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Available in 33 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-33" 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">33 kalbų</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%B1%D9%83%D8%B2_%D8%AB%D9%82%D9%84" title="مركز ثقل – arabų" lang="ar" hreflang="ar" data-title="مركز ثقل" data-language-autonym="العربية" data-language-local-name="arabų" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Te%C5%BEi%C5%A1te" title="Težište – bosnių" lang="bs" hreflang="bs" data-title="Težište" data-language-autonym="Bosanski" data-language-local-name="bosnių" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Centre_de_massa" title="Centre de massa – katalonų" lang="ca" hreflang="ca" data-title="Centre de massa" data-language-autonym="Català" data-language-local-name="katalonų" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%82%D9%88%D8%B1%D8%B3%D8%A7%DB%8C%DB%8C%DA%AF%DB%95" title="قورساییگە – soranių kurdų" lang="ckb" hreflang="ckb" data-title="قورساییگە" data-language-autonym="کوردی" data-language-local-name="soranių kurdų" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/T%C4%9B%C5%BEi%C5%A1t%C4%9B" title="Těžiště – čekų" lang="cs" hreflang="cs" data-title="Těžiště" data-language-autonym="Čeština" data-language-local-name="čekų" 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/Tyngdepunkt" title="Tyngdepunkt – danų" lang="da" hreflang="da" data-title="Tyngdepunkt" data-language-autonym="Dansk" data-language-local-name="danų" 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/Massenmittelpunkt" title="Massenmittelpunkt – vokiečių" lang="de" hreflang="de" data-title="Massenmittelpunkt" data-language-autonym="Deutsch" data-language-local-name="vokiečių" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%AD%CE%BD%CF%84%CF%81%CE%BF_%CE%BC%CE%AC%CE%B6%CE%B1%CF%82" title="Κέντρο μάζας – graikų" lang="el" hreflang="el" data-title="Κέντρο μάζας" data-language-autonym="Ελληνικά" data-language-local-name="graikų" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en badge-Q70893996 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Center_of_gravity" title="Center of gravity – anglų" lang="en" hreflang="en" data-title="Center of gravity" data-language-autonym="English" data-language-local-name="anglų" 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/Centro_de_masas" title="Centro de masas – ispanų" lang="es" hreflang="es" data-title="Centro de masas" data-language-autonym="Español" data-language-local-name="ispanų" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Raskuskese" title="Raskuskese – estų" lang="et" hreflang="et" data-title="Raskuskese" data-language-autonym="Eesti" data-language-local-name="estų" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Grabitate-zentro" title="Grabitate-zentro – baskų" lang="eu" hreflang="eu" data-title="Grabitate-zentro" data-language-autonym="Euskara" data-language-local-name="baskų" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa badge-Q70893996 mw-list-item" title=""><a href="https://fa.wikipedia.org/wiki/%DA%AF%D8%B1%D8%A7%D9%86%DB%8C%E2%80%8C%DA%AF%D8%A7%D9%87" title="گرانی‌گاه – persų" lang="fa" hreflang="fa" data-title="گرانی‌گاه" data-language-autonym="فارسی" data-language-local-name="persų" 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/Painopiste" title="Painopiste – suomių" lang="fi" hreflang="fi" data-title="Painopiste" data-language-autonym="Suomi" data-language-local-name="suomių" 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/Barycentre_(physique)" title="Barycentre (physique) – prancūzų" lang="fr" hreflang="fr" data-title="Barycentre (physique)" data-language-autonym="Français" data-language-local-name="prancūzų" 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/Centro_de_gravidade" title="Centro de gravidade – galisų" lang="gl" hreflang="gl" data-title="Centro de gravidade" data-language-autonym="Galego" data-language-local-name="galisų" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%97%E0%A5%81%E0%A4%B0%E0%A5%81%E0%A4%A4%E0%A5%8D%E0%A4%B5_%E0%A4%95%E0%A5%87%E0%A4%A8%E0%A5%8D%E0%A4%A6%E0%A5%8D%E0%A4%B0" title="गुरुत्व केन्द्र – hindi" lang="hi" hreflang="hi" data-title="गुरुत्व केन्द्र" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Te%C5%BEi%C5%A1te" title="Težište – kroatų" lang="hr" hreflang="hr" data-title="Težište" data-language-autonym="Hrvatski" data-language-local-name="kroatų" 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/%D4%BE%D5%A1%D5%B6%D6%80%D5%B8%D6%82%D5%A9%D5%B5%D5%A1%D5%B6_%D5%AF%D5%A5%D5%B6%D5%BF%D6%80%D5%B8%D5%B6" title="Ծանրության կենտրոն – armėnų" lang="hy" hreflang="hy" data-title="Ծանրության կենտրոն" data-language-autonym="Հայերեն" data-language-local-name="armėnų" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Baricentro" title="Baricentro – ido" lang="io" hreflang="io" data-title="Baricentro" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%83%D1%8B%D1%80%D0%BB%D1%8B%D2%9B_%D1%86%D0%B5%D0%BD%D1%82%D1%80%D1%96" title="Ауырлық центрі – kazachų" lang="kk" hreflang="kk" data-title="Ауырлық центрі" data-language-autonym="Қазақша" data-language-local-name="kazachų" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%97%E0%B3%81%E0%B2%B0%E0%B3%81%E0%B2%A4%E0%B3%8D%E0%B2%B5_%E0%B2%95%E0%B3%87%E0%B2%82%E0%B2%A6%E0%B3%8D%E0%B2%B0" title="ಗುರುತ್ವ ಕೇಂದ್ರ – kanadų" lang="kn" hreflang="kn" data-title="ಗುರುತ್ವ ಕೇಂದ್ರ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kanadų" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Navenda_giraniy%C3%AA" title="Navenda giraniyê – kurdų" lang="ku" hreflang="ku" data-title="Navenda giraniyê" data-language-autonym="Kurdî" data-language-local-name="kurdų" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/%C5%9Arodek_masy" title="Środek masy – lenkų" lang="pl" hreflang="pl" data-title="Środek masy" data-language-autonym="Polski" data-language-local-name="lenkų" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Bariss%C3%A8nter" title="Barissènter – italų kalbos Pjemonto tarmė" lang="pms" hreflang="pms" data-title="Barissènter" data-language-autonym="Piemontèis" data-language-local-name="italų kalbos Pjemonto tarmė" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Centro_de_massas" title="Centro de massas – portugalų" lang="pt" hreflang="pt" data-title="Centro de massas" data-language-autonym="Português" data-language-local-name="portugalų" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Te%C5%BEi%C5%A1te" title="Težište – serbų-kroatų" lang="sh" hreflang="sh" data-title="Težište" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbų-kroatų" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C5%A4a%C5%BEisko_(fyzika)" title="Ťažisko (fyzika) – slovakų" lang="sk" hreflang="sk" data-title="Ťažisko (fyzika)" data-language-autonym="Slovenčina" data-language-local-name="slovakų" 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/Masno_sredi%C5%A1%C4%8De" title="Masno središče – slovėnų" lang="sl" hreflang="sl" data-title="Masno središče" data-language-autonym="Slovenščina" data-language-local-name="slovėnų" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AF%8A%E0%AE%A4%E0%AF%81_%E0%AE%A8%E0%AE%BF%E0%AE%B1%E0%AF%88_%E0%AE%AE%E0%AF%88%E0%AE%AF%E0%AE%AE%E0%AF%8D" title="பொது நிறை மையம் – tamilų" lang="ta" hreflang="ta" data-title="பொது நிறை