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href="#Energia"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Energia</span> </div> </a> <ul id="toc-Energia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Trajetória_parabólica_radial" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Trajetória_parabólica_radial"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Trajetória parabólica radial</span> </div> </a> <ul id="toc-Trajetória_parabólica_radial-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ver_também" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ver_também"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Ver também</span> </div> </a> <ul id="toc-Ver_também-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referências" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referências"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Referências</span> </div> </a> <ul id="toc-Referências-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="Conteúdo" 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="Alternar o índice" > <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">Alternar o índice</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">Trajetória parabólica</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="Ir para um artigo noutra língua. Disponível em 17 línguas" > <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-17" 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">17 línguas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B3%D8%A7%D8%B1_%D9%85%D9%83%D8%A7%D9%81%D8%A6" title="مسار مكافئ — árabe" lang="ar" hreflang="ar" data-title="مسار مكافئ" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Traject%C3%B2ria_parab%C3%B2lica" title="Trajectòria parabòlica — catalão" lang="ca" hreflang="ca" data-title="Trajectòria parabòlica" data-language-autonym="Català" data-language-local-name="catalão" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Parabolic_trajectory" title="Parabolic trajectory — inglês" lang="en" hreflang="en" data-title="Parabolic trajectory" data-language-autonym="English" data-language-local-name="inglês" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Trayectoria_parab%C3%B3lica" title="Trayectoria parabólica — espanhol" lang="es" hreflang="es" data-title="Trayectoria parabólica" data-language-autonym="Español" data-language-local-name="espanhol" 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/%D9%85%D8%B3%DB%8C%D8%B1_%D8%B3%D9%87%D9%85%D9%88%DB%8C" title="مسیر سهموی — persa" lang="fa" hreflang="fa" data-title="مسیر سهموی" data-language-autonym="فارسی" data-language-local-name="persa" 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/Paraabelirata" title="Paraabelirata — finlandês" lang="fi" hreflang="fi" data-title="Paraabelirata" data-language-autonym="Suomi" data-language-local-name="finlandês" 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/Trajectoire_parabolique" title="Trajectoire parabolique — francês" lang="fr" hreflang="fr" data-title="Trajectoire parabolique" data-language-autonym="Français" data-language-local-name="francês" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8A%D5%A1%D6%80%D5%A1%D5%A2%D5%B8%D5%AC%D5%AB%D5%AF_%D5%B0%D5%A5%D5%BF%D5%A1%D5%A3%D5%AB%D5%AE" title="Պարաբոլիկ հետագիծ — arménio" lang="hy" hreflang="hy" data-title="Պարաբոլիկ հետագիծ" data-language-autonym="Հայերեն" data-language-local-name="arménio" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Traiettoria_parabolica" title="Traiettoria parabolica — italiano" lang="it" hreflang="it" data-title="Traiettoria parabolica" data-language-autonym="Italiano" data-language-local-name="italiano" 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/%E6%94%BE%E7%89%A9%E7%B7%9A%E8%BB%8C%E9%81%93" title="放物線軌道 — japonês" lang="ja" hreflang="ja" data-title="放物線軌道" data-language-autonym="日本語" data-language-local-name="japonês" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Parabolisk_bane" title="Parabolisk bane — norueguês bokmål" lang="nb" hreflang="nb" data-title="Parabolisk bane" data-language-autonym="Norsk bokmål" data-language-local-name="norueguês bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%B0%D1%80%D0%B0%D0%B1%D0%BE%D0%BB%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D1%82%D1%80%D0%B0%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8%D1%8F" title="Параболическая