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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Meld aan</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"> Bladsye vir uitgemelde redakteurs <a href="/wiki/Hulp:Inleiding" aria-label="Leer meer oor redigering"><span>leer meer</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/Spesiaal:Mybydrae" title="A list of edits made from this IP address [y]" accesskey="y"><span>Bydraes</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Spesiaal:Mybespreking" title="Bespreking oor bydraes van hierdie IP-adres [n]" accesskey="n"><span>Bespreking</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div 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href="#Multi-liggaamprobleem"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Multi-liggaamprobleem</span> </div> </a> <ul id="toc-Multi-liggaamprobleem-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Meganika_van_die_melkwegstelsel" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Meganika_van_die_melkwegstelsel"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Meganika van die melkwegstelsel</span> </div> </a> <ul id="toc-Meganika_van_die_melkwegstelsel-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bron" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bron"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Bron</span> </div> </a> <ul id="toc-Bron-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="Inhoud" 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="Wissel die inhoudsopgawe" > <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">Wissel die inhoudsopgawe</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">Hemelmeganika</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="Gaan na 'n artikel in 'n ander taal. Beskikbaar in 63 tale" > <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-63" 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">63 tale</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%D9%8A%D9%83%D8%A7%D9%86%D9%8A%D9%83%D8%A7_%D8%B3%D9%85%D8%A7%D9%88%D9%8A%D8%A9" title="ميكانيكا سماوية – Arabies" lang="ar" hreflang="ar" data-title="ميكانيكا سماوية" data-language-autonym="العربية" data-language-local-name="Arabies" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%85%D9%8A%D9%83%D8%A7%D9%86%D9%8A%D9%83%D8%A7_%D8%B3%D9%85%D8%A7%D9%88%D9%8A%D9%87" title="ميكانيكا سماويه – Egyptian Arabic" lang="arz" hreflang="arz" data-title="ميكانيكا سماويه" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Mec%C3%A1nica_celeste" title="Mecánica celeste – Asturies" lang="ast" hreflang="ast" data-title="Mecánica celeste" data-language-autonym="Asturianu" data-language-local-name="Asturies" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/G%C3%B6y_mexanikas%C4%B1" title="Göy mexanikası – Azerbeidjans" lang="az" hreflang="az" data-title="Göy mexanikası" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbeidjans" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9D%D1%8F%D0%B1%D0%B5%D1%81%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0" title="Нябесная механіка – Belarussies" lang="be" hreflang="be" data-title="Нябесная механіка" data-language-autonym="Беларуская" data-language-local-name="Belarussies" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9D%D1%8F%D0%B1%D0%B5%D1%81%D0%BD%D0%B0%D1%8F_%D0%BC%D1%8D%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0" title="Нябесная мэханіка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Нябесная мэханіка" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9D%D0%B5%D0%B1%D0%B5%D1%81%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Небесна механика – Bulgaars" lang="bg" hreflang="bg" data-title="Небесна механика" data-language-autonym="Български" data-language-local-name="Bulgaars" 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/Mec%C3%A0nica_celeste" title="Mecànica celeste – Katalaans" lang="ca" hreflang="ca" data-title="Mecànica