மையம்" data-language-autonym="தமிழ்" data-language-local-name="tamilų" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/A%C4%9F%C4%B1rl%C4%B1k_merkezi" title="Ağırlık merkezi – turkų" lang="tr" hreflang="tr" data-title="Ağırlık merkezi" data-language-autonym="Türkçe" data-language-local-name="turkų" 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%90%D0%B2%D1%8B%D1%80%D0%BB%D1%8B%D0%BA_%D2%AF%D0%B7%D3%99%D0%B3%D0%B5" title="Авырлык үзәге – totorių" lang="tt" hreflang="tt" data-title="Авырлык үзәге" data-language-autonym="Татарча / tatarça" data-language-local-name="totorių" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Og%CA%BBirlik_markazi" title="Ogʻirlik markazi – uzbekų" lang="uz" hreflang="uz" data-title="Ogʻirlik markazi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbekų" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</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/Q114084#sitelinks-wikipedia" title="Keisti tarpkalbines nuorodas" class="wbc-editpage">Keisti nuorodas</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Vardų sritys"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs 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Vikipedijos, laisvosios enciklopedijos.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="lt" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Vaizdas:Solar_system_barycenter.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Solar_system_barycenter.svg/380px-Solar_system_barycenter.svg.png" decoding="async" width="380" height="377" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Solar_system_barycenter.svg/570px-Solar_system_barycenter.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Solar_system_barycenter.svg/760px-Solar_system_barycenter.svg.png 2x" data-file-width="463" data-file-height="459" /></a><figcaption>Saulės sistemos baricentro judėjimas Saulės atžvilgiu.</figcaption></figure> <p><b>Baricentras</b> yra dviejų arba daugiau kūnų bendras <a href="/wiki/Mas%C4%97s_centras" title="Masės centras">masės centras</a>. Pavyzdžiui, tai yra taškas tarp dviejų <a href="/wiki/Dangaus_k%C5%ABnas" title="Dangaus kūnas">dangaus kūnų</a>, aplink kurį jie abu sukasi. <a href="/wiki/Palydovas" title="Palydovas">Palydovui</a> sukantis aplink <a href="/wiki/Planeta" title="Planeta">planetą</a>, arba <a href="/wiki/Planeta" title="Planeta">planetai</a> sukantis aplink <a href="/wiki/Saul%C4%97" title="Saulė">Saulę</a>, abu kūnai iš tiesų sukasi aplink tašką, esantį už didesniojo kūno masės centro. Pavyzdžiui, <a href="/wiki/M%C4%97nulis" title="Mėnulis">Mėnulis</a> neskrieja lygiai aplink <a href="/wiki/%C5%BDem%C4%97" title="Žemė">Žemės</a> masės centrą, tačiau aplink tašką, esantį tarp Žemės ir Mėnulio, esantį maždaug 1710 km po Žemės paviršiumi. Tai yra taškas, aplink kurį skrieja Žemė ir Mėnulis, jiems keliaujant aplink Saulę. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Matematinis_pagrindimas">Matematinis pagrindimas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Baricentras&veaction=edit&section=1" title="Redaguoti skyrelį: Matematinis pagrindimas" class="mw-editsection-visualeditor"><span>redaguoti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Baricentras&action=edit&section=1" title="Edit section's source code: Matematinis pagrindimas"><span>redaguoti vikitekstą</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Baricentras dviejų kūnų atveju yra jų elipsinių <a href="/wiki/Orbita" title="Orbita">orbitų</a> bendras židinys. Dviejų kūnų judėjimo uždavinyje, <i>r</i><sub>1</sub> yra atstumas tarp didesnės masės kūno ir baricentro: </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_{1}=a\cdot {m_{2} \over