%83%E9%81%93" class="mw-redirect" title="黃道">黃道</a>的上方。</li> <li>近日點共振的經度與海王星相關聯</li></ul> <p>這些共振的一個結果是當冥王星越過海王星的軌道時，兩者之間的距離至少在30天文單位以上，而兩者之間最小的距離大約是17天文單位，而冥王星和天王星之間的距離最小距離只有11天文單位<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>。（詳細的解釋和圖說請參見<a href="/wiki/%E5%86%A5%E7%8E%8B%E6%98%9F#軌道和自轉" title="冥王星">冥王星的軌道</a>。) </p><p>同樣和海王星有著2:3共振的天體，稱為<i><a href="/wiki/%E5%86%A5%E6%97%8F%E5%B0%8F%E5%A4%A9%E9%AB%94" title="冥族小天體">冥族小天體</a></i>，是可能成為矮行星的<a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F90482" class="mw-redirect" title="小行星90482">亡神星</a>。亡神星的軌道離心率和傾角都與冥王星相似，然而與海王星有著相同的共振使它很不自然的總在與冥王星相對的相位上；所以亡神星有時會被描述為<i>反冥王星</i><sup id="cite_ref-MBP_13-0" class="reference"><a href="#cite_note-MBP-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="系外行星的平均運動共振"><span id=".E7.B3.BB.E5.A4.96.E8.A1.8C.E6.98.9F.E7.9A.84.E5.B9.B3.E5.9D.87.E9.81.8B.E5.8B.95.E5.85.B1.E6.8C.AF"></span>系外行星的平均運動共振</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&action=edit&section=6" title="编辑章节：系外行星的平均運動共振"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>雖然大多數以經被發現的<a href="/wiki/%E7%B3%BB%E5%A4%96%E8%A1%8C%E6%98%9F" class="mw-redirect" title="系外行星">系外行星</a>系統還沒有被發現有平均運動共振，但已有一些明顯的例子被揭漏： </p> <ul><li>如前述題道的<a href="/wiki/%E6%A0%BC%E5%88%A9%E6%BE%A4876" title="格利澤876">格利澤876</a>e、b和c，有著1:2:4的軌道共振，週期分別為124.3、61.1和30天<sup id="cite_ref-rivera2010_2-2" class="reference"><a href="#cite_note-rivera2010-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Marcy_2001_14-0" class="reference"><a href="#cite_note-Marcy_2001-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>。</li> <li><a href="/wiki/KOI-730" class="mw-redirect" title="KOI-730">KOI-730</a> d、b、c和e出現3:4:6:8的共振，軌道週期為19.72、14.79、9.85和7.38天<sup id="cite_ref-EPE-KOI730_15-0" class="reference"><a href="#cite_note-EPE-KOI730-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Beatty_16-0" class="reference"><a href="#cite_note-Beatty-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Lissauer_2011_17-0" class="reference"><a href="#cite_note-Lissauer_2011-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>。</li> <li><a href="/wiki/KOI-500" class="mw-redirect" title="KOI-500">KOI-500</a> c、b、e、d和f，出現接近20:27:41:62:193的共振，週期分別為9.522、7.053、4.645、3.072和0.9868天<sup id="cite_ref-Lissauer_2011_17-1" class="reference"><a href="#cite_note-Lissauer_2011-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-EPE-KOI500_18-0" class="reference"><a href="#cite_note-EPE-KOI500-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Choi_2012_19-0" class="reference"><a href="#cite_note-Choi_2012-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>。</li> <li><a href="/w/index.php?title=KOI-738&action=edit&redlink=1" class="new" title="KOI-738（页面不存在）">KOI-738</a>和<a href="/w/index.php?title=KOI-787&action=edit&redlink=1" class="new" title="KOI-787（页面不存在）">KOI-787</a>出現一對7:9共振的行星（比率各自為1/1.285871和1/1.284008）<sup id="cite_ref-Lissauer_2011_17-2" class="reference"><a href="#cite_note-Lissauer_2011-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/%E5%85%8B%E5%8D%9C%E5%8B%9237" title="克卜勒37">克卜勒37</a> d、c和b出現誤差在1%內的5:8:15共振，週期分別為39.792187、21.301886和13.367308天<sup id="cite_ref-BarclayRowe2013_20-0" class="reference"><a href="#cite_note-BarclayRowe2013-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup>。</li></ul> <p>系外行星中呈現接近1:2共振平均運動的現象非常普遍。<a href="/wiki/%E5%87%8C%E6%97%A5%E6%B3%95" class="mw-redirect" title="凌日法">凌日法</a>發現的系統有16%的報告中有這樣的事例（週期比例的範圍在1.83-2.18）<sup id="cite_ref-Lissauer_2011_17-3" class="reference"><a href="#cite_note-Lissauer_2011-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>。以<a href="/wiki/%E9%83%BD%E5%8D%9C%E5%8B%92%E5%85%89%E8%AD%9C%E5%AD%B8" title="都卜勒光譜學">都卜勒光譜</a>特徵發現的系外行星系統也有六分之一的比例（在這種情況下週期比率的範圍更窄）<sup id="cite_ref-Wright_2011_21-0" class="reference"><a href="#cite_note-Wright_2011-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup>。由於對系統的知識還不完整，實際的比例可能會更高<sup id="cite_ref-Lissauer_2011_17-4" class="reference"><a href="#cite_note-Lissauer_2011-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>。整體而言，約三分之一徑向速度系統的特徵有一對行星接近<a href="/wiki/%E9%80%9A%E7%BA%A6%E6%80%A7_(%E5%A4%A9%E6%96%87%E5%AD%A6)" title="通约性 (天文学)">通約性</a><sup id="cite_ref-Lissauer_2011_17-5" class="reference"><a href="#cite_note-Lissauer_2011-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Wright_2011_21-1" class="reference"><a href="#cite_note-Wright_2011-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup>。更常見的視一對行星的軌道週期有著接近平均運動共振的比率，不是高了幾個百分點就是低了幾個百分點（特別是在第一階的共振，整數上的比率只有一個有不同）<sup id="cite_ref-Lissauer_2011_17-6" class="reference"><a href="#cite_note-Lissauer_2011-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>。在與恆星有<a href="/wiki/%E6%BD%AE%E6%B1%90%E5%8A%A0%E9%80%9F" title="潮汐加速">潮汐作用</a>的情況下，這樣的預測是很接近真實的<sup id="cite_ref-Terquem_2007_22-0" class="reference"><a href="#cite_note-Terquem_2007-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="符合'接近'比率的平均運動"><span id=".E7.AC.A6.E5.90.88.27.E6.8E.A5.E8.BF.91.27.E6.AF.94.E7.8E.87.E7.9A.84.E5.B9.B3.E5.9D.87.E9.81.8B.E5.8B.95"></span>符合'接近'比率的平均運動</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&action=edit&section=7" title="编辑章节：符合'接近'比率的平均運動"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:PallasJupiter.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/PallasJupiter.GIF/300px-PallasJupiter.GIF" decoding="async" width="300" height="261" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/PallasJupiter.GIF/450px-PallasJupiter.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/5/5b/PallasJupiter.GIF 2x" data-file-width="590" data-file-height="514" /></a><figcaption>描繪的是在旋轉框架中<a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F2" class="mw-redirect" title="小行星2">（2）智神星</a>與木星之間接近18:7的共振（點擊觀看動畫）。木星（在左上角的粉紅色橢圓環）平穩的類似固定不動。智神星軌道的漂移與木星對正的方隨著時間改變；它沒有反轉的路徑（也就是說沒有天秤動）。</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Venus_pentagram.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Venus_pentagram.png/300px-Venus_pentagram.png" decoding="async" width="300" height="279" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Venus_pentagram.png/450px-Venus_pentagram.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Venus_pentagram.png/600px-Venus_pentagram.png 2x" data-file-width="853" data-file-height="792" /></a><figcaption>描繪的是<a href="/wiki/%E5%9C%B0%E7%90%83" title="地球">地球</a>：<a href="/wiki/%E9%87%91%E6%98%9F" title="金星">金星</a>接近8:13的共振。地球被固定在非旋轉框架圖的中心，連續追蹤金星的<a href="/w/index.php?title=%E5%85%A7%E5%90%88&action=edit&redlink=1" class="new" title="內合（页面不存在）">內合</a>超過8個地球年，反映出<a href="/wiki/%E4%BA%94%E8%A7%92%E6%98%9F" title="五角星">五角星</a>的模式（數值的比率不同反射出的模式也就不同）。</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Moons_of_Pluto.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Moons_of_Pluto.png/300px-Moons_of_Pluto.png" decoding="async" width="300" height="240" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Moons_of_Pluto.png/450px-Moons_of_Pluto.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/Moons_of_Pluto.png/600px-Moons_of_Pluto.png 2x" data-file-width="2750" data-file-height="2200" /></a><figcaption>描繪出<a href="/wiki/%E5%86%A5%E7%8E%8B%E6%98%9F" title="冥王星">冥王星</a>較外面4顆小衛星的軌道，它們遵循著3:4:5:6的序列，相對於最大的衛星<a href="/wiki/%E5%86%A5%E8%A1%9B%E4%B8%80" class="mw-redirect" title="冥衛一">卡戎</a>的週期有著近共振。</figcaption></figure> <p>在行星或主要衛星之間的軌道頻率有時會指出有接近<a href="/wiki/%E6%95%B4%E6%95%B8" class="mw-redirect" title="整數">整數</a>數值的比率關係（見下面的清單）。然而，這並沒有任何動力學上的意義，因為沒有適當的<a href="/wiki/%E8%BF%91%E6%97%A5%E9%BB%9E" class="mw-redirect" title="近日點">近日點</a>進動或其它振動使共振更為完美（詳細的討論參見前<a href="/wiki/%E8%BB%8C%E9%81%93%E5%85%B1%E6%8C%AF#在太陽系的平均運動共振" class="mw-redirect" title="軌道共振">節</a>的敘述）。即使這種不匹配相當的小（不同于真正的共振），這種接近共振的動態還是無意義的，因為在每個周期後，這些天體的相對位置還是會偏移。在天文學的短時間尺度平均值，它們相對的位置是隨機的，就像完全不靠近共振狀態的機構。例如，考慮地球和金星的軌道，它們在金星公轉13週和地球公轉8週之後，又配置在軌道上幾乎相同的對位置上。正確的比率是0.61518624，和精確的8：13只有0.032%的偏差。在8年後，金星在軌道位置上的偏移只有的1.5°。不過，這依然可以讓金星和地球經過120個循環後，也就是960年後，發現彼此在對面的位置上。因此，在數千年或更長時間尺度上（以天文學的標準仍然很小），它們的相對位置實質上依然是隨機的。 </p><p>近共振的存在可能會反映出在過去存在著一個完美的共振，或是系統正朝向完美的共振來演進。 </p><p>一些軌道頻率的巧合包括： </p> <table align="center" class="wikitable"> <tbody><tr> <th>（比率）和天體</th> <th>一個循環後的偏差<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup></th> <th>隨機化時間<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup></th> <th>或然率<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>c<span class="cite-bracket">]</span></a></sup> </th></tr> <tr> <th colspan="4"><i>行星</i> </th></tr> <tr> <td>（9:23）<a href="/wiki/%E9%87%91%E6%98%9F" title="金星">金星</a>−<a href="/wiki/%E6%B0%B4%E6%98%9F" title="水星">水星</a></td> <td>4.0°</td> <td>200 <a href="/wiki/%E5%B9%B4" title="年">y</a></td> <td>0.19 </td></tr> <tr> <td>（8:13）<a href="/wiki/%E5%9C%B0%E7%90%83" title="地球">地球</a>−<a href="/wiki/%E9%87%91%E6%98%9F" title="金星">金星</a><sup id="cite_ref-Langford_26-0" class="reference"><a href="#cite_note-Langford-26"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Bazsó_27-0" class="reference"><a href="#cite_note-Bazsó-27"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>d<span class="cite-bracket">]</span></a></sup></td> <td>1.5°</td> <td>1000 <a href="/wiki/%E5%B9%B4" title="年">y</a></td> <td>0.065 </td></tr> <tr> <td>（243:395）<a href="/wiki/%E5%9C%B0%E7%90%83" title="地球">地球</a>−<a href="/wiki/%E9%87%91%E6%98%9F" title="金星">金星</a><sup id="cite_ref-Langford_26-2" class="reference"><a href="#cite_note-Langford-26"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Shortt_28-1" class="reference"><a href="#cite_note-Shortt-28"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup></td> <td>0.8°</td> <td>50,000 <a href="/wiki/%E5%B9%B4" title="年">y</a></td> <td>0.68 </td></tr> <tr> <td>（1:3）<a href="/wiki/%E7%81%AB%E6%98%9F" title="火星">火星</a>−<a href="/wiki/%E9%87%91%E6%98%9F" title="金星">金星</a></td> <td>20.6°</td> <td>20 y</td> <td>0.11 </td></tr> <tr> <td>（1:2）<a href="/wiki/%E7%81%AB%E6%98%9F" title="火星">火星</a>−<a href="/wiki/%E5%9C%B0%E7%90%83" title="地球">地球</a></td> <td>42.9°</td> <td>8 y</td> <td>0.24 </td></tr> <tr> <td>（1:12）<a href="/wiki/%E6%9C%A8%E6%98%9F" title="木星">木星</a>−<a href="/wiki/%E5%9C%B0%E7%90%83" title="地球">地球</a><sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>e<span class="cite-bracket">]</span></a></sup></td> <td>49.1°</td> <td>40 y</td> <td>0.28 </td></tr> <tr> <td>（2:5）<a href="/wiki/%E5%9C%9F%E6%98%9F" title="土星">土星</a>–<a href="/wiki/%E6%9C%A8%E6%98%9F" title="木星">木星</a><sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>f<span class="cite-bracket">]</span></a></sup></td> <td>12.8°</td> <td>800 y</td> <td>0.13 </td></tr> <tr> <td>（1:7）<a href="/wiki/%E5%A4%A9%E7%8E%8B%E6%98%9F" title="天王星">天王星</a>−<a href="/wiki/%E6%9C%A8%E6%98%9F" title="木星">木星</a></td> <td>31.1°</td> <td>500 y</td> <td>0.18 </td></tr> <tr> <td>（7:20）<a href="/wiki/%E5%A4%A9%E7%8E%8B%E6%98%9F" title="天王星">天王星</a>−<a href="/wiki/%E5%9C%9F%E6%98%9F" title="土星">土星</a></td> <td>5.7°</td> <td>20,000 y</td> <td>0.20 </td></tr> <tr> <td>（5:28）<a href="/wiki/%E6%B5%B7%E7%8E%8B%E6%98%9F" title="海王星">海王星</a>−<a href="/wiki/%E5%9C%9F%E6%98%9F" title="土星">土星</a></td> <td>1.9°</td> <td>80,000 y</td> <td>0.052 </td></tr> <tr> <td>（1:2）<a href="/wiki/%E6%B5%B7%E7%8E%8B%E6%98%9F" title="海王星">海王星</a>−<a href="/wiki/%E5%A4%A9%E7%8E%8B%E6%98%9F" title="天王星">天王星</a></td> <td>14.0°</td> <td>2000 y</td> <td>0.078 </td></tr> <tr> <th colspan="4"><i>火星系統</i> </th></tr> <tr> <td>（1:4）<a href="/wiki/%E7%81%AB%E8%A1%9B%E4%BA%8C" class="mw-redirect" title="火衛二">Deimos</a>−<a href="/wiki/%E7%81%AB%E8%A1%9B%E4%B8%80" class="mw-redirect" title="火衛一">Phobos</a></td> <td>14.9°</td> <td>0.04 y</td> <td>0.083 </td></tr> <tr> <th colspan="4"><i>主要的小行星</i> </th></tr> <tr> <td>（1:1）<a href="/wiki/%E6%99%BA%E7%A5%9E%E6%98%9F" title="智神星">智神星</a>− <a href="/wiki/%E7%A9%80%E7%A5%9E%E6%98%9F" title="穀神星">穀神星</a><sup id="cite_ref-Goffin2001_32-0" class="reference"><a href="#cite_note-Goffin2001-32"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kovačević_33-0" class="reference"><a href="#cite_note-Kovačević-33"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup></td> <td>1.2°</td> <td>700 y</td> <td>0.0066 </td></tr> <tr> <td>（7:18）<a href="/wiki/%E6%9C%A8%E6%98%9F" title="木星">木星</a>− <a href="/wiki/%E6%99%BA%E7%A5%9E%E6%98%9F" title="智神星">智神星</a><sup id="cite_ref-Taylor1982_34-0" class="reference"><a href="#cite_note-Taylor1982-34"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup></td> <td>4.1°</td> <td>4000 y</td> <td>0.15 </td></tr> <tr> <th colspan="4"><i><a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F87" class="mw-redirect" title="小行星87">（87）Sylvia</a>系統</i><sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>g<span class="cite-bracket">]</span></a></sup> </th></tr> <tr> <td>（17:45）<a href="/w/index.php?title=Romulus_(moon)&action=edit&redlink=1" class="new" title="Romulus (moon)（页面不存在）">Romulus</a>−<a href="/w/index.php?title=Remus_(moon)&action=edit&redlink=1" class="new" title="Remus (moon)（页面不存在）">Remus</a></td> <td>0.7°</td> <td>40 y</td> <td>0.067 </td></tr> <tr> <th colspan="4"><i>木星系統</i> </th></tr> <tr> <td>（1:6）<a href="/wiki/%E6%9C%A8%E8%A1%9B%E4%B8%80" class="mw-redirect" title="木衛一">Io</a>−<a href="/wiki/%E6%9C%A8%E5%8D%AB%E5%8D%81%E5%85%AD" title="木卫十六">Metis</a></td> <td>0.6°</td> <td>2 y</td> <td>0.0031 </td></tr> <tr> <td>（3:5）<a href="/wiki/%E6%9C%A8%E5%8D%AB%E4%BA%94" title="木卫五">Amalthea</a>−<a href="/wiki/%E6%9C%A8%E5%8D%AB%E5%8D%81%E4%BA%94" title="木卫十五">Adrastea</a></td> <td>3.9°</td> <td>0.2 y</td> <td>0.064 </td></tr> <tr> <td>（3:7）<a href="/w/index.php?title=%E6%9C%A8%E8%A1%9B%E5%9B%9BCallisto_(moon)&action=edit&redlink=1" class="new" title="木衛四Callisto (moon)（页面不存在）">Callisto</a>−<a href="/w/index.php?title=%E6%9C%A8%E8%A1%9B%E4%B8%89Ganymede_(moon)&action=edit&redlink=1" class="new" title="木衛三Ganymede (moon)（页面不存在）">Ganymede</a><sup id="cite_ref-Goldreich_1965_36-0" class="reference"><a href="#cite_note-Goldreich_1965-36"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup></td> <td>0.7°</td> <td>30 y</td> <td>0.012 </td></tr> <tr> <th colspan="4"><i>土星系統</i> </th></tr> <tr> <td>（2:3）<a href="/wiki/%E5%9C%9F%E5%8D%AB%E4%BA%8C" title="土卫二">Enceladus</a>−<a href="/wiki/%E5%9C%9F%E5%8D%AB%E4%B8%80" title="土卫一">Mimas</a></td> <td>33.2°</td> <td>0.04 y</td> <td>0.33 </td></tr> <tr> <td>（2:3）<a href="/wiki/%E5%9C%9F%E5%8D%AB%E5%9B%9B" title="土卫四">Dione</a>−<a href="/wiki/%E5%9C%9F%E5%8D%AB%E4%B8%89" title="土卫三">Tethys</a><sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>h<span class="cite-bracket">]</span></a></sup></td> <td>36.2°</td> <td>0.07 y</td> <td>0.36 </td></tr> <tr> <td>（3:5）<a href="/wiki/%E5%9C%9F%E5%8D%AB%E4%BA%94" title="土卫五">Rhea</a>−<a href="/wiki/%E5%9C%9F%E5%8D%AB%E5%9B%9B" title="土卫四">Dione</a></td> <td>17.1°</td> <td>0.4 y</td> <td>0.26 </td></tr> <tr> <td>（2:7）<a href="/wiki/%E5%9C%9F%E8%A1%9B%E5%85%AD" class="mw-redirect" title="土衛六">Titan</a>−<a href="/wiki/%E5%9C%9F%E5%8D%AB%E4%BA%94" title="土卫五">Rhea</a></td> <td>21.0°</td> <td>0.7 y</td> <td>0.22 </td></tr> <tr> <td>（1:5）<a href="/wiki/%E5%9C%9F%E8%A1%9B%E5%85%AB" class="mw-redirect" title="土衛八">Iapetus</a>−<a href="/wiki/%E5%9C%9F%E8%A1%9B%E5%85%AD" class="mw-redirect" title="土衛六">Titan</a></td> <td>9.2°</td> <td>4 y</td> <td>0.051 </td></tr> <tr> <th colspan="4"><i>主要<a href="/wiki/%E5%8D%8A%E4%BA%BA%E9%A9%AC%E5%B0%8F%E8%A1%8C%E6%98%9F" title="半人马小行星">半人馬小行星</a></i><sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>i<span class="cite-bracket">]</span></a></sup> </th></tr> <tr> <td>（3:4）<a href="/wiki/%E5%A4%A9%E7%8E%8B%E6%98%9F" title="天王星">天王星</a>−<a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F10199" class="mw-redirect" title="小行星10199">（10199）Chariklo</a></td> <td>4.5°</td> <td>10,000 y</td> <td>0.073 </td></tr> <tr> <th colspan="4"><i>天王星系統</i> </th></tr> <tr> <td>（3:5）<a href="/wiki/%E5%A4%A9%E5%8D%AB%E5%8D%81%E4%B8%89" title="天卫十三">Rosalind</a>−<a href="/wiki/%E5%A4%A9%E5%8D%AB%E5%85%AD" title="天卫六">Cordelia</a><sup id="cite_ref-Murray_1990_40-0" class="reference"><a href="#cite_note-Murray_1990-40"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></td> <td>0.22°</td> <td>4 y</td> <td>0.0037 </td></tr> <tr> <td>（1:3）<a href="/wiki/%E5%A4%A9%E5%8D%AB%E4%BA%8C" title="天卫二">Umbriel</a>−<a href="/wiki/%E5%A4%A9%E5%8D%AB%E4%BA%94" title="天卫五">Miranda</a><sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>j<span class="cite-bracket">]</span></a></sup></td> <td>24.5°</td> <td>0.08 y</td> <td>0.14 </td></tr> <tr> <td>（3:5）<a href="/wiki/%E5%A4%A9%E5%8D%AB%E4%BA%8C" title="天卫二">Umbriel</a>−<a href="/wiki/%E5%A4%A9%E5%8D%AB%E4%B8%80" title="天卫一">Ariel</a><sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>k<span class="cite-bracket">]</span></a></sup></td> <td>24.2°</td> <td>0.3 y</td> <td>0.35 </td></tr> <tr> <td>（1:2）<a href="/wiki/%E5%A4%A9%E5%8D%AB%E4%B8%89" title="天卫三">Titania</a>−<a href="/wiki/%E5%A4%A9%E5%8D%AB%E4%BA%8C" title="天卫二">Umbriel</a></td> <td>36.3°</td> <td>0.1 y</td> <td>0.20 </td></tr> <tr> <td>（2:3）<a href="/wiki/%E5%A4%A9%E5%8D%AB%E5%9B%9B" title="天卫四">Oberon</a>−<a href="/wiki/%E5%A4%A9%E5%8D%AB%E4%B8%89" title="天卫三">Titania</a></td> <td>33.4°</td> <td>0.4 y</td> <td>0.34 </td></tr> <tr> <th colspan="4"><i>海王星系統</i> </th></tr> <tr> <td>（1:20）<a