celeste" data-language-autonym="Català" data-language-local-name="Katalaans" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/Ti%C4%95ng-t%C4%81%CC%A4_l%C4%ADk-h%C5%8Fk" title="Tiĕng-tā̤ lĭk-hŏk – Mindong" lang="cdo" hreflang="cdo" data-title="Tiĕng-tā̤ lĭk-hŏk" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%85%DB%8C%DA%A9%D8%A7%D9%86%DB%8C%DA%A9%DB%8C_%D8%A6%D8%A7%D8%B3%D9%85%D8%A7%D9%86%DB%8C" title="میکانیکی ئاسمانی – Sorani" lang="ckb" hreflang="ckb" data-title="میکانیکی ئاسمانی" data-language-autonym="کوردی" data-language-local-name="Sorani" 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/Nebesk%C3%A1_mechanika" title="Nebeská mechanika – Tsjeggies" lang="cs" hreflang="cs" data-title="Nebeská mechanika" data-language-autonym="Čeština" data-language-local-name="Tsjeggies" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%D3%B3%D0%BF%D0%B5%D1%80%D0%B8_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Тӳпери механика – Chuvash" lang="cv" hreflang="cv" data-title="Тӳпери механика" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Himmelmekanik" title="Himmelmekanik – Deens" lang="da" hreflang="da" data-title="Himmelmekanik" data-language-autonym="Dansk" data-language-local-name="Deens" 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/Himmelsmechanik" title="Himmelsmechanik – Duits" lang="de" hreflang="de" data-title="Himmelsmechanik" data-language-autonym="Deutsch" data-language-local-name="Duits" 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%9F%CF%85%CF%81%CE%AC%CE%BD%CE%B9%CE%B1_%CE%BC%CE%B7%CF%87%CE%B1%CE%BD%CE%B9%CE%BA%CE%AE" title="Ουράνια μηχανική – Grieks" lang="el" hreflang="el" data-title="Ουράνια μηχανική" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Celestial_mechanics" title="Celestial mechanics – Engels" lang="en" hreflang="en" data-title="Celestial mechanics" data-language-autonym="English" data-language-local-name="Engels" 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/%C4%88iela_mekaniko" title="Ĉiela mekaniko – Esperanto" lang="eo" hreflang="eo" data-title="Ĉiela mekaniko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" 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/Mec%C3%A1nica_celeste" title="Mecánica celeste – Spaans" lang="es" hreflang="es" data-title="Mecánica celeste" data-language-autonym="Español" data-language-local-name="Spaans" 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/Taevamehaanika" title="Taevamehaanika – Estnies" lang="et" hreflang="et" data-title="Taevamehaanika" data-language-autonym="Eesti" data-language-local-name="Estnies" 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/Zeruko_mekanika" title="Zeruko mekanika – Baskies" lang="eu" hreflang="eu" data-title="Zeruko mekanika" data-language-autonym="Euskara" data-language-local-name="Baskies" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%DA%A9%D8%A7%D9%86%DB%8C%DA%A9_%D8%B3%D9%85%D8%A7%D9%88%DB%8C" title="مکانیک سماوی – Persies" lang="fa" hreflang="fa" data-title="مکانیک سماوی" data-language-autonym="فارسی" data-language-local-name="Persies" 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/Taivaanmekaniikka" title="Taivaanmekaniikka – Fins" lang="fi" hreflang="fi" data-title="Taivaanmekaniikka" data-language-autonym="Suomi" data-language-local-name="Fins" 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/M%C3%A9canique_c%C3%A9leste" title="Mécanique céleste – Frans" lang="fr" hreflang="fr" data-title="Mécanique céleste" data-language-autonym="Français" data-language-local-name="Frans" 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/Mec%C3%A1nica_celeste" title="Mecánica celeste – Galisies" lang="gl" hreflang="gl" data-title="Mecánica celeste" data-language-autonym="Galego" data-language-local-name="Galisies" 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%96%E0%A4%97%E0%A5%8B%E0%A4%B2%E0%A5%80%E0%A4%AF_%E0%A4%AF%E0%A4%BE%E0%A4%82%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A5%80" title="खगोलीय यांत्रिकी – Hindi" lang="hi" hreflang="hi" data-title="खगोलीय यांत्रिकी" 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/Nebeska_mehanika" title="Nebeska mehanika – Kroaties" lang="hr" hreflang="hr" data-title="Nebeska mehanika" data-language-autonym="Hrvatski" data-language-local-name="Kroaties" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/%C3%89gi_mechanika" title="Égi mechanika – Hongaars" lang="hu" hreflang="hu" data-title="Égi mechanika" data-language-autonym="Magyar" data-language-local-name="Hongaars" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B5%D6%80%D5%AF%D5%B6%D5%A1%D5%B5%D5%AB%D5%B6_%D5%B4%D5%A5%D5%AD%D5%A1%D5%B6%D5%AB%D5%AF%D5%A1" title="Երկնային մեխանիկա – Armeens" lang="hy" hreflang="hy" data-title="Երկնային մեխանիկա" data-language-autonym="Հայերեն" data-language-local-name="Armeens" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Mechanica_celestial" title="Mechanica celestial – Interlingua" lang="ia" hreflang="ia" data-title="Mechanica celestial" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Mekanika_benda_langit" title="Mekanika benda langit – Indonesies" lang="id" hreflang="id" data-title="Mekanika benda langit" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesies" 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/Meccanica_celeste" title="Meccanica celeste – Italiaans" lang="it" hreflang="it" data-title="Meccanica celeste" data-language-autonym="Italiano" data-language-local-name="Italiaans" 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/%E5%A4%A9%E4%BD%93%E5%8A%9B%E5%AD%A6" title="天体力学 – Japannees" lang="ja" hreflang="ja" data-title="天体力学" data-language-autonym="日本語" data-language-local-name="Japannees" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%AA%E1%83%98%E1%83%A1_%E1%83%9B%E1%83%94%E1%83%A5%E1%83%90%E1%83%9C%E1%83%98%E1%83%99%E1%83%90" title="ცის მექანიკა – Georgies" lang="ka" hreflang="ka" data-title="ცის მექანიკა" data-language-autonym="ქართული" data-language-local-name="Georgies" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%81%D0%BF%D0%B0%D0%BD_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0%D1%81%D1%8B" title="Аспан механикасы – Kazaks" lang="kk" hreflang="kk" data-title="Аспан механикасы" data-language-autonym="Қазақша" data-language-local-name="Kazaks" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%B2%9C%EC%B2%B4%EC%97%AD%ED%95%99" title="천체역학 – Koreaans" lang="ko" hreflang="ko" data-title="천체역학" data-language-autonym="한국어" data-language-local-name="Koreaans" 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/Himmelsmechanik" title="Himmelsmechanik – Luxemburgs" lang="lb" hreflang="lb" data-title="Himmelsmechanik" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxemburgs" 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/Dangaus_mechanika" title="Dangaus mechanika – Litaus" lang="lt" hreflang="lt" data-title="Dangaus mechanika" data-language-autonym="Lietuvių" data-language-local-name="Litaus" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Mekanika_bando_langik" title="Mekanika bando langik – Minangkabaus" lang="min" hreflang="min" data-title="Mekanika bando langik" data-language-autonym="Minangkabau" data-language-local-name="Minangkabaus" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9D%D0%B5%D0%B1%D0%B5%D1%81%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Небесна механика – Masedonies" lang="mk" hreflang="mk" data-title="Небесна механика" data-language-autonym="Македонски" data-language-local-name="Masedonies" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Hemelmechanica" title="Hemelmechanica – Nederlands" lang="nl" hreflang="nl" data-title="Hemelmechanica" data-language-autonym="Nederlands" data-language-local-name="Nederlands" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Celestmekanikk" title="Celestmekanikk – Nuwe Noors" lang="nn" hreflang="nn" data-title="Celestmekanikk" data-language-autonym="Norsk nynorsk" data-language-local-name="Nuwe