m_{1}+m_{2}}={a \over 1+m_{1}/m_{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mi>a</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{1}=a\cdot {m_{2} \over m_{1}+m_{2}}={a \over 1+m_{1}/m_{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9304137fef4b9635e195f70ddc3a1fc3d1e5a03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:33.265ex; height:5.509ex;" alt="{\displaystyle r_{1}=a\cdot {m_{2} \over m_{1}+m_{2}}={a \over 1+m_{1}/m_{2}}}"></span></dd></dl> <p>kur <i>a</i> yra atstumas tarp abiejų kūnų; </p> <dl><dd><i>m</i><sub>1</sub> ir <i>m</i><sub>2</sub> yra tų kūnų <a href="/wiki/Mas%C4%97" title="Masė">masės</a>.</dd></dl> <p><br /> <i>r</i><sub>1</sub> yra pirmojo kūno orbitos <a href="/wiki/Didysis_pusa%C5%A1is" class="mw-redirect" title="Didysis pusašis">didysis pusašis</a> ir <i>r</i><sub>2</sub> = <i>a</i> – <i>r</i><sub>1</sub> yra antro kūno didysis pusašis. Baricentrui esant didesnio kūno <i>viduje</i>, atrodys, kad kūnas svyruoja, o ne skrieja kažkokia orbita. </p><p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Kai_kurie_Saulės_sistemos_baricentrai"><span id="Kai_kurie_Saul.C4.97s_sistemos_baricentrai"></span>Kai kurie Saulės sistemos baricentrai</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Baricentras&veaction=edit&section=2" title="Redaguoti skyrelį: Kai kurie Saulės sistemos baricentrai" class="mw-editsection-visualeditor"><span>redaguoti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Baricentras&action=edit&section=2" title="Edit section's source code: Kai kurie Saulės sistemos baricentrai"><span>redaguoti vikitekstą</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Toliau pateikiami keli <a href="/wiki/Saul%C4%97s_sistema" title="Saulės sistema">Saulės sistemos</a> baricentrų pavyzdžiai. Paskutinėse dviejose eilutėse pateiktas <i>R</i><sub>1</sub>, masyvesniojo kūno spindulys, bei <i>r</i><sub>1</sub>/<i>R</i><sub>1</sub>, atstumo iki baricentro ir spindulio santykis – reikšmei esant <0, baricentras yra pirmojo kūno viduje. </p> <table class="wikitable" style="text-align:center"> <caption><b>Pavyzdžiai</b> </caption> <tbody><tr> <th>Didesnysis <br />kūnas </th> <th><i>m</i><sub>1</sub> <br />(<i>m</i><sub>E</sub>=1) </th> <th>Mažesnysis <br />kūnas </th> <th><i>m</i><sub>2</sub> <br />(<i>m</i><sub>E</sub>=1) </th> <th><i>a</i> <br />(<a href="/wiki/Kilometras" class="mw-redirect" title="Kilometras">km</a>) </th> <th><i>r</i><sub>1</sub> <br />(km) </th> <th><i>R</i><sub>1</sub> <br />(km) </th> <th><i>r</i><sub>1</sub>/<i>R</i><sub>1</sub> </th></tr> <tr> <th colspan="8">Remarks </th></tr> <tr> <td><a href="/wiki/%C5%BDem%C4%97" title="Žemė">Žemė</a> </td> <td>1 </td> <td><a href="/wiki/M%C4%97nulis" title="Mėnulis">Mėnulis</a> </td> <td>0,0123 </td> <td>384 000 </td> <td>4 670 </td> <td>6 380 </td> <td>0,732 </td></tr> <tr> <td colspan="8">Žemė turi pastebimą svyravimą </td></tr> <tr> <td><a href="/wiki/Plutonas_(nyk%C5%A1tukin%C4%97_planeta)" title="Plutonas (nykštukinė planeta)">Plutonas</a> </td> <td>0,0021 </td> <td><a href="/wiki/Charonas_(palydovas)" title="Charonas (palydovas)">Charonas</a> </td> <td>0,000254 <br /> (0,121 <i>m</i><sub>Plutonas</sub>) </td> <td>  19 600 </td> <td>2 110 </td> <td>1 150 </td> <td>1,83 </td></tr> <tr> <td colspan="8">Abu kūnai turi aiškias orbitas aplink baricentrą, dėl to <a href="/wiki/Plutonas_(nyk%C5%A1tukin%C4%97_planeta)" title="Plutonas (nykštukinė planeta)">Plutonas</a> ir <a href="/wiki/Charonas_(palydovas)" title="Charonas (palydovas)">Charonas</a> buvo laikomi dvinare planetų sistema iki planetos sąvokos pasikeitimo 2006 m.