href="/wiki/%E6%B5%B7%E8%A1%9B%E4%B8%80" class="mw-redirect" title="海衛一">Triton</a>−<a href="/wiki/%E6%B5%B7%E5%8D%AB%E4%BA%8C" title="海卫二">Naiad</a></td> <td>13.5°</td> <td>0.2 y</td> <td>0.075 </td></tr> <tr> <td>（1:2）<a href="/wiki/%E6%B5%B7%E5%8D%AB%E5%85%AB" title="海卫八">Proteus</a>−<a href="/wiki/%E6%B5%B7%E5%8D%AB%E4%B8%83" title="海卫七">Larissa</a><sup id="cite_ref-ZhangHamilton2007_45-0" class="reference"><a href="#cite_note-ZhangHamilton2007-45"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ZhangHamilton2008_46-0" class="reference"><a href="#cite_note-ZhangHamilton2008-46"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup></td> <td>8.4°</td> <td>0.07 y</td> <td>0.047 </td></tr> <tr> <td>（5:6）<a href="/wiki/%E6%B5%B7%E5%8D%AB%E5%85%AB" title="海卫八">Proteus</a>−<a href="/wiki/S/2004_N_1" class="mw-redirect" title="S/2004 N 1">S/2004 N 1</a></td> <td>2.1°</td> <td>1 y</td> <td>0.057 </td></tr> <tr> <th colspan="4"><i>冥王星系統</i> </th></tr> <tr> <td>（1:3）<a href="/wiki/%E5%86%A5%E5%8D%AB%E4%BA%94" title="冥卫五">Styx</a>−<a href="/wiki/%E5%86%A5%E8%A1%9B%E4%B8%80" class="mw-redirect" title="冥衛一">Charon</a><sup id="cite_ref-Matson_47-0" class="reference"><a href="#cite_note-Matson-47"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup></td> <td>58.5°</td> <td>0.2 y</td> <td>0.33 </td></tr> <tr> <td>（1:4）<a href="/wiki/%E5%86%A5%E8%A1%9B%E4%BA%8C" class="mw-redirect" title="冥衛二">Nix</a>−<a href="/wiki/%E5%86%A5%E8%A1%9B%E4%B8%80" class="mw-redirect" title="冥衛一">Charon</a><sup id="cite_ref-WardCanup2006_48-0" class="reference"><a href="#cite_note-WardCanup2006-48"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Matson_47-1" class="reference"><a href="#cite_note-Matson-47"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup></td> <td>39.1°</td> <td>0.3 y</td> <td>0.22 </td></tr> <tr> <td>（1:5）<a href="/wiki/%E5%86%A5%E5%8D%AB%E5%9B%9B" title="冥卫四">Kerberos</a>−<a href="/wiki/%E5%86%A5%E8%A1%9B%E4%B8%80" class="mw-redirect" title="冥衛一">Charon</a><sup id="cite_ref-Matson_47-2" class="reference"><a href="#cite_note-Matson-47"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup></td> <td>9.2°</td> <td>2 y</td> <td>0.05 </td></tr> <tr> <td>（1:6）<a href="/wiki/%E5%86%A5%E8%A1%9B%E4%B8%89" class="mw-redirect" title="冥衛三">Hydra</a>−<a href="/wiki/%E5%86%A5%E8%A1%9B%E4%B8%80" class="mw-redirect" title="冥衛一">Charon</a><sup id="cite_ref-WardCanup2006_48-1" class="reference"><a href="#cite_note-WardCanup2006-48"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Matson_47-3" class="reference"><a href="#cite_note-Matson-47"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup></td> <td>6.6°</td> <td>3 y</td> <td>0.037 </td></tr> <tr> <th colspan="4"><i>妊神星系統</i> </th></tr> <tr> <td>（3:8）<a href="/wiki/%E5%A6%8A%E5%8D%AB%E4%B8%80" title="妊卫一">Hi<span class="unicode">ʻ</span>iaka</a>−<a href="/w/index.php?title=%E5%A7%99%E8%A1%9B%E4%BA%8C)&action=edit&redlink=1" class="new" title="姙衛二)（页面不存在）">Namaka</a><sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>l<span class="cite-bracket">]</span></a></sup></td> <td>42.5°</td> <td>2 y</td> <td>0.55 </td></tr> </tbody></table> <div class="reflist" style="list-style-type: lower-alpha;"> <ol class="references"> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"> Mismatch in orbital longitude of the inner body, as compared to its position at the beginning of the cycle（with the cycle defined as <i>n</i> orbits of the outer body – see below）. Circular orbits are assumed（i.e., precession is ignored）. </span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"> The time needed for the mismatch from the initial relative longitudinal orbital positions of the bodies to grow to 180°, rounded to the nearest first <a href="/w/index.php?title=Significant_digit&action=edit&redlink=1" class="new" title="Significant digit（页面不存在）">significant digit</a>.</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"> The <a href="/w/index.php?title=Probability&action=edit&redlink=1" class="new" title="Probability（页面不存在）">probability</a> of obtaining an orbital coincidence of equal or smaller mismatch by chance at least once in <i>n</i> attempts, where <i>n</i> is the integer number of orbits of the outer body per cycle, and the mismatch is assumed to vary between 0° and 180° at random. The value is calculated as 1-（1- mismatch/180°）^<i>n</i>. The smaller the probability, the more remarkable the coincidence. This is a crude calculation that only attempts to give a rough idea of relative probabilities.</span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"> The two near <a href="/w/index.php?title=Commensurability_(astronomy)&action=edit&redlink=1" class="new" title="Commensurability (astronomy)（页面不存在）">commensurabilities</a> listed for Earth and Venus are reflected in the timing of <a href="/w/index.php?title=Transit_of_Venus&action=edit&redlink=1" class="new" title="Transit of Venus（页面不存在）">transits of Venus</a>, which occur in pairs 8 years apart, in a cycle that repeats every 243 years.<sup id="cite_ref-Langford_26-1" class="reference"><a href="#cite_note-Langford-26"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Shortt_28-0" class="reference"><a href="#cite_note-Shortt-28"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"> The near 1:12 resonance between Jupiter and Earth causes the <a href="/w/index.php?title=Alinda_family&action=edit&redlink=1" class="new" title="Alinda family（页面不存在）">Alinda asteroids</a>, which occupy (or are close to) the 3:1 resonance with Jupiter, to be close to a 1:4 resonance with Earth. </span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"> This near resonance has been termed the <i><a href="/w/index.php?title=Great_Inequality&action=edit&redlink=1" class="new" title="Great Inequality（页面不存在）">Great Inequality</a></i>. It was first described by <a href="/wiki/Pierre-Simon_Laplace" class="mw-redirect" title="Pierre-Simon Laplace">Laplace</a> in a series of papers published 1784–1789. </span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"> <a href="/wiki/87_Sylvia" class="mw-redirect" title="87 Sylvia">87 Sylvia</a> is the first asteroid discovered to have more than one moon. </span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"> This resonance may have been occupied in the past.<sup id="cite_ref-Chen2008_37-0" class="reference"><a href="#cite_note-Chen2008-37"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"> Some <a href="/w/index.php?title=Centaur_(minor_planet)&action=edit&redlink=1" class="new" title="Centaur (minor planet)（页面不存在）">definitions of centaurs</a> stipulate that they are nonresonant bodies. </span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"> This resonance may have been occupied in the past.<sup id="cite_ref-Tittemore_Wisdom_1990_41-0" class="reference"><a href="#cite_note-Tittemore_Wisdom_1990-41"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text"> This resonance may have been occupied in the past.<sup id="cite_ref-Tittemore1988_43-0" class="reference"><a href="#cite_note-Tittemore1988-43"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </span> </li> <li id="cite_note-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-50">^</a></b></span> <span class="reference-text"> The results for the Haumea system aren't very meaningful because, contrary to the assumptions implicit in the calculations, Namaka has an eccentric, <a href="/w/index.php?title=Osculating_orbit&action=edit&redlink=1" class="new" title="Osculating orbit（页面不存在）">non-Keplerian</a> orbit that precesses rapidly (see below). Hiʻiaka and Namaka are much closer to a 3:8 resonance than indicated, and may actually be in it.<sup id="cite_ref-Ragozzine&Brown2009_49-0" class="reference"><a href="#cite_note-Ragozzine&Brown2009-49"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </span> </li> </ol></div> <p>在清單中最值得關注（最不可能）的是木衛一（Io）和木衛十六（Metis）的軌道關係，其次是天衛十三（羅莎琳德，Rosalind）和天衛六（Cordelia，科迪）、智神星和穀神星、木衛四（Callisto）和木衛三（Ganymede）、以及冥衛三（Hydra）和冥衛一（Charon）。 </p> <div class="mw-heading mw-heading2"><h2 id="相關條目"><span id=".E7.9B.B8.E9.97.9C.E6.A2.9D.E7.9B.AE"></span>相關條目</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&action=edit&section=8" title="编辑章节：相關條目"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F1685" title="小行星1685">（1685）托羅</a>：一顆與地球有著5:8共振的小行星。</li> <li><a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F3753" title="小行星3753">（3753）克魯特尼</a>：與地球1:1共振的小行星。