траектория — russo" lang="ru" hreflang="ru" data-title="Параболическая траектория" data-language-autonym="Русский" data-language-local-name="russo" 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/Parabolic_trajectory" title="Parabolic trajectory — Simple English" lang="en-simple" hreflang="en-simple" data-title="Parabolic trajectory" 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/Parabolick%C3%A1_dr%C3%A1ha" title="Parabolická dráha — eslovaco" lang="sk" hreflang="sk" data-title="Parabolická dráha" data-language-autonym="Slovenčina" data-language-local-name="eslovaco" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%96%E0%B8%B5%E0%B9%82%E0%B8%84%E0%B8%88%E0%B8%A3%E0%B8%9E%E0%B8%B2%E0%B8%A3%E0%B8%B2%E0%B9%82%E0%B8%9A%E0%B8%A5%E0%B8%B2" title="วิถีโคจรพาราโบลา — tailandês" lang="th" hreflang="th" data-title="วิถีโคจรพาราโบลา" data-language-autonym="ไทย" data-language-local-name="tailandês" 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/Parabolik_y%C3%B6r%C3%BCnge" title="Parabolik yörünge — turco" lang="tr" hreflang="tr" data-title="Parabolik yörünge" data-language-autonym="Türkçe" data-language-local-name="turco" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%8B%8B%E7%89%A9%E7%B7%9A%E8%BB%8C%E9%81%93" title="拋物線軌道 — chinês" lang="zh" hreflang="zh" data-title="拋物線軌道" data-language-autonym="中文" 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0;text-align:center}.mw-parser-output .tmbox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .tmbox .mbox-invalid-type{text-align:center}@media(min-width:720px){.mw-parser-output .tmbox{margin:4px 10%}.mw-parser-output .tmbox.mbox-small{clear:right;float:right;margin:4px 0 4px 1em;width:238px}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-night .mw-parser-output .tmbox-speedy{background-color:#310402}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-os .mw-parser-output .tmbox-speedy{background-color:#310402}}body.skin--responsive .mw-parser-output table.tmbox img{max-width:none!important}</style><table class="box-Sem_notas plainlinks metadata ambox ambox-content ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Cite_as_fontes" title="Wikipédia:Livro de estilo/Cite as fontes"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/40px-Text_document_with_red_question_mark.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/60px-Text_document_with_red_question_mark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/80px-Text_document_with_red_question_mark.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">Este artigo ou secção contém <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Cite_as_fontes#Referências_no_fim" title="Wikipédia:Livro de estilo/Cite as fontes">uma lista de referências no fim do texto</a>, mas as suas fontes não são claras porque <b>não são <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Cite_as_fontes#Referências_no_texto" title="Wikipédia:Livro de estilo/Cite as fontes">citadas no corpo do artigo</a></b>, o que <b>compromete a <a href="/wiki/Wikip%C3%A9dia:V" class="mw-redirect" title="Wikipédia:V">confiabilidade</a></b> das informações.<span class="hide-when-compact"> Ajude a <span class="plainlinks"><a class="external text" href="https://pt.wikipedia.org/w/index.php?title=Trajet%C3%B3ria_parab%C3%B3lica&action=edit">melhorar</a></span> este artigo <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Refer%C3%AAncias_e_notas_de_rodap%C3%A9" title="Wikipédia:Livro de estilo/Referências e notas de rodapé">inserindo citações no corpo do artigo</a>.</span> <small class="date-container"><i>(<span class="date">Agosto de 2021</span>)</i></small></div></td></tr></tbody></table> <p>Em <a href="/wiki/Astrodin%C3%A2mica" title="Astrodinâmica">astrodinâmica</a> ou <a href="/wiki/Mec%C3%A2nica_celeste" title="Mecânica celeste">mecânica celeste</a> uma <b>trajetória parabólica</b> é uma <a href="/wiki/%C3%93rbita_kepleriana" title="Órbita kepleriana">órbita kepleriana</a> com <a href="/wiki/Excentricidade_(matem%C3%A1tica)" title="Excentricidade (matemática)">excentricidade</a> igual a 1. Quando se movendo para longe de sua origem é chamada de órbita de escape, caso contrário é uma órbita de captura. </p><p>Sob pressupostos padrões um corpo viajando em uma órbita de escape irá tender ao infinito, com velocidade relativa ao corpo central tendendo a zero, e portando não deverá retornar jamais. Trajetórias parabólicas são um tipo de trajetória de escape de mínimo de energia. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Velocidade">Velocidade</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trajet%C3%B3ria_parab%C3%B3lica&veaction=edit&section=1" title="Editar secção: Velocidade" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trajet%C3%B3ria_parab%C3%B3lica&action=edit&section=1" title="Editar código-fonte da secção: Velocidade"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sob os pressupostos padrões, a <a href="/wiki/Velocidade_orbital" title="Velocidade orbital">velocidade orbital</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 v\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b67d1fd725a759a151374b793113d7a78a65da4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.515ex; height:1.676ex;" alt="{\displaystyle v\,}"></span>) de um corpo viajando ao longo de uma trajetória parabólica pode ser calculada como: </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 v={\sqrt {2\mu \over {r}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>2</mn> <mi>μ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v={\sqrt {2\mu \over {r}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dcaa895efed097dd9e420d787bc17327814b0c24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.95ex; height:6.343ex;" alt="{\displaystyle v={\sqrt {2\mu \over {r}}}}"></span></dd></dl> <p>onde: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86937851b7cb70e8802197a7b5ddcf39c0b02445" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:1.436ex; height:1.676ex;" alt="{\displaystyle r\,\!}"></span> é a <a href="/wiki/Dist%C3%A2ncia_radial_(geometria)" class="mw-redirect" title="Distância radial (geometria)">distância radial</a> do corpo em órbita do <a href="/wiki/Prim%C3%A1rio_(astronomia)" title="Primário (astronomia)">corpo primário</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 \mu \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a66ee9ba05f9085943a89364f6c674143a1881f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:1.789ex; height:2.176ex;" alt="{\displaystyle \mu \,\!}"></span> é o <a href="/wiki/Constante_gravitacional_universal" title="Constante gravitacional universal">parâmetro gravitacional padrão</a>.</li></ul> <p>Em qualquer posição o corpo em órbita tem a <a href="/wiki/Velocidade_de_escape" title="Velocidade de escape">velocidade de escape</a> para aquela posição. </p><p>Se o corpo tem a velocidade de escape em relação à Terra, ele ainda não tem velocidade suficiente para escapar do Sistema Solar, desta forma próximo da Terra a órbita irá se assemelhar a uma parábola, mas mais adiante ela irá se curvar em uma órbita elíptica em torno do Sol. </p><p>Esta velocidade (<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 v\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b67d1fd725a759a151374b793113d7a78a65da4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.515ex; height:1.676ex;" alt="{\displaystyle v\,}"></span>) é similar à <a href="/wiki/Velocidade_orbital" title="Velocidade orbital">velocidade orbital</a> de um corpo em <a href="/wiki/%C3%93rbita_circular" title="Órbita circular">órbita circular</a> de raio igual à posição radial do corpo orbitante na trajetória parabólica: </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 v={\sqrt {2}}\cdot v_{O}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>⋅</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>O</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v={\sqrt {2}}\cdot v_{O}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7976c203ec82273275a09797d32587ee8296961c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.617ex; height:3.009ex;" alt="{\displaystyle v={\sqrt {2}}\cdot v_{O}}"></span></dd></dl> <p>onde: </p> <ul><li><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 v_{O}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>O</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{O}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c08ad410946c74d7201af0a73e096814518c22bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:3.001ex; height:2.009ex;" alt="{\displaystyle v_{O}\,\!