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/Saul%C4%97" title="Saulė">Saulė</a> </td> <td>333 000 </td> <td><a href="/wiki/%C5%BDem%C4%97" title="Žemė">Žemė</a> </td> <td>1 </td> <td>150 000 000 <br /> (1 <a href="/wiki/Astronominis_vienetas" title="Astronominis vienetas">AV</a>) </td> <td>449 </td> <td>696 000 </td> <td>0,000646 </td></tr> <tr> <td colspan="8">Saulės svyravimai vos pastebimi. </td></tr> <tr> <td><a href="/wiki/Saul%C4%97" title="Saulė">Saulė</a> </td> <td>333 000 </td> <td><a href="/wiki/Jupiteris_(planeta)" title="Jupiteris (planeta)">Jupiteris</a> </td> <td>318 <br /> (0,000955 <i>m</i><sub>Saulės</sub>) </td> <td>778 000 000 <br />(5,20 AV) </td> <td>742 000 </td> <td>696 000 </td> <td>1,07 </td></tr> <tr> <td colspan="8">Saulė skrieja aplink baricentrą, esantį tiesiai virš jos paviršiaus. </td></tr></tbody></table> <p>Jei <i>m</i><sub>1</sub>≫<i>m</i><sub>2</sub>– kas yra teisinga Saulės ir bet kurios planetos atveju, tai <i>r</i><sub>1</sub>/<i>R</i><sub>1</sub> santykis aproksimuojasi į: </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 {a \over R_{1}}\cdot {m_{2} \over m_{1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {a \over R_{1}}\cdot {m_{2} \over m_{1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25423c556c451df3b63d8009cc519dc7e2137952" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:9.264ex; height:5.009ex;" alt="{\displaystyle {a \over R_{1}}\cdot {m_{2} \over m_{1}}}"></span></dd></dl> <p>Taigi, Saulės – planetos sistemos baricentras bus už Saulės ribų tik jei: </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 {a \over R_{\bigodot }}\cdot {m_{planeta} \over m_{\bigodot }}>1\;\Rightarrow \;{a\cdot m_{planeta}}>{R_{\bigodot }\cdot m_{\bigodot }}\approx 2,3\times 10^{11}\;m_{Zeme}\;{\mbox{km}}\approx 1530\;m_{Zeme}\;{\mbox{AV}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⨀</mo> </mrow> </msub> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>l</mi> <mi>a</mi> <mi>n</mi> <mi>e</mi> <mi>t</mi> <mi>a</mi> </mrow> </msub> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⨀</mo> </mrow> </msub> </mfrac> </mrow> <mo>></mo> <mn>1</mn> <mspace width="thickmathspace" /> <mo stretchy="false">⇒</mo> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mo>⋅</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>l</mi> <mi>a</mi> <mi>n</mi> <mi>e</mi> <mi>t</mi> <mi>a</mi> </mrow> </msub> </mrow> <mo>></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⨀</mo> </mrow> </msub> <mo>⋅</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⨀</mo> </mrow> </msub> </mrow> <mo>≈</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>11</mn> </mrow> </msup> <mspace width="thickmathspace" /> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Z</mi> <mi>e</mi> <mi>m</mi> <mi>e</mi> </mrow> </msub> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>km</mtext> </mstyle> </mrow> <mo>≈</mo> <mn>1530</mn> <mspace width="thickmathspace" /> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Z</mi> <mi>e</mi> <mi>m</mi> <mi>e</mi> </mrow> </msub> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>AV</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {a \over R_{\bigodot }}\cdot {m_{planeta} \over m_{\bigodot }}>1\;\Rightarrow \;{a\cdot m_{planeta}}>{R_{\bigodot }\cdot m_{\bigodot }}\approx 2,3\times 10^{11}\;m_{Zeme}\;{\mbox{km}}\approx 1530\;m_{Zeme}\;{\mbox{AV}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9f492461a865c1e6cb22f06f4ccba6b90ed623a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:90.644ex; height:5.843ex;" alt="{\displaystyle {a \over R_{\bigodot }}\cdot {m_{planeta} \over m_{\bigodot }}>1\;\Rightarrow \;{a\cdot m_{planeta}}>{R_{\bigodot }\cdot m_{\bigodot }}\approx 2,3\times 