Noors" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Himmelmekanikk" title="Himmelmekanikk – Boeknoors" lang="nb" hreflang="nb" data-title="Himmelmekanikk" data-language-autonym="Norsk bokmål" data-language-local-name="Boeknoors" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Mechanika_nieba" title="Mechanika nieba – Pools" lang="pl" hreflang="pl" data-title="Mechanika nieba" data-language-autonym="Polski" data-language-local-name="Pools" 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/Mec%C3%A2nica_celeste" title="Mecânica celeste – Portugees" lang="pt" hreflang="pt" data-title="Mecânica celeste" data-language-autonym="Português" data-language-local-name="Portugees" 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/Mecanic%C4%83_cereasc%C4%83" title="Mecanică cerească – Roemeens" lang="ro" hreflang="ro" data-title="Mecanică cerească" data-language-autonym="Română" data-language-local-name="Roemeens" 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%9D%D0%B5%D0%B1%D0%B5%D1%81%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Небесная механика – Russies" lang="ru" hreflang="ru" data-title="Небесная механика" data-language-autonym="Русский" data-language-local-name="Russies" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Nebeska_mehanika" title="Nebeska mehanika – Serwo-Kroaties" lang="sh" hreflang="sh" data-title="Nebeska mehanika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serwo-Kroaties" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Celestial_mechanics" title="Celestial mechanics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Celestial mechanics" 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/Nebesk%C3%A1_mechanika" title="Nebeská mechanika – Slowaaks" lang="sk" hreflang="sk" data-title="Nebeská mechanika" data-language-autonym="Slovenčina" data-language-local-name="Slowaaks" 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/Nebesna_mehanika" title="Nebesna mehanika – Sloweens" lang="sl" hreflang="sl" data-title="Nebesna mehanika" data-language-autonym="Slovenščina" data-language-local-name="Sloweens" 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%9D%D0%B5%D0%B1%D0%B5%D1%81%D0%BA%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0" title="Небеска механика – Serwies" lang="sr" hreflang="sr" data-title="Небеска механика" data-language-autonym="Српски / srpski" data-language-local-name="Serwies" 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/Celest_mekanik" title="Celest mekanik – Sweeds" lang="sv" hreflang="sv" data-title="Celest mekanik" data-language-autonym="Svenska" data-language-local-name="Sweeds" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Umakanika_wa_anga" title="Umakanika wa anga – Swahili" lang="sw" hreflang="sw" data-title="Umakanika wa anga" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%A5%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C%E0%B8%97%E0%B9%89%E0%B8%AD%E0%B8%87%E0%B8%9F%E0%B9%89%E0%B8%B2" title="กลศาสตร์ท้องฟ้า – Thai" lang="th" hreflang="th" data-title="กลศาสตร์ท้องฟ้า" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/G%C3%B6k_mekani%C4%9Fi" title="Gök mekaniği – Turks" lang="tr" hreflang="tr" data-title="Gök mekaniği" data-language-autonym="Türkçe" data-language-local-name="Turks" 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%9A%D2%AF%D0%BA_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA%D0%B0%D1%81%D1%8B" title="Күк механикасы – Tataars" lang="tt" hreflang="tt" data-title="Күк механикасы" data-language-autonym="Татарча / tatarça" data-language-local-name="Tataars" 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%9D%D0%B5%D0%B1%D0%B5%D1%81%D0%BD%D0%B0_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D1%96%D0%BA%D0%B0" title="Небесна механіка – Oekraïens" lang="uk" hreflang="uk" data-title="Небесна механіка" data-language-autonym="Українська" data-language-local-name="Oekraïens" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Samoviy_mexanika" title="Samoviy