}"></span> é a <a href="/wiki/Velocidade_orbital" title="Velocidade orbital">velocidade orbital</a> de um corpo em <a href="/wiki/%C3%93rbita_circular" title="Órbita circular">órbita circular</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Equação_do_deslocamento"><span id="Equa.C3.A7.C3.A3o_do_deslocamento"></span>Equação do deslocamento</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trajet%C3%B3ria_parab%C3%B3lica&veaction=edit&section=2" title="Editar secção: Equação do deslocamento" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trajet%C3%B3ria_parab%C3%B3lica&action=edit&section=2" title="Editar código-fonte da secção: Equação do deslocamento"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sob os pressupostos padrões, para um corpo que se move neste tipo de trajetória, a <a href="/w/index.php?title=Equa%C3%A7%C3%A3o_orbital&action=edit&redlink=1" class="new" title="Equação orbital (página não existe)">equação orbital</a> é: </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 r={{h^{2}} \over {\mu }}{{1} \over {1+\cos \nu }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>μ</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mi>ν</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={{h^{2}} \over {\mu }}{{1} \over {1+\cos \nu }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba9f178925b00c50cce44b9de349ae8b68840dd9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.946ex; height:6.176ex;" alt="{\displaystyle r={{h^{2}} \over {\mu }}{{1} \over {1+\cos \nu }}}"></span></dd></dl> <p>onde: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f08ce4d4c86c5b43f36c8435fb598da6471047c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.436ex; height:1.676ex;" alt="{\displaystyle r\,}"></span> é a distância radial do <a href="/w/index.php?title=Corpo_orbitante&action=edit&redlink=1" class="new" title="Corpo orbitante (página não existe)">corpo orbitante</a> ao <a href="/wiki/Prim%C3%A1rio_(astronomia)" title="Primário (astronomia)">corpo primário</a>,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cecd947e6666832fcc39909b00dbde70caa9cf8c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.726ex; height:2.176ex;" alt="{\displaystyle h\,}"></span> é o <a href="/w/index.php?title=Momento_angular_espec%C3%ADfico&action=edit&redlink=1" class="new" title="Momento angular específico (página não existe)">momento angular específico</a> do <a href="/w/index.php?title=Corpo_orbitante&action=edit&redlink=1" class="new" title="Corpo orbitante (página não existe)">corpo orbitante</a>,</li> <li><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 \nu \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32a13ab64f1a72c7827e70aed42c8fcb323bd7bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.619ex; height:1.676ex;" alt="{\displaystyle \nu \,}"></span> é a <a href="/wiki/Anomalia_verdadeira" title="Anomalia verdadeira">anomalia verdadeira</a> do <a href="/w/index.php?title=Corpo_orbitante&action=edit&redlink=1" class="new" title="Corpo orbitante (página não existe)">corpo orbitante</a>,</li> <li><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 \mu \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d20addf0d9f04e185714134b97726c4bf17d340" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.789ex; height:2.176ex;" alt="{\displaystyle \mu \,}"></span> é o <a href="/wiki/Constante_gravitacional_universal" title="Constante gravitacional universal">parâmetro gravitacional padrão</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Energia">Energia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trajet%C3%B3ria_parab%C3%B3lica&veaction=edit&section=3" title="Editar secção: Energia" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trajet%C3%B3ria_parab%C3%B3lica&action=edit&section=3" title="Editar código-fonte da secção: Energia"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sob os pressupostos padrões, a <a href="/wiki/Energia_orbital_espec%C3%ADfica" title="Energia orbital específica">energia orbital específica</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 \epsilon \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϵ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/587ec0778f84a86a9567b2e296aec908d895ff21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.331ex; height:1.676ex;" alt="{\displaystyle \epsilon \,}"></span>) da trajetória parabólica é zero, assim a <a href="/w/index.php?title=Equa%C3%A7%C3%A3o_de_conserva%C3%A7%C3%A3o_de_energia_orbital&action=edit&redlink=1" class="new" title="Equação