</li> <li><a href="/wiki/%E9%80%9A%E7%BA%A6%E6%80%A7_(%E5%A4%A9%E6%96%87%E5%AD%A6)" title="通约性 (天文学)">通约性 (天文学)</a></li> <li><a href="/wiki/%E5%BE%B7%E8%8E%AB%E7%89%B9%E5%AE%9A%E5%BE%8B" title="德莫特定律">德莫特定律</a></li> <li><a href="/wiki/%E9%A6%AC%E8%B9%84%E5%BD%A2%E8%BB%8C%E9%81%93" title="馬蹄形軌道">馬蹄形軌道</a>：以另一種1:1共振型態跟隨著的天體</li> <li><a href="/wiki/%E5%8F%A4%E5%9C%A8%E6%A9%9F%E5%88%B6" title="古在機制">古在共振</a></li> <li><a href="/wiki/%E6%8B%89%E6%A0%BC%E6%9C%97%E6%97%A5%E9%BB%9E" class="mw-redirect" title="拉格朗日點">拉格朗日點</a></li> <li><a href="/wiki/%E6%B0%B4%E6%98%9F#自旋軌道共振" title="水星">水星</a>：3:2的自旋軌道共振</li> <li><a href="/wiki/%E9%9F%B3%E4%B9%90%E5%AE%87%E5%AE%99" title="音乐宇宙">音樂宇宙</a>（"music of the spheres"）</li> <li><a href="/wiki/%E5%85%B1%E6%8C%AF%E6%B5%B7%E7%8E%8B%E6%98%9F%E5%A4%96%E5%A4%A9%E9%AB%94" title="共振海王星外天體">共振海王星外天體</a></li> <li><a href="/wiki/%E6%BD%AE%E6%B1%90%E9%8E%96%E5%AE%9A" title="潮汐鎖定">潮汐鎖定</a></li> <li><a href="/w/index.php?title=%E6%BD%AE%E6%B1%90%E5%85%B1%E6%8C%AF&action=edit&redlink=1" class="new" title="潮汐共振（页面不存在）">潮汐共振</a></li> <li><a href="/wiki/%E6%8F%90%E4%B8%A2%E6%96%AF-%E6%B3%A2%E5%BE%97%E5%AE%9A%E5%88%99" title="提丢斯-波得定则">提丟斯-波德定律</a></li> <li><a href="/wiki/%E7%89%B9%E6%B4%9B%E4%BC%8A%E5%A4%A9%E4%BD%93" title="特洛伊天体">特洛伊天體</a>：1:1共振型態的天體</li></ul> <div class="mw-heading mw-heading2"><h2 id="参考文献"><span id=".E5.8F.82.E8.80.83.E6.96.87.E7.8C.AE"></span>参考文献</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&action=edit&section=9" title="编辑章节：参考文献"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="引用"><span id=".E5.BC.95.E7.94.A8"></span>引用</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&action=edit&section=10" title="编辑章节：引用"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-Morais_2013-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Morais_2013_1-0"><sup><b>1.0</b></sup></a> <a href="#cite_ref-Morais_2013_1-1"><sup><b>1.1</b></sup></a></span> <span class="reference-text"><cite class="citation journal">Morais, M. H. M.; Namouni, F. 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SkyAndTelescope.Com. 2003-07-23 <span class="reference-accessdate"> [<span class="nowrap">2009-02-25</span>]</span>. （<a rel="nofollow" class="external text" href="http://www.skyandtelescope.com/news/3306806.html?page=1&c=y">原始内容</a>存档于2009-09-03）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Why+Is+Saturn+Tipsy%3F&rft.aufirst=J.+K.&rft.aulast=Beatty&rft.date=2003-07-23&rft.genre=unknown&rft.jtitle=SkyAndTelescope.Com&rft_id=http%3A%2F%2Fwww.skyandtelescope.com%2Fnews%2F3306806.html%3Fpage%3D1%26c%3Dy&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></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"><cite class="citation journal">Ward, W. R.; Hamilton, D. 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November 2004, <b>128</b> (5): 2501–2509 <span class="reference-accessdate"> [<span class="nowrap">2009-02-25</span>]</span>. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004AJ....128.2501W"><span title="Bibcode">Bibcode:2004AJ....128.2501W</span></a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F424533"><span title="數位物件識別號">doi:10.1086/424533</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Tilting+Saturn.+I.+Analytic+Model&rft.aufirst=W.+R.&rft.aulast=Ward&rft.date=2004-11&rft.genre=article&rft.issue=5&rft.jtitle=Astronomical+Journal&rft.pages=2501-2509&rft.volume=128&rft_id=http%3A%2F%2Fwww.iop.org%2FEJ%2Fabstract%2F1538-3881%2F128%2F5%2F2501%2F&rft_id=info%3Abibcode%2F2004AJ....128.2501W&rft_id=info%3Adoi%2F10.1086%2F424533&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span> <span style="display:none;font-size:100%" class="error citation-comment">引文使用过时参数<code style="color:inherit; border:inherit; padding:inherit;">coauthors</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#deprecated_params" title="Help:引文格式1错误">帮助</a>)</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"><cite class="citation journal">Hamilton, D. 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Numerical Simulations of the Orbits of the Galilean Satellites. <a href="/w/index.php?title=Icarus_(journal)&action=edit&redlink=1" class="new" title="Icarus (journal)（页面不存在）">Icarus</a>. 2002, <b>159</b> (2): 500–504. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002Icar..159..500M"><span title="Bibcode">Bibcode:2002Icar..159..500M</span></a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1006%2Ficar.2002.6939"><span title="數位物件識別號">doi:10.1006/icar.2002.6939</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Numerical+Simulations+of+the+Orbits+of+the+Galilean+Satellites&rft.aufirst=S.&rft.aulast=Musotto&rft.date=2002&rft.genre=article&rft.issue=2&rft.jtitle=Icarus&rft.pages=500-504&rft.volume=159&rft_id=info%3Abibcode%2F2002Icar..159..500M&rft_id=info%3Adoi%2F10.1006%2Ficar.2002.6939&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span> <span style="display:none;font-size:100%" class="error citation-comment">引文使用过时参数<code style="color:inherit; border:inherit; padding:inherit;">coauthors</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#deprecated_params" title="Help:引文格式1错误">帮助</a>)</span></span> </li> <li id="cite_note-Brown_2007-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Brown_2007_9-0">^</a></b></span> <span class="reference-text"><cite class="citation journal"><a href="/w/index.php?title=Michael_E._Brown&action=edit&redlink=1" class="new" title="Michael E. Brown（页面不存在）">Brown, M. E.</a>; Barkume, K. M.; Ragozzine, D.; Schaller, E. L. <a rel="nofollow" class="external text" href="http://www.nature.com/nature/journal/v446/n7133/abs/nature05619.html">A collisional family of icy objects in the Kuiper belt</a>. <a href="/wiki/Nature_(journal)" class="mw-redirect" title="Nature (journal)">Nature</a>. 2007-03-15, <b>446</b> (7133): 294–296 <span class="reference-accessdate"> [<span class="nowrap">2012-02-18</span>]</span>. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007Natur.446..294B"><span title="Bibcode">Bibcode:2007Natur.446..294B</span></a>. <a rel="nofollow" class="external text" href="//www.ncbi.nlm.nih.gov/pubmed/17361177"><span title="公共医学识别码">PMID 17361177</span></a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fnature05619"><span title="數位物件識別號">doi:10.1038/nature05619</span></a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20170210130547/http://www.nature.com/nature/journal/v446/n7133/abs/nature05619.html">存档</a>于2017-02-10）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=A+collisional+family+of+icy+objects+in+the+Kuiper+belt&rft.aufirst=M.+E.&rft.aulast=Brown&rft.date=2007-03-15&rft.genre=article&rft.issue=7133&rft.jtitle=Nature&rft.pages=294-296&rft.volume=446&rft_id=http%3A%2F%2Fwww.nature.com%2Fnature%2Fjournal%2Fv446%2Fn7133%2Fabs%2Fnature05619.html&rft_id=info%3Abibcode%2F2007Natur.446..294B&rft_id=info%3Adoi%2F10.1038%2Fnature05619&rft_id=info%3Apmid%2F17361177&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span> <span style="display:none;font-size:100%" class="error citation-comment">引文使用过时参数<code style="color:inherit; border:inherit; padding:inherit;">coauthors</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#deprecated_params" title="Help:引文格式1错误">帮助</a>)</span></span> </li> <li id="cite_note-Ragozzine-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ragozzine_10-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Ragozzine, D.; Brown, M. E. <a rel="nofollow" class="external text" href="http://iopscience.iop.org/1538-3881/134/6/2160">Candidate members and age estimate of the family of Kuiper Belt object 2003 EL61</a>. <a href="/wiki/The_Astronomical_Journal" class="mw-redirect" title="The Astronomical Journal">The Astronomical Journal</a>. 2007-10-18, <b>134</b> (6): 2160–2167 <span class="reference-accessdate"> [<span class="nowrap">2012-02-18</span>]</span>. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007AJ....134.2160R"><span title="Bibcode">Bibcode:2007AJ....134.2160R</span></a>. <span class="plainlinks"><a rel="nofollow" class="external text" href="//arxiv.org/abs/0709.0328"><span title="arXiv">arXiv:0709.0328</span></a> <span typeof="mw:File"><span title="可免费查阅"><img alt="可免费查阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span></span>. <a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F522334"><span title="數位物件識別號">doi:10.1086/522334</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Candidate+members+and+age+estimate+of+the+family+of+Kuiper+Belt+object+2003+EL61&rft.aufirst=D.