mexanika – Oezbeeks" lang="uz" hreflang="uz" data-title="Samoviy mexanika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Oezbeeks" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/C%C6%A1_h%E1%BB%8Dc_thi%C3%AAn_th%E1%BB%83" title="Cơ học thiên thể – Viëtnamees" lang="vi" hreflang="vi" data-title="Cơ học thiên thể" data-language-autonym="Tiếng Việt" data-language-local-name="Viëtnamees" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%A4%A9%E4%BD%93%E5%8A%9B%E5%AD%A6" title="天体力学 – Wu-Sjinees" lang="wuu" hreflang="wuu" data-title="天体力学" data-language-autonym="吴语" data-language-local-name="Wu-Sjinees" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A4%A9%E9%AB%94%E5%8A%9B%E5%AD%B8" title="天體力學 – Chinees" lang="zh" hreflang="zh" data-title="天體力學" data-language-autonym="中文" data-language-local-name="Chinees" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%A4%A9%E9%AB%94%E5%8A%9B%E5%AD%B8" title="天體力學 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="天體力學" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%A4%A9%E9%AB%94%E5%8A%9B%E5%AD%B8" title="天體力學 – Kantonees" lang="yue" hreflang="yue" data-title="天體力學" data-language-autonym="粵語" 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<button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">skuif na kantbalk</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">versteek</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">in Wikipedia, die vrye ensiklopedie</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="af" dir="ltr"><p><b>Hemelmeganika</b> is die studieveld waarin kennis van die <a href="/wiki/Sterrekunde" title="Sterrekunde">sterrekunde</a> in terme van die wette van die meganika verklaar word. Hierdie kennis stel die mens in staat om die bewegings van hemelliggame en mensgemaakte ruimtetuie akkuraat te voorspel en is veral belangrik vir <a href="/wiki/Ruimtevaart" title="Ruimtevaart">ruimtevaart</a>. Die beweging van meer as twee liggame kan nie analities-wiskundig bepaal word nie, maar met die koms van rekenaars het dit wel moontlik geword om hul bane te bereken. Die sterrekunde is seker die oudste wetenskap en sedert duisende jare gelede neem die mens al die verskynsels in die hemelruim waar. </p><p>Reeds sedert die vroegste tye is besef dat hemelliggame beweeg en baie van die bewegings is akkuraat opgeteken. Die ingewikkelde bewegings is egter nie verstaan nie en die Grieke het dit sonder welslae met ingewikkelde meetkundige modelle probeer verklaar. Teen die einde van die <a href="/wiki/Middeleeue" title="Middeleeue">Middeleeue</a> het <a href="/wiki/Nicolaas_Copernicus" title="Nicolaas Copernicus">Nicolaus Copernicus</a> groot vordering gemaak deur te veronderstel dat die aarde en alle ander planete in sirkelvormige bane om die <a href="/wiki/Son" title="Son">son</a> beweeg. <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a> het die noukeurige waarnemings van die sterrekundige <a href="/wiki/Tycho_Brahe" title="Tycho Brahe">Tycho Brahe</a> bestudeer en in 1619 drie wette aangaande die beweging van planete vasgestel, wat bekend staan as <a href="/wiki/Kepler_se_wette" title="Kepler se wette">Kepler se wette</a>: </p><p>- Alle planete beweeg in elliptiese bane om die son, met die son as een brandpunt van die <a href="/wiki/Ellips" title="Ellips">ellips</a>. </p><p>- Die verbindingslyn tussen die son en 'n planeet bestryk in gelyke tye gelyke oppervlaktes van die baan. </p><p>- Die kwadraat van die omwentelingstyd van 'n planeet is eweredig aan die derdemag van sy gemiddelde afstand van die son. </p><p>Kepler kon sy wette nie verklaar nie, maar dit is in 1687 wel gedoen deur <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> in sy beroemde werk <i><a href="/w/index.php?title=Principia&action=edit&redlink=1" class="new" title="Principia (bladsy bestaan nie)">Principia</a></i>. Hierin het Newton sy wet van die swaartekrag (gravitasiewet) gestel naamlik: Enige twee voorwerpe trek mekaar aan deur <a href="/wiki/Swaartekrag" title="Swaartekrag">swaartekrag</a>, en die krag is eweredig aan die produk van die twee massas en omgekeerd eweredig aan die kwadraat van die afstand tussen hulle. Hierdie swaartekrag hou die planete in hul bane en word gebalanseer deur die middelpuntvliedende krag as gevolg van die planeet se rotasiespoed. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Die_tweeliggaamprobleem">Die tweeliggaamprobleem</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hemelmeganika&veaction=edit&section=1" title="Wysig afdeling: Die tweeliggaamprobleem" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hemelmeganika&action=edit&section=1" title="Edit section's source code: Die tweeliggaamprobleem"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hier word 'n afgeslote sisteem beskou wat bestaan uit slegs twee hemelliggame wat om hul gemeenskaplike swaartepunt roteer, byvoorbeeld die aarde en die maan, die aarde en die son of 'n dubbelster. Newton het die tweeliggaam- probleem wiskundig verklaar en aangetoon dat die baan van albei hemelliggame 'n <a href="/wiki/Sirkel" title="Sirkel">sirkel</a>, <a href="/wiki/Ellips" title="Ellips">ellips</a>, <a href="/wiki/Parabool" title="Parabool">parabool</a> of <a href="/wiki/Hiperbool" title="Hiperbool">hiperbool</a> die swaartepunt sal wees. </p><p>Hierdie krommes is bekend as die kegelsnedes en die aanvanklike grootte en rigting van ŉ planeet se snelheid bepaal watter tipe baan dit sal volg. Die eerste twee tipes is geslote bane terwyl die laaste twee oop bane is. In die geval van oop bane sal die hemelliggaam slegs een keer by die son verbybeweeg en dan vir altyd wegbeweeg, soos in die geval van sommige komete. Indien slegs drie posisies op verskillende tye van die planeet se baan bekend is, is dit moontlik om sy totale baan te bepaal, maar in die praktyk word soveel moontlik data ingesamel ten einde die baan akkuraat te bepaal. In die sonnestelsel is die planeetbane volgens Newton se teorie nie perfekte ellipse nie. Dit is omdat daar nie werklik net twee liggame, die son en die planeet, betrokke is nie. Veral die groot planete <a href="/wiki/Jupiter" title="Jupiter">Jupiter</a> en <a href="/wiki/Saturnus" title="Saturnus">Saturnus</a> se swaartekragveld veroorsaak afwykings in die bane van ander planete. Die bane ondergaan oor lang tydperke geleidelike veranderings en die <a href="/wiki/Ellips" title="Ellips">ellips</a> se lang as draai stadig. Afwykings in die baan van 'n snel bewegende planeet, byvoorbeeld <a href="/wiki/Mercurius" title="Mercurius">Mercurius</a>, kan met behulp van <a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a> se algemene relatiwiteitsteorie verklaar word. </p><p>Verdere steurings in die baan kan ook veroorsaak word deur 'n kegelvormige beweging van die planeet as sy massa nie eweredig om die rotasie-as versprei is nie. Die aarde is byvoorbeeld effens afgeplat by die pole en die son en die <a href="/wiki/Maan" title="Maan">maan</a> oefen ŉ gesamentlike krag uit op die massabult by die ewenaar. Indien al hierdie steurings in ag geneem word, kan die bane van <a href="/wiki/Hemelliggaam" title="Hemelliggaam">hemelliggame</a> baie akkuraat voorspel word. Sedert 1967 gee die VSA se vlootsterrewag jaarliks ŉ seevaartkundige almanak uit waarin die bane beskryf word. </p> <div class="mw-heading mw-heading2"><h2 id="Multi-liggaamprobleem">Multi-liggaamprobleem</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hemelmeganika&veaction=edit&section=2" title="Wysig afdeling: Multi-liggaamprobleem" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hemelmeganika&action=edit&section=2" title="Edit section's source code: Multi-liggaamprobleem"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Indien daar drie of meer hemelliggame teenwoordig is wat vergelykbare kragte op mekaar uitoefen, is dit nie meer moontlik om hul beweging analities volgens Newton se wet uit te werk nie. Die grootte en rigting