10^{11}\;m_{Zeme}\;{\mbox{km}}\approx 1530\;m_{Zeme}\;{\mbox{AV}}}"></span></dd></dl> <p>T.y., kai planeta yra sunki <i>ir</i> yra toli nuo Saulės. </p><p>Jei Jupiteris turėtų <a href="/wiki/Merkurijus_(planeta)" title="Merkurijus (planeta)">Merkurijaus</a> orbitą (57 900 000 km, 0,387 <a href="/wiki/Astronominis_vienetas" title="Astronominis vienetas">AV</a>), Saulės – Jupiterio baricentras būtų vos už 5500 km nuo Saulės centro (<i>r</i><sub>1</sub>/<i>R</i><sub>1</sub>~ 0.08). Bet net jei Žemė turėtų [[Eridė (nykštukinė planeta). |Eridės]] orbitą (68 AV), Saulės – Žemės baricentras ir vis tiek būtų Saulės viduje (vos už 30 000 km nuo centro). </p><p>Norint apskaičiuoti tikrą Saulės judėjimą, reikia susumuoti visų <a href="/wiki/Planeta" title="Planeta">planetų</a>, <a href="/wiki/Kometa" title="Kometa">kometų</a>, <a href="/wiki/Asteroidas" title="Asteroidas">asteroidų</a>, bei kitų Saulės sistemos kūnų įtaką. Jei visos planetos išsilygiuotų vienoje tiesėje, bendras masės centras būtų maždaug už 500 000 km virš Saulės paviršiaus. </p><p>Aukščiau esantys skaičiavimai yra paremti vidutiniu atstumu tarp kūnų, taip pat ir <i>r</i><sub>1</sub>. Tačiau visų dangaus kūnų <a href="/wiki/Orbita" title="Orbita">orbitos</a> yra <a href="/wiki/Elips%C4%97" title="Elipsė">elipsės</a> formos, taigi atstumas tarp kūnų varijuoja priklausomai nuo <a href="/wiki/Ekscentricitetas" title="Ekscentricitetas">ekscentriciteto</a>. Tuo pačiu kinta ir baricentro vieta, ir yra įmanoma, kad kai kuriose sistemose baricentras yra tai didesniojo kūno <i>viduje, tai išorėje</i>. Taip nutinka, kai </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 {1 \over {1-e}}>{r_{1} \over R_{1}}>{1 \over {1+e}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>−</mo> <mi>e</mi> </mrow> </mfrac> </mrow> <mo>></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>+</mo> <mi>e</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {1 \over {1-e}}>{r_{1} \over R_{1}}>{1 \over {1+e}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a918b2fed40eeca4565667280a5aa2f2215841cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:21.696ex; height:5.509ex;" alt="{\displaystyle {1 \over {1-e}}>{r_{1} \over R_{1}}>{1 \over {1+e}}}"></span></dd></dl> <p>Pažymėtina, kad Saulės – Jupiterio sistemos su <i>e</i><sub>Jupiter</sub>= 0,0484 beveik atitinka sąlygą: 1.05 <b>≯</b> 1.07 > 0.954 </p> <div class="mw-heading mw-heading3"><h3 id="Animacijos">Animacijos</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Baricentras&veaction=edit&section=3" title="Redaguoti skyrelį: Animacijos" class="mw-editsection-visualeditor"><span>redaguoti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Baricentras&action=edit&section=3" title="Edit section's source code: Animacijos"><span>redaguoti vikitekstą</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Baricentrą atvaizduojančios animacijos </p> <table class="wikitable" width="640"> <tbody><tr> <td valign="top"><span typeof="mw:File"><a href="/wiki/Vaizdas:Orbit1.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/73/Orbit1.gif" decoding="async" width="200" height="200" class="mw-file-element" data-file-width="200" data-file-height="200" /></a></span><br />Du vienodos masės kūnai, skriejantys aplink baricentrą. (pvz., <a href="https://en.wikipedia.org/wiki/90_Antiope" class="extiw" title="en:90 Antiope">90 antiope </a> sistema) </td> <td valign="top"><span typeof="mw:File"><a href="/wiki/Vaizdas:Orbit2.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/f/f2/Orbit2.gif" decoding="async" width="200" height="200" class="mw-file-element" data-file-width="200" data-file-height="200" /></a></span><br />Du skirtingos masės kūnai, skriejantys aplink baricentrą. (pvz.