&rft.aulast=Ragozzine&rft.date=2007-10-18&rft.genre=article&rft.issue=6&rft.jtitle=The+Astronomical+Journal&rft.pages=2160-2167&rft.volume=134&rft_id=http%3A%2F%2Fiopscience.iop.org%2F1538-3881%2F134%2F6%2F2160&rft_id=info%3Aarxiv%2F0709.0328&rft_id=info%3Abibcode%2F2007AJ....134.2160R&rft_id=info%3Adoi%2F10.1086%2F522334&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span> <span style="display:none;font-size:100%" class="error citation-comment">引文使用过时参数<code style="color:inherit; border:inherit; padding:inherit;">coauthors</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#deprecated_params" title="Help:引文格式1错误">帮助</a>)</span></span> </li> <li id="cite_note-10th_Planet-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-10th_Planet_11-0">^</a></b></span> <span class="reference-text"><cite class="citation web">Dunn, T. <a rel="nofollow" class="external text" href="http://www.orbitsimulator.com/gravity/articles/newtno.html">The 10th Planet</a>. <a rel="nofollow" class="external text" href="http://www.orbitsimulator.com/gravity/articles/what.html">GravitySimulator.Com</a>. <span class="reference-accessdate"> [<span class="nowrap">2012-02-18</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20190902034836/http://www.orbitsimulator.com/gravity/articles/newtno.html">存档</a>于2019-09-02）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=The+10th+Planet&rft.aufirst=T.&rft.aulast=Dunn&rft.genre=unknown&rft.jtitle=%5Bhttp%3A%2F%2Fwww.orbitsimulator.com%2Fgravity%2Farticles%2Fwhat.html+GravitySimulator.Com%5D&rft_id=http%3A%2F%2Fwww.orbitsimulator.com%2Fgravity%2Farticles%2Fnewtno.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span> <span style="font-size:100%" class="error citation-comment">外部链接存在于<code style="color:inherit; border:inherit; padding:inherit;">|work=</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#param_has_ext_link" title="Help:引文格式1错误">帮助</a>)</span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><cite class="citation web"><a href="/w/index.php?title=Renu_Malhotra&action=edit&redlink=1" class="new" title="Renu Malhotra（页面不存在）">Renu Malhotra</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070403061837/http://nineplanets.org/plutodyn.html">Pluto's Orbit</a>. 1997 <span class="reference-accessdate"> [<span class="nowrap">2007-03-26</span>]</span>. （<a rel="nofollow" class="external text" href="http://www.nineplanets.org/plutodyn.html">原始内容</a>存档于2007-04-03）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.au=Renu+Malhotra&rft.btitle=Pluto%27s+Orbit&rft.date=1997&rft.genre=unknown&rft_id=http%3A%2F%2Fwww.nineplanets.org%2Fplutodyn.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-MBP-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-MBP_13-0">^</a></b></span> <span class="reference-text"><cite class="citation web"><a href="/w/index.php?title=Michael_E._Brown&action=edit&redlink=1" class="new" title="Michael E. 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Mike Brown's Planets (blog). 2009-03-23 <span class="reference-accessdate"> [<span class="nowrap">2009-03-25</span>]</span>. （<a rel="nofollow" class="external text" href="http://www.mikebrownsplanets.com/2009/03/s1-90482-2005-needs-your-help.html">原始内容</a>存档于2012-02-08）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.au=Michael+E.+Brown&rft.btitle=S%2F2005+%2890482%29+1+needs+your+help&rft.date=2009-03-23&rft.genre=unknown&rft.pub=Mike+Brown%27s+Planets+%28blog%29&rft_id=http%3A%2F%2Fwww.mikebrownsplanets.com%2F2009%2F03%2Fs1-90482-2005-needs-your-help.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Marcy_2001-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-Marcy_2001_14-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Marcy, Geoffrey W.; Butler, R. 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A Pair of Resonant Planets Orbiting GJ 876. <a href="/wiki/The_Astrophysical_Journal" class="mw-redirect" title="The Astrophysical Journal">The Astrophysical Journal</a>. 2001, <b>556</b> (1): 296–301. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001ApJ...556..296M"><span title="Bibcode">Bibcode:2001ApJ...556..296M</span></a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F321552"><span title="數位物件識別號">doi:10.1086/321552</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=A+Pair+of+Resonant+Planets+Orbiting+GJ+876&rft.au=Butler%2C+R.+Paul&rft.au=Fischer%2C+Debra&rft.au=Lissauer%2C+Jack+J.&rft.au=Rivera%2C+Eugenio+J.&rft.au=Vogt%2C+Steven+S.&rft.aufirst=Geoffrey+W.&rft.aulast=Marcy&rft.date=2001&rft.genre=article&rft.issue=1&rft.jtitle=The+Astrophysical+Journal&rft.pages=296-301&rft.volume=556&rft_id=info%3Abibcode%2F2001ApJ...556..296M&rft_id=info%3Adoi%2F10.1086%2F321552&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-EPE-KOI730-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-EPE-KOI730_15-0">^</a></b></span> <span class="reference-text">Extrasolar Planets Encyclopaedia, <a rel="nofollow" class="external text" href="http://exoplanet.eu/star.php?st=KOI-730">KOI-730</a> <a href="/wiki/Wayback_Machine" class="mw-redirect" title="Wayback Machine">互联网档案馆</a>的<a rel="nofollow" class="external text" href="https://web.archive.org/web/20120616124736/http://exoplanet.eu/star.php?st=KOI-730">存檔</a>，存档日期2012-06-16.</span> </li> <li id="cite_note-Beatty-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-Beatty_16-0">^</a></b></span> <span class="reference-text"><cite class="citation web">Beatty, Kelley. <a rel="nofollow" class="external text" href="https://archive.today/20120529195155/http://www.skyandtelescope.com/news/117467488.html">Kepler Finds Planets in Tight Dance</a>. <a href="/w/index.php?title=Sky_and_Telescope&action=edit&redlink=1" class="new" title="Sky and Telescope（页面不存在）">Sky and Telescope</a>. 2011-03-05 <span class="reference-accessdate"> [<span class="nowrap">2012-10-16</span>]</span>. （<a rel="nofollow" class="external text" href="http://www.skyandtelescope.com/news/117467488.html">原始内容</a>存档于2012-05-29）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.aufirst=Kelley&rft.aulast=Beatty&rft.btitle=Kepler+Finds+Planets+in+Tight+Dance&rft.date=2011-03-05&rft.genre=unknown&rft.pub=Sky+and+Telescope&rft_id=http%3A%2F%2Fwww.skyandtelescope.com%2Fnews%2F117467488.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Lissauer_2011-17"><span class="mw-cite-backlink">^ <a href="#cite_ref-Lissauer_2011_17-0"><sup><b>17.0</b></sup></a> <a href="#cite_ref-Lissauer_2011_17-1"><sup><b>17.1</b></sup></a> <a href="#cite_ref-Lissauer_2011_17-2"><sup><b>17.2</b></sup></a> <a href="#cite_ref-Lissauer_2011_17-3"><sup><b>17.3</b></sup></a> <a href="#cite_ref-Lissauer_2011_17-4"><sup><b>17.4</b></sup></a> <a href="#cite_ref-Lissauer_2011_17-5"><sup><b>17.5</b></sup></a> <a href="#cite_ref-Lissauer_2011_17-6"><sup><b>17.6</b></sup></a></span> <span class="reference-text"><cite class="citation journal"><a href="/w/index.php?title=Jack_J._Lissauer&action=edit&redlink=1" class="new" title="Jack J. Lissauer（页面不存在）">Lissauer, J.</a>; Ragozzine, D.; Fabrycky, D. C.; <i>et al.</i>. <a rel="nofollow" class="external text" href="http://iopscience.iop.org/0067-0049/197/1/8">Architecture and dynamics of Kepler's candidate multiple transiting planet systems</a>. <a href="/w/index.php?title=The_Astrophysical_Journal_Supplement_Series&action=edit&redlink=1" class="new" title="The Astrophysical Journal Supplement Series（页面不存在）">The Astrophysical Journal Supplement Series</a>. 2011-10-13, <b>197</b> (1): 1–26 <span class="reference-accessdate"> [<span class="nowrap">2012-10-16</span>]</span>. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011ApJS..197....8L"><span title="Bibcode">Bibcode:2011ApJS..197....8L</span></a>. <span class="plainlinks"><a rel="nofollow" class="external text" href="//arxiv.org/abs/1102.0543"><span title="arXiv">arXiv:1102.0543</span></a> <span typeof="mw:File"><span title="可免费查阅"><img alt="可免费查阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span></span>. <a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0067-0049%2F197%2F1%2F8"><span title="數位物件識別號">doi:10.1088/0067-0049/197/1/8</span></a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20140714030311/http://iopscience.iop.org/0067-0049/197/1/8">存档</a>于2014-07-14）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Architecture+and+dynamics+of+Kepler%27s+candidate+multiple+transiting+planet+systems&rft.aufirst=J.