van die kragte verander wanneer die liggame beweeg en hul bewegings moet dus stap vir stap in klein intervalle bereken word. Met die koms van rekenaars het dit moontlik geword om hierdie berekenings te doen. Die wiskundige <a href="/w/index.php?title=Joseph_Lagrange&action=edit&redlink=1" class="new" title="Joseph Lagrange (bladsy bestaan nie)">Joseph Lagrange</a> (1736-1813) het ook die probleem van drie liggame ondersoek en bewys dat daar sogenaamde <a href="/wiki/Lagrange-punt" title="Lagrange-punt">Lagrange-punte</a> in die ruim bestaan wat heeltemal vry is van enige swaartekragveld. Twee sulke punte bestaan vir die son-aarde-maan-sisteem en soortgelyke punte geld ook vir Jupiter. </p> <div class="mw-heading mw-heading2"><h2 id="Meganika_van_die_melkwegstelsel">Meganika van die melkwegstelsel</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hemelmeganika&veaction=edit&section=3" title="Wysig afdeling: Meganika van die melkwegstelsel" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hemelmeganika&action=edit&section=3" title="Edit section's source code: Meganika van die melkwegstelsel"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Die Son is deel van die sterrekonstellasie wat as die melkwegstelsel bekend staan. In die melkwegstelsel beweeg duisende miljoene sterre in byna sirkelvormige bane om die galaktiese middelpunt. Die wette van Kepler geld nie vir die beweging van die sterre in die konstellasie nie, aangesien die massa van die stelsel deur die hele stelsel versprei is. </p><p>Die bane van sterre wat vinnig deur die newel beweeg, die sogenaamde snellopers, toon groot afwykings vanaf sirkelvormige bane. Uit beskikbare gegewens en met behulp van rekenaars kan hierdie bane nie alleen vooruit nie maar ook terug in die verlede bereken word. Die <a href="/wiki/Spiraal" title="Spiraal">spiraalstruktuur</a> van die melkwegstelsel word ook met behulp van die hemelmeganika bestudeer. </p><p>Die afgeplatte vorm van die <a href="/wiki/Melkweg" title="Melkweg">melkwegstelsel</a> dui op rotasie. Volgens die jongste teorieë sal die melkwegstelsel nie weens die rotasie uitmekaarspat nie, maar word die sterre bymekaar gehou deur ŉ swaartekragdrukgolf wat van die galaktiese middelpunt af versprei word. In ander sterrestelsels is die verspreiding van sterre soms bolvormig en beweeg almal om ŉ sentrale <a href="/wiki/Massamiddelpunt" title="Massamiddelpunt">massamiddelpunt</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Bron">Bron</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hemelmeganika&veaction=edit&section=4" title="Wysig afdeling: Bron" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Hemelmeganika&action=edit&section=4" title="Edit section's source code: Bron"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/W%C3%AAreldspektrum" title="Wêreldspektrum">Wêreldspektrum</a>, 1982, <a href="/wiki/Spesiaal:Boekbronne/0908409508" class="internal mw-magiclink-isbn">ISBN 0908409508</a> band</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="">Ontsluit van "<a dir="ltr" href="https://af.wikipedia.org/w/index.php?title=Hemelmeganika&oldid=2652846">https://af.wikipedia.org/w/index.php?title=Hemelmeganika&oldid=2652846</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Spesiaal:Kategorie%C3%AB" title="Spesiaal:Kategorieë">Kategorie</a>: <ul><li><a href="/wiki/Kategorie:Hemelmeganika" title="Kategorie:Hemelmeganika">Hemelmeganika</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Versteekte kategorie: <ul><li><a href="/wiki/Kategorie:Pages_using_ISBN_magic_links" title="Kategorie:Pages using ISBN magic links">Pages using ISBN magic links</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"> Die bladsy is laas op 15 Februarie 2024 om 11:05 bygewerk.</li> <li id="footer-info-copyright">Die teks is beskikbaar onder die lisensie <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Erkenning-Insgelyks Deel</a>. 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