de conservação de energia orbital (página não existe)">equação de conservação de energia orbital</a> para esta trajetória assume a forma: </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 \epsilon ={v^{2} \over 2}-{\mu \over {r}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϵ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \epsilon ={v^{2} \over 2}-{\mu \over {r}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82a0b65e3fcb6a9b7d3441c35f21d10b21302dbb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.4ex; height:5.676ex;" alt="{\displaystyle \epsilon ={v^{2} \over 2}-{\mu \over {r}}=0}"></span></dd></dl> <p>onde: </p> <ul><li><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 v\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b67d1fd725a759a151374b793113d7a78a65da4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.515ex; height:1.676ex;" alt="{\displaystyle v\,}"></span> é a <a href="/wiki/Velocidade_orbital" title="Velocidade orbital">velocidade orbital</a> do <a href="/w/index.php?title=Corpo_orbitante&action=edit&redlink=1" class="new" title="Corpo orbitante (página não existe)">corpo orbitante</a>,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f08ce4d4c86c5b43f36c8435fb598da6471047c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.436ex; height:1.676ex;" alt="{\displaystyle r\,}"></span> é a distância radial do <a href="/w/index.php?title=Corpo_orbitante&action=edit&redlink=1" class="new" title="Corpo orbitante (página não existe)">corpo orbitante</a> ao <a href="/wiki/Prim%C3%A1rio_(astronomia)" title="Primário (astronomia)">corpo primário</a>,</li> <li><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 \mu \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d20addf0d9f04e185714134b97726c4bf17d340" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.789ex; height:2.176ex;" alt="{\displaystyle \mu \,}"></span> é o <a href="/wiki/Constante_gravitacional_universal" title="Constante gravitacional universal">parâmetro gravitacional padrão</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Trajetória_parabólica_radial"><span id="Trajet.C3.B3ria_parab.C3.B3lica_radial"></span>Trajetória parabólica radial</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trajet%C3%B3ria_parab%C3%B3lica&veaction=edit&section=4" title="Editar secção: Trajetória parabólica radial" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trajet%C3%B3ria_parab%C3%B3lica&action=edit&section=4" title="Editar código-fonte da secção: Trajetória parabólica radial"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Uma <i>trajetória parabólica radial</i>, é uma <a href="/wiki/Trajet%C3%B3ria_Radial" class="mw-redirect" title="Trajetória Radial">trajetória em linha reta</a> não periódica onde a velocidade relativa dos dois objetos, sempre excedem a <a href="/wiki/Velocidade_de_escape" title="Velocidade de escape">velocidade de escape</a>. Existem dois casos: os corpos se movem se aproximando ou se afastando um do outro. </p><p>Existe uma fórmula simples para a posição em função do tempo: </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 r=(4.5\mu t^{2})^{1/3}\!\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>4.5</mn> <mi>μ</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=(4.5\mu t^{2})^{1/3}\!\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58fc29308997d4232e8f695051d0cc1696d0648c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.922ex; height:3.343ex;" alt="{\displaystyle r=(4.5\mu t^{2})^{1/3}\!\,}"></span></dd></dl> <p>onde </p> <ul><li>μ é a <a href="/wiki/Constante_gravitacional_universal" title="Constante gravitacional universal">Constante Gravitacional</a></li> <li><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 t=0\!\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mn>0</mn> <mspace width="negativethinmathspace" /> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t=0\!\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1f2e6561a8afba8ecb5c84369fd8a0f575477b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.101ex; height:2.176ex;" alt="{\displaystyle t=0\!\,}"></span> corresponde ao tempo estimado de início ou fim no centro do corpo central.