&rft.aulast=Lissauer&rft.date=2011-10-13&rft.genre=article&rft.issue=1&rft.jtitle=The+Astrophysical+Journal+Supplement+Series&rft.pages=1-26&rft.volume=197&rft_id=http%3A%2F%2Fiopscience.iop.org%2F0067-0049%2F197%2F1%2F8&rft_id=info%3Aarxiv%2F1102.0543&rft_id=info%3Abibcode%2F2011ApJS..197....8L&rft_id=info%3Adoi%2F10.1088%2F0067-0049%2F197%2F1%2F8&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span> <span style="display:none;font-size:100%" class="error citation-comment">引文使用过时参数<code style="color:inherit; border:inherit; padding:inherit;">coauthors</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#deprecated_params" title="Help:引文格式1错误">帮助</a>)</span></span> </li> <li id="cite_note-EPE-KOI500-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-EPE-KOI500_18-0">^</a></b></span> <span class="reference-text">Extrasolar Planets Encyclopaedia, <a rel="nofollow" class="external text" href="http://exoplanet.eu/star.php?st=KOI-500">KOI-500</a><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<a href="/wiki/Wikipedia:%E5%A4%B1%E6%95%88%E9%93%BE%E6%8E%A5" title="Wikipedia:失效链接"><span title="自2018年1月失效">永久失效連結</span></a>]</span></sup></span> </li> <li id="cite_note-Choi_2012-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-Choi_2012_19-0">^</a></b></span> <span class="reference-text"><cite class="citation web">Choi, Charles Q. <a rel="nofollow" class="external text" href="http://www.space.com/18073-tiny-alien-solar-system-exopl">anets.html Tiniest Alien Solar System Discovered: 5 Packed Planets</a><span style="font-size:100%" class="error citation-comment"> 请检查<code style="color:inherit; border:inherit; padding:inherit;">|url=</code>值 (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#bad_url" title="Help:引文格式1错误">帮助</a>)</span>. <a rel="nofollow" class="external text" href="http://www.space.com">Space.Com web site</a>. TechMediaNetwork.com. 2012-10-15 <span class="reference-accessdate"> [<span class="nowrap">2012-10-16</span>]</span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Tiniest+Alien+Solar+System+Discovered%3A+5+Packed+Planets&rft.aufirst=Charles+Q.&rft.aulast=Choi&rft.date=2012-10-15&rft.genre=unknown&rft.jtitle=%5Bhttp%3A%2F%2Fwww.space.com+Space.Com+web+site%5D&rft_id=http%3A%2F%2Fwww.space.com%2F18073-tiny-alien-solar-system-exopl+anets.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span> <span style="font-size:100%" class="error citation-comment">外部链接存在于<code style="color:inherit; border:inherit; padding:inherit;">|work=</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#param_has_ext_link" title="Help:引文格式1错误">帮助</a>)</span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<a href="/wiki/Wikipedia:%E5%A4%B1%E6%95%88%E9%93%BE%E6%8E%A5" title="Wikipedia:失效链接"><span title="自2018年4月失效">永久失效連結</span></a>]</span></sup></span> </li> <li id="cite_note-BarclayRowe2013-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-BarclayRowe2013_20-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Barclay, T.; Rowe, J. 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April 2011, <b>123</b> (902): 412–42 <span class="reference-accessdate"> [<span class="nowrap">2012-11-07</span>]</span>. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011PASP..123..412W"><span title="Bibcode">Bibcode:2011PASP..123..412W</span></a>. <span class="plainlinks"><a rel="nofollow" class="external text" href="//arxiv.org/abs/1012.5676"><span title="arXiv">arXiv:1012.5676</span></a> <span typeof="mw:File"><span title="可免费查阅"><img alt="可免费查阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span></span>. <a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F659427"><span title="數位物件識別號">doi:10.1086/659427</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=The+Exoplanet+Orbit+Database&rft.aufirst=J.+T.&rft.aulast=Wright&rft.date=2011-04&rft.genre=article&rft.issue=902&rft.jtitle=Publications+of+the+Astronomical+Society+of+the+Pacific&rft.pages=412-42&rft.volume=123&rft_id=http%3A%2F%2Fwww.jstor.org%2Fstable%2Finfo%2F10.1086%2F659427&rft_id=info%3Aarxiv%2F1012.5676&rft_id=info%3Abibcode%2F2011PASP..123..412W&rft_id=info%3Adoi%2F10.1086%2F659427&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span> <span style="display:none;font-size:100%" class="error citation-comment">引文使用过时参数<code style="color:inherit; border:inherit; padding:inherit;">coauthors</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#deprecated_params" title="Help:引文格式1错误">帮助</a>)</span></span> </li> <li id="cite_note-Terquem_2007-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-Terquem_2007_22-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Terquem, C.; Papaloizou, J. C. B. <a rel="nofollow" class="external text" href="http://iopscience.iop.org/0004-637X/654/2/1110/">Migration and the Formation of Systems of Hot Super-Earths and Neptunes</a>. <a href="/wiki/The_Astrophysical_Journal" class="mw-redirect" title="The Astrophysical Journal">The Astrophysical Journal</a>. 2007-01-10, <b>654</b> (2): 1110–1120 <span class="reference-accessdate"> [<span class="nowrap">2012-11-08</span>]</span>. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007ApJ...654.1110T"><span title="Bibcode">Bibcode:2007ApJ...654.1110T</span></a>. <span class="plainlinks"><a rel="nofollow" class="external text" href="//arxiv.org/abs/astro-ph/0609779"><span title="arXiv">arXiv:astro-ph/0609779</span></a> <span typeof="mw:File"><span title="可免费查阅"><img alt="可免费查阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span></span>. <a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F509497"><span title="數位物件識別號">doi:10.1086/509497</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Migration+and+the+Formation+of+Systems+of+Hot+Super-Earths+and+Neptunes&rft.aufirst=C.&rft.aulast=Terquem&rft.date=2007-01-10&rft.genre=article&rft.issue=2&rft.jtitle=The+Astrophysical+Journal&rft.pages=1110-1120&rft.volume=654&rft_id=http%3A%2F%2Fiopscience.iop.org%2F0004-637X%2F654%2F2%2F1110%2F&rft_id=info%3Aarxiv%2Fastro-ph%2F0609779&rft_id=info%3Abibcode%2F2007ApJ...654.1110T&rft_id=info%3Adoi%2F10.1086%2F509497&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span> <span style="display:none;font-size:100%" class="error citation-comment">引文使用过时参数<code style="color:inherit; border:inherit; padding:inherit;">coauthors</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#deprecated_params" title="Help:引文格式1错误">帮助</a>)</span></span> </li> <li id="cite_note-Langford-26"><span class="mw-cite-backlink">^ <a href="#cite_ref-Langford_26-0"><sup><b>23.0</b></sup></a> <a href="#cite_ref-Langford_26-1"><sup><b>23.1</b></sup></a> <a href="#cite_ref-Langford_26-2"><sup><b>23.2</b></sup></a></span> <span class="reference-text"><cite class="citation web">Langford, Peter M. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120111153545/http://www.astronomy.org.gg/venustransitsb.htm">Transits of Venus</a>. <a rel="nofollow" class="external text" href="http://www.astronomy.org.gg/">La Société Guernesiaise Astronomy Section web site</a>. Astronomical Society of the Channel Island of Guernsey. September 1998 <span class="reference-accessdate"> [<span class="nowrap">2012-03-01</span>]</span>. （<a rel="nofollow" class="external text" href="http://www.astronomy.org.gg/venustransitsb.htm">原始内容</a>存档于2012-01-11）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Transits+of+Venus&rft.aufirst=Peter+M.&rft.aulast=Langford&rft.date=1998-09&rft.genre=unknown&rft.jtitle=%5Bhttp%3A%2F%2Fwww.astronomy.org.gg%2F+La+Soci%C3%A9t%C3%A9+Guernesiaise+Astronomy+Section+web+site%5D&rft_id=http%3A%2F%2Fwww.astronomy.org.gg%2Fvenustransitsb.htm&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Bazsó-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bazsó_27-0">^</a></b></span> <span class="reference-text"> <cite class="citation journal">Bazsó, A.; Eybl, V.; Dvorak, R.; Pilat-Lohinger, E.; Lhotka, C. A survey of near-mean-motion resonances between Venus and Earth. <a href="/w/index.php?title=Celestial_Mechanics_and_Dynamical_Astronomy&action=edit&redlink=1" class="new" title="Celestial Mechanics and Dynamical Astronomy（页面不存在）">Celestial Mechanics and Dynamical Astronomy</a>. 2010, <b>107</b> (1): 63–76. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010CeMDA.107...63B"><span title="Bibcode">Bibcode:2010CeMDA.107...63B</span></a>. <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:117795811"><span title="Semantic Scholar">S2CID 117795811</span></a>. <span class="plainlinks"><a rel="nofollow" class="external text" href="//arxiv.org/abs/0911.2357"><span title="arXiv">arXiv:0911.2357</span></a> <span typeof="mw:File"><span title="可免费查阅"><img alt="可免费查阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span></span>. <a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10569-010-9266-6"><span title="數位物件識別號">doi:10.1007/s10569-010-9266-6</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=A+survey+of+near-mean-motion+resonances+between+Venus+and+Earth&rft.au=Dvorak%2C+R.&rft.au=Eybl%2C+V.&rft.au=Lhotka%2C+C.&rft.au=Pilat-Lohinger%2C+E.&rft.aufirst=A.