<a href="/wiki/Plutonas_(nyk%C5%A1tukin%C4%97_planeta)" title="Plutonas (nykštukinė planeta)">Plutono</a>-<a href="/wiki/Charonas_(palydovas)" title="Charonas (palydovas)">Charono</a> sistema. </td> <td valign="top"><span typeof="mw:File"><a href="/wiki/Vaizdas:Orbit3.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/59/Orbit3.gif" decoding="async" width="200" height="200" class="mw-file-element" data-file-width="200" data-file-height="200" /></a></span><br />Du labai skirtingos masės kūnai, skriejantys aplink baricentrą. (pvz., <a href="/wiki/%C5%BDem%C4%97" title="Žemė">Žemės</a>-<a href="/wiki/M%C4%97nulis" title="Mėnulis">Mėnulio</a> sistema) </td> <td valign="top"><span typeof="mw:File"><a href="/wiki/Vaizdas:Orbit4.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/5/5a/Orbit4.gif" decoding="async" width="200" height="200" class="mw-file-element" data-file-width="200" data-file-height="200" /></a></span><br />Du labai smarkiai besiskiriančios masės kūnai, skriejantys aplink baricentrą. (pvz., <a href="/wiki/Saul%C4%97" title="Saulė">Saulės</a>-<a href="/wiki/%C5%BDem%C4%97" title="Žemė">Žemės</a> sistema) </td></tr> <tr> <td valign="top" colspan="2"><span typeof="mw:File"><a href="/wiki/Vaizdas:Orbit5.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/0/0e/Orbit5.gif" decoding="async" width="400" height="200" class="mw-file-element" data-file-width="400" data-file-height="200" /></a></span><br />Du vienodos masės kūnai, turintys elipsines orbitas, skrieja aplink baricentrą (dažnai pasitaiko tarp dvinarių žvaigždžių) </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Nuorodos">Nuorodos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Baricentras&veaction=edit&section=4" title="Redaguoti skyrelį: Nuorodos" class="mw-editsection-visualeditor"><span>redaguoti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Baricentras&action=edit&section=4" title="Edit section's source code: Nuorodos"><span>redaguoti vikitekstą</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://arxiv.org/abs/astro-ph/0512491">Orbits and photometry of Pluto’s satellites: Charon, S/2005 P1 and S/2005 P2</a> Eliot F. Young, Leslie A. Young, and S. Alan Stern at Southwest Research Institute, Boulder, Colorado</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.plutopetition.com/unplanet.php">Much Ado about Pluto</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20121001025947/http://www.plutopetition.com/unplanet.php">Archyvuota kopija</a> 2012-10-01 iš <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> projekto. plutopetition.com</span> </li> </ol>    </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="">Rodomas puslapis "<a dir="ltr" href="https://lt.wikipedia.org/w/index.php?title=Baricentras&oldid=6735576">https://lt.wikipedia.org/w/index.php?title=Baricentras&oldid=6735576</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Specialus:Kategorijos" title="Specialus:Kategorijos">Kategorija</a>: <ul><li><a href="/wiki/Kategorija:Mechanika" title="Kategorija:Mechanika">Mechanika</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Paslėpta kategorija: <ul><li><a href="/wiki/Kategorija:Webarchive_%C5%A1ablono_Wayback_nuorodos" title="Kategorija:Webarchive šablono Wayback nuorodos">Webarchive šablono Wayback nuorodos</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"> Šis puslapis paskutinį kartą keistas 28 spalio 2022 15:29.</li> <li id="footer-info-copyright">Tekstas pateikiamas pagal <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution/Share-Alike Licenciją</a>; gali būti taikomos papildomos sąlygos. 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