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Ver_também"><span id="Ver_tamb.C3.A9m"></span>Ver também</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Trajet%C3%B3ria_parab%C3%B3lica&veaction=edit&section=5" title="Editar secção: Ver também" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Trajet%C3%B3ria_parab%C3%B3lica&action=edit&section=5" title="Editar código-fonte da secção: Ver também"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%C3%93rbita" title="Órbita">Órbita</a></li> <li><a href="/wiki/%C3%93rbita_circular" title="Órbita circular">Órbita circular</a></li> <li><a href="/wiki/%C3%93rbita_el%C3%ADptica" title="Órbita elíptica">Órbita elíptica</a></li> <li><a href="/wiki/%C3%93rbita_kepleriana" title="Órbita kepleriana">Órbita kepleriana</a></li> <li><a href="/wiki/Par%C3%A1bola" title="Parábola">Parábola</a></li> <li><a href="/wiki/Trajet%C3%B3ria_hiperb%C3%B3lica" title="Trajetória hiperbólica">Trajetória hiperbólica</a></li></ul> <h2 id="Referências" style="cursor: help;" title="Esta seção foi configurada para não ser editável diretamente. Edite a página toda ou a seção anterior em vez disso."><span id="Refer.C3.AAncias"></span>Referências</h2> <div class="reflist" style="list-style-type: decimal;"></div> <ul><li><cite class="citation book">Bate, Roger R.; Donald D. Mueller, Jerry E. White (1971). <a rel="nofollow" class="external text" href="http://books.google.com.br/books/about/Fundamentals_of_astrodynamics.html?id=UtJK8cetqGkC&redir_esc=y"><i>Fundamentals of astrodynamics</i></a> (em inglês) illustrated ed. [S.l.]: Courier Dover Publications. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Especial:Fontes_de_livros/0486600610" title="Especial:Fontes de livros/0486600610">0486600610</a><span class="reference-accessdate">. Consultado em 18 de abril de 2013</span></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3ATrajet%C3%B3ria+parab%C3%B3lica&rft.aufirst=Roger+R.&rft.aulast=Bate&rft.btitle=Fundamentals+of+astrodynamics&rft.date=1971&rft.edition=illustrated&rft.genre=book&rft.isbn=0486600610&rft.pub=Courier+Dover+Publications&rft_id=http%3A%2F%2Fbooks.google.com.br%2Fbooks%2Fabout%2FFundamentals_of_astrodynamics.html%3Fid%3DUtJK8cetqGkC%26redir_esc%3Dy&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span> <span style="display:none;font-size:100%" class="error citation-comment">A referência emprega parâmetros obsoletos <code style="color:inherit; border:inherit; padding:inherit;">|coautor=</code> (<a href="/wiki/Ajuda:Erros_nas_refer%C3%AAncias#deprecated_params" title="Ajuda:Erros nas referências">ajuda</a>)</span></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Obtida de "<a dir="ltr" href="https://pt.wikipedia.org/w/index.php?title=Trajetória_parabólica&oldid=68175160">https://pt.wikipedia.org/w/index.php?title=Trajetória_parabólica&oldid=68175160</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Especial:Categorias" title="Especial:Categorias">Categoria</a>: <ul><li><a href="/wiki/Categoria:%C3%93rbitas" title="Categoria:Órbitas">Órbitas</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categorias ocultas: <ul><li><a href="/wiki/Categoria:!Artigos_que_carecem_de_notas_de_rodap%C3%A9_desde_agosto_de_2021" title="Categoria:!Artigos que carecem de notas de rodapé desde agosto de 2021">!Artigos que carecem de notas de rodapé desde agosto de 2021</a></li><li><a href="/wiki/Categoria:!Artigos_que_carecem_de_notas_de_rodap%C3%A9_sem_indica%C3%A7%C3%A3o_de_tema" title="Categoria:!Artigos que carecem de notas de rodapé sem indicação de tema">!Artigos que carecem de notas de rodapé sem indicação de tema</a></li><li><a href="/wiki/Categoria:!P%C3%A1ginas_que_usam_refer%C3%AAncias_com_par%C3%A2metros_obsoletas" title="Categoria:!Páginas que usam referências com parâmetros obsoletas">!Páginas que usam referências com parâmetros obsoletas</a></li><li><a href="/wiki/Categoria:!CS1_ingl%C3%AAs-fontes_em_l%C3%ADngua_(en)" title="Categoria:!CS1 inglês-fontes em língua (en)">!CS1 inglês-fontes em língua (en)</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Esta página foi editada pela última vez às 23h27min de 24 de junho de 2024.</li> <li id="footer-info-copyright">Este texto é disponibilizado nos termos da licença <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.pt">Atribuição-CompartilhaIgual 4.0 Internacional (CC BY-SA 4.0) da Creative Commons</a>; pode estar sujeito a condições adicionais. 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