&rft.aulast=Bazs%C3%B3&rft.date=2010&rft.genre=article&rft.issue=1&rft.jtitle=Celestial+Mechanics+and+Dynamical+Astronomy&rft.pages=63-76&rft.volume=107&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A117795811&rft_id=info%3Aarxiv%2F0911.2357&rft_id=info%3Abibcode%2F2010CeMDA.107...63B&rft_id=info%3Adoi%2F10.1007%2Fs10569-010-9266-6&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Shortt-28"><span class="mw-cite-backlink">^ <a href="#cite_ref-Shortt_28-0"><sup><b>25.0</b></sup></a> <a href="#cite_ref-Shortt_28-1"><sup><b>25.1</b></sup></a></span> <span class="reference-text"><cite class="citation web">Shortt, David. <a rel="nofollow" class="external text" href="http://www.planetary.org/blogs/guest-blogs/Some-Details-About-Transits-of-Venus.html">Some Details About Transits of Venus</a>. Planetary Society web site. <a href="/wiki/The_Planetary_Society" class="mw-redirect" title="The Planetary Society">The Planetary Society</a>. 22 May 2012 <span class="reference-accessdate"> [<span class="nowrap">22 May</span> 2012]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20120607075150/http://www.planetary.org/blogs/guest-blogs/Some-Details-About-Transits-of-Venus.html">存档</a>于2012-06-07）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Some+Details+About+Transits+of+Venus&rft.aufirst=David&rft.aulast=Shortt&rft.date=2012-05-22&rft.genre=unknown&rft.jtitle=Planetary+Society+web+site&rft_id=http%3A%2F%2Fwww.planetary.org%2Fblogs%2Fguest-blogs%2FSome-Details-About-Transits-of-Venus.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Goffin2001-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-Goffin2001_32-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Goffin, E. 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Astronomy and Astrophysics. 2001, <b>365</b> (3): 627–630. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001A&A...365..627G"><span title="Bibcode">Bibcode:2001A&A...365..627G</span></a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1051%2F0004-6361%3A20000023"><span title="數位物件識別號">doi:10.1051/0004-6361:20000023</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=New+determination+of+the+mass+of+Pallas&rft.aufirst=E.&rft.aulast=Goffin&rft.date=2001&rft.genre=article&rft.issue=3&rft.jtitle=Astronomy+and+Astrophysics&rft.pages=627-630&rft.volume=365&rft_id=info%3Abibcode%2F2001A%26A...365..627G&rft_id=info%3Adoi%2F10.1051%2F0004-6361%3A20000023&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Kovačević-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kovačević_33-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Kovačević, A. 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Royal Astronomical Society. 1982, <b>199</b>: 255–265. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1982MNRAS.199..255T"><span title="Bibcode">Bibcode:1982MNRAS.199..255T</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=The+secular+motion+of+Pallas&rft.aufirst=D.+B.&rft.aulast=Taylor&rft.date=1982&rft.genre=article&rft.jtitle=Royal+Astronomical+Society&rft.pages=255-265&rft.volume=199&rft_id=info%3Abibcode%2F1982MNRAS.199..255T&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Goldreich_1965-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-Goldreich_1965_36-0">^</a></b></span> <span class="reference-text"><cite class="citation journal"><a href="/w/index.php?title=Peter_Goldreich&action=edit&redlink=1" class="new" title="Peter Goldreich（页面不存在）">Goldreich, P.</a> <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1965MNRAS.130..159G">An explanation of the frequent occurrence of commensurable mean motions in the solar system</a>. <a href="/wiki/Monthly_Notices_of_the_Royal_Astronomical_Society" class="mw-redirect" title="Monthly Notices of the Royal Astronomical Society">Monthly Notices of the Royal Astronomical Society</a>. 1965, <b>130</b> (3): 159–181 <span class="reference-accessdate"> [<span class="nowrap">2012-11-07</span>]</span>. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1965MNRAS.130..159G"><span title="Bibcode">Bibcode:1965MNRAS.130..159G</span></a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20190419023334/http://adsabs.harvard.edu/abs/1965MNRAS.130..159G">存档</a>于2019-04-19）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=An+explanation+of+the+frequent+occurrence+of+commensurable+mean+motions+in+the+solar+system&rft.aufirst=P.&rft.aulast=Goldreich&rft.date=1965&rft.genre=article&rft.issue=3&rft.jtitle=Monthly+Notices+of+the+Royal+Astronomical+Society&rft.pages=159-181&rft.volume=130&rft_id=http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1965MNRAS.130..159G&rft_id=info%3Abibcode%2F1965MNRAS.130..159G&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Chen2008-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-Chen2008_37-0">^</a></b></span> <span class="error mw-ext-cite-error" lang="zh" dir="ltr">引用错误：没有为名为<code>Chen2008</code>的参考文献提供内容</span></li> <li id="cite_note-Murray_1990-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-Murray_1990_40-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Murray, C. 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P. <a rel="nofollow" class="external text" href="http://www.nature.com/nature/journal/v348/n6301/abs/348499a0.html">Orbits of shepherd satellites deduced from the structure of the rings of Uranus</a>. <a href="/wiki/Nature_(journal)" class="mw-redirect" title="Nature (journal)">Nature</a>. 1990-12-06, <b>348</b> (6301): 499–502 <span class="reference-accessdate"> [<span class="nowrap">2012-02-20</span>]</span>. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1990Natur.348..499M"><span title="Bibcode">Bibcode:1990Natur.348..499M</span></a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F348499a0"><span title="數位物件識別號">doi:10.1038/348499a0</span></a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20131231000604/http://www.nature.com/nature/journal/v348/n6301/abs/348499a0.html">存档</a>于2013-12-31）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Orbits+of+shepherd+satellites+deduced+from+the+structure+of+the+rings+of+Uranus&rft.aufirst=C.+D.&rft.aulast=Murray&rft.date=1990-12-06&rft.genre=article&rft.issue=6301&rft.jtitle=Nature&rft.pages=499-502&rft.volume=348&rft_id=http%3A%2F%2Fwww.nature.com%2Fnature%2Fjournal%2Fv348%2Fn6301%2Fabs%2F348499a0.html&rft_id=info%3Abibcode%2F1990Natur.348..499M&rft_id=info%3Adoi%2F10.1038%2F348499a0&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span> <span style="display:none;font-size:100%" class="error citation-comment">引文使用过时参数<code style="color:inherit; border:inherit; padding:inherit;">coauthors</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#deprecated_params" title="Help:引文格式1错误">帮助</a>)</span></span> </li> <li id="cite_note-Tittemore_Wisdom_1990-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-Tittemore_Wisdom_1990_41-0">^</a></b></span> <span class="error mw-ext-cite-error" lang="zh" dir="ltr">引用错误：没有为名为<code>Tittemore Wisdom 1990</code>的参考文献提供内容</span></li> <li id="cite_note-Tittemore1988-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-Tittemore1988_43-0">^</a></b></span> <span class="error mw-ext-cite-error" lang="zh" dir="ltr">引用错误：没有为名为<code>Tittemore1988</code>的参考文献提供内容</span></li> <li id="cite_note-ZhangHamilton2007-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-ZhangHamilton2007_45-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Zhang, K.; Hamilton, D. P. Orbital resonances in the inner neptunian system: I. The 2:1 Proteus–Larissa mean-motion resonance. Icarus. 2007-06, <b>188</b> (2): 386–399. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2007Icar..188..386Z"><span title="Bibcode">Bibcode:2007Icar..188..386Z</span></a>. <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/0019-1035"><span title="国际标准连续出版物号">ISSN 0019-1035</span></a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.icarus.2006.12.002"><span title="數位物件識別號">doi:10.1016/j.icarus.2006.12.002</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Orbital+resonances+in+the+inner+neptunian+system%3A+I.+The+2%3A1+Proteus%E2%80%93Larissa+mean-motion+resonance&rft.au=Hamilton%2C+D.+P.&rft.aufirst=K.&rft.aulast=Zhang&rft.date=2007-06&rft.genre=article&rft.issn=00191035&rft.issue=2&rft.jtitle=Icarus&rft.pages=386-399&rft.volume=188&rft_id=info%3Abibcode%2F2007Icar..188..386Z&rft_id=info%3Adoi%2F10.1016%2Fj.icarus.2006.12.002&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-ZhangHamilton2008-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-ZhangHamilton2008_46-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Zhang, K.; Hamilton, D. P. Orbital resonances in the inner neptunian system: II. Resonant history of Proteus, Larissa, Galatea, and Despina. Icarus. 2008-01, <b>193</b> (1): 267–282. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008Icar..193..267Z"><span title="Bibcode">Bibcode:2008Icar..193..267Z</span></a>. <a rel="nofollow" class="external text" href="//www.worldcat.org/issn/0019-1035"><span title="国际标准连续出版物号">ISSN 0019-1035</span></a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.icarus.2007.08.024"><span title="數位物件識別號">doi:10.1016/j.icarus.2007.08.024</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Orbital+resonances+in+the+inner+neptunian+system%3A+II.+Resonant+history+of+Proteus%2C+Larissa%2C+Galatea%2C+and+Despina&rft.au=Hamilton%2C+D.+P.&rft.aufirst=K.&rft.aulast=Zhang&rft.date=2008-01&rft.genre=article&rft.issn=00191035&rft.issue=1&rft.jtitle=Icarus&rft.pages=267-282&rft.volume=193&rft_id=info%3Abibcode%2F2008Icar..193..267Z&rft_id=info%3Adoi%2F10.1016%2Fj.icarus.2007.08.024&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Matson-47"><span class="mw-cite-backlink">^ <a href="#cite_ref-Matson_47-0"><sup><b>36.0</b></sup></a> <a href="#cite_ref-Matson_47-1"><sup><b>36.1</b></sup></a> <a href="#cite_ref-Matson_47-2"><sup><b>36.2</b></sup></a> <a href="#cite_ref-Matson_47-3"><sup><b>36.3</b></sup></a></span> <span class="reference-text"><cite class="citation web">Matson, J. <a rel="nofollow" class="external text" href="http://www.scientificamerican.com/article.cfm?id=pluto-moon-p5">New Moon for Pluto: Hubble Telescope Spots a 5th Plutonian Satellite</a>. <a href="/wiki/Scientific_American" class="mw-redirect" title="Scientific American">Scientific American</a> web site. 11 July 2012 <span class="reference-accessdate"> [<span class="nowrap">12 July</span> 2012]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20121021144023/http://www.scientificamerican.com/article.cfm?id=pluto-moon-p5">存档</a>于2012-10-21）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=New+Moon+for+Pluto%3A+Hubble+Telescope+Spots+a+5th+Plutonian+Satellite&rft.aufirst=J.&rft.aulast=Matson&rft.date=2012-07-11&rft.genre=unknown&rft.jtitle=Scientific+American+web+site&rft_id=http%3A%2F%2Fwww.scientificamerican.com%2Farticle.cfm%3Fid%3Dpluto-moon-p5&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-WardCanup2006-48"><span class="mw-cite-backlink">^ <a href="#cite_ref-WardCanup2006_48-0"><sup><b>37.0</b></sup></a> <a href="#cite_ref-WardCanup2006_48-1"><sup><b>37.1</b></sup></a></span> <span class="reference-text"><cite class="citation journal">Ward, William R.; Canup, Robin M. Forced Resonant Migration of Pluto's Outer Satellites by Charon. Science. 2006, <b>313</b> (5790): 1107–1109. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2006Sci...313.1107W"><span title="Bibcode">Bibcode:2006Sci...313.1107W</span></a>. <a rel="nofollow" class="external text" href="//www.ncbi.nlm.nih.gov/pubmed/16825533"><span title="公共医学识别码">PMID 16825533</span></a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.1127293"><span title="數位物件識別號">doi:10.1126/science.1127293</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Forced+Resonant+Migration+of+Pluto%27s+Outer+Satellites+by+Charon&rft.au=Canup%2C+Robin+M.&rft.aufirst=William+R.&rft.aulast=Ward&rft.date=2006&rft.genre=article&rft.issue=5790&rft.jtitle=Science&rft.pages=1107-1109&rft.volume=313&rft_id=info%3Abibcode%2F2006Sci...313.1107W&rft_id=info%3Adoi%2F10.1126%2Fscience.1127293&rft_id=info%3Apmid%2F16825533&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Ragozzine&Brown2009-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ragozzine&Brown2009_49-0">^</a></b></span> <span class="reference-text"> <cite class="citation journal">Ragozzine, D.; Brown, M.E. Orbits and Masses of the Satellites of the Dwarf Planet Haumea = 2003 EL61. The Astronomical Journal. 2009, <b>137</b> (6): 4766–4776. <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009AJ....137.4766R"><span title="Bibcode">Bibcode:2009AJ....137.4766R</span></a>. <span class="plainlinks"><a rel="nofollow" class="external text" href="//arxiv.org/abs/0903.4213"><span title="arXiv">arXiv:0903.4213</span></a> <span typeof="mw:File"><span title="可免费查阅"><img alt="可免费查阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span></span>. <a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F0004-6256%2F137%2F6%2F4766"><span title="數位物件識別號">doi:10.1088/0004-6256/137/6/4766</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Orbits+and+Masses+of+the+Satellites+of+the+Dwarf+Planet+Haumea+%3D+2003+EL61&rft.aufirst=D.&rft.aulast=Ragozzine&rft.date=2009&rft.genre=article&rft.issue=6&rft.jtitle=The+Astronomical+Journal&rft.pages=4766-4776&rft.volume=137&rft_id=info%3Aarxiv%2F0903.4213&rft_id=info%3Abibcode%2F2009AJ....137.4766R&rft_id=info%3Adoi%2F10.1088%2F0004-6256%2F137%2F6%2F4766&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span> <span style="display:none;font-size:100%" class="error citation-comment">引文使用过时参数<code style="color:inherit; border:inherit; padding:inherit;">coauthors</code> (<a href="/wiki/Help:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E9%94%99%E8%AF%AF#deprecated_params" title="Help:引文格式1错误">帮助</a>)</span></span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="书目"><span id=".E4.B9.A6.E7.9B.AE"></span>书目</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&action=edit&section=11" title="编辑章节：书目"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>C. D. Murray, S. F. Dermott (1999). <i>Solar System Dynamics</i>, Cambridge University Press, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9780521575973" class="internal mw-magiclink-isbn">ISBN 978-0-521-57597-3</a>.</li> <li>Renu Malhotra <i>Orbital Resonances and Chaos in the Solar System</i>. In <i>Solar System Formation and Evolution</i>, ASP Conference Series, <b>149</b>（1998）<a rel="nofollow" class="external text" href="https://web.archive.org/web/20131211165545/http://www.lpl.arizona.edu/people/faculty/malhotra_preprints/rio97.pdf">preprint</a>.</li> <li>Renu Malhotra, <i>The Origin of Pluto's Orbit: Implications for the Solar System Beyond Neptune</i>, The Astronomical Journal, <b>110</b>（1995）, p. 420 <a rel="nofollow" class="external text" href="http://arxiv.org/abs/astro-ph/9504036">Preprint</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20160110075851/http://arxiv.org/abs/astro-ph/9504036">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）.</li> <li><cite class="citation book">Lemaître, A. Resonances: Models and Captures. Souchay, J.; Dvorak, R. (编). Dynamics of Small Solar System Bodies and Exoplanets. Lecture Notes in Physics <b>790</b>. <a href="/wiki/Springer_Science%2BBusiness_Media" class="mw-redirect" title="Springer Science+Business Media">Springer</a>. 2010: 1–62. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-3-642-04457-1" title="Special:网络书源/978-3-642-04457-1"><span title="国际标准书号">ISBN</span> 978-3-642-04457-1</a>. <a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-642-04458-8"><span title="數位物件識別號">doi:10.1007/978-3-642-04458-8</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&rft.atitle=Resonances%3A+Models+and+Captures&rft.aufirst=A.&rft.aulast=Lema%C3%AEtre&rft.btitle=Dynamics+of+Small+Solar+System+Bodies+and+Exoplanets&rft.date=2010&rft.genre=bookitem&rft.isbn=978-3-642-04457-1&rft.pages=1-62&rft.pub=Springer&rft.series=Lecture+Notes+in+Physics&rft_id=info%3Adoi%2F10.1007%2F978-3-642-04458-8&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="外部連結"><span id=".E5.A4.96.E9.83.A8.E9.80.A3.E7.B5.90"></span>外部連結</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF&action=edit&section=12" title="编辑章节：外部連結"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070322212846/http://www.alpheratz.net/murison/asteroids/resonances/">Locations of Solar System Planetary Mean-Motion Resonances</a>. Web calculator that plots distributions of the semimajor axes (or in one case the perihelion distances) of the minor planets in relation to mean-motion resonances of the planets（website maintained by M.A. Murison）。</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">检索自“<a dir="ltr" href="https://zh.wikipedia.org/w/index.php?title=轨道共振&oldid=82749833">https://zh.wikipedia.org/w/index.php?title=轨道共振&oldid=82749833</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:%E9%A1%B5%E9%9D%A2%E5%88%86%E7%B1%BB" title="Special:页面分类">分类</a>：<ul><li><a href="/wiki/Category:%E8%BD%A8%E9%81%93%E5%85%B1%E6%8C%AF" title="Category:轨道共振">轨道共振</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks 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