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title=\"Википедија:Уређивачки маратон Вики воли споменике 2024.\"\u003EУређивачки маратон Вики воли споменике 2024\u003C/a\u003E\u003C/b\u003E.\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\n\u003Cdiv class=\"noticebanner\"\u003E\u003Cdiv class=\"plainlinks\" style=\"background-color: #FBEBEA; border-radius:5px; margin-top:10px; position:relative; border: 1px solid #aaa; font-family: \u0026#39;Helvetica\u0026#39;, \u0026#39;Arial\u0026#39;, sans-serif; line-height: 18px; box-shadow: 0 1px 1px rgba( 0, 0, 0, 0.15 ); overflow:hidden;\"\u003E\u003Cdiv style=\"display:block; top:4px; width:100%; text-align:center;;\"\u003E\u003Cdiv style=\"color:#000085; font-size:25px; line-height:25px\"\u003E\u003Cdiv style=\"padding-left:50px;\"\u003E\u003C/div\u003E\u003C/div\u003E\u003Cdiv style=\"padding-top:2px; color:#444; font-size:1.15em; line-height:1.5;\"\u003E\u003Cdiv style=\"padding-left:8px; padding-right:8px;\"\u003EУ току је такмичење у писању чланака на тему \u003Cb\u003E\u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A2%D0%B0%D0%BA%D0%BC%D0%B8%D1%87%D0%B5%D1%9A%D0%B5_%D1%83_%D0%BF%D0%B8%D1%81%D0%B0%D1%9A%D1%83_%D1%87%D0%BB%D0%B0%D0%BD%D0%B0%D0%BA%D0%B0/%D0%A3_%D1%81%D0%B2%D0%B5%D1%82%D1%83_%D0%A4%D0%BB%D0%BE%D1%80%D0%B5_%D0%B8_%D0%A4%D0%B0%D1%83%D0%BD%D0%B5\" title=\"Википедија:Такмичење у писању чланака/У свету Флоре и Фауне\"\u003EФлоре и фауне\u003C/a\u003E\u003C/b\u003E.\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\n\u003Cdiv class=\"noticebanner\"\u003E\u003Cdiv class=\"plainlinks\" style=\"background-color: #FBEBEA; border-radius:5px; margin-top:10px; position:relative; border: 1px solid #aaa; font-family: \u0026#39;Helvetica\u0026#39;, \u0026#39;Arial\u0026#39;, sans-serif; line-height: 18px; box-shadow: 0 1px 1px rgba( 0, 0, 0, 0.15 ); overflow:hidden;\"\u003E\u003Cdiv style=\"display:block; top:4px; width:100%; text-align:center;;\"\u003E\u003Cdiv style=\"color:#000085; font-size:25px; line-height:25px\"\u003E\u003Cdiv style=\"padding-left:50px;\"\u003E\u003C/div\u003E\u003C/div\u003E\u003Cdiv style=\"padding-top:2px; color:#444; font-size:1.15em; line-height:1.5;\"\u003E\u003Cdiv style=\"padding-left:8px; padding-right:8px;\"\u003EПридружите се \u003Cb\u003E\u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A3%D1%80%D0%B5%D1%92%D0%B8%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%BC%D0%B0%D1%80%D0%B0%D1%82%D0%BE%D0%BD_%D0%92%D0%B8%D0%BA%D0%B8_%D0%B2%D0%BE%D0%BB%D0%B8_%D1%98%D0%B0%D0%B2%D0%BD%D1%83_%D1%83%D0%BC%D0%B5%D1%82%D0%BD%D0%BE%D1%81%D1%82_%D0%B8_%D0%B3%D1%80%D0%BE%D0%B1%D0%BD%D0%B0_%D0%BE%D0%B1%D0%B5%D0%BB%D0%B5%D0%B6%D1%98%D0%B0_2024.\" title=\"Википедија:Уређивачки маратон Вики воли јавну уметност и гробна обележја 2024.\"\u003EУређивачком маратону Вики воли јавну уметност и гробна обележја 2024\u003C/a\u003E\u003C/b\u003E.\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\n\u003Cdiv class=\"noticebanner\"\u003E\u003Cdiv class=\"plainlinks\" style=\"background-color: #FBEBEA; border-radius:5px; margin-top:10px; position:relative; border: 1px solid #aaa; font-family: \u0026#39;Helvetica\u0026#39;, \u0026#39;Arial\u0026#39;, sans-serif; line-height: 18px; box-shadow: 0 1px 1px rgba( 0, 0, 0, 0.15 ); overflow:hidden;\"\u003E\u003Cdiv style=\"display:block; top:4px; width:100%; text-align:center;;\"\u003E\u003Cdiv style=\"color:#000085; font-size:25px; line-height:25px\"\u003E\u003Cdiv style=\"padding-left:50px;\"\u003E\u003C/div\u003E\u003C/div\u003E\u003Cdiv style=\"padding-top:2px; color:#444; font-size:1.15em; line-height:1.5;\"\u003E\u003Cdiv style=\"padding-left:8px; padding-right:8px;\"\u003EУчествујте у \u003Cb\u003E\u003Ca href=\"https://sr.wikiquote.org/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D1%86%D0%B8%D1%82%D0%B0%D1%82:%D0%9A%D0%B0%D0%BC%D0%BF%D0%B0%D1%9A%D0%B0_SheSaid_2024\" class=\"extiw\" title=\"q:Викицитат:Кампања SheSaid 2024\"\u003Eкампањи писања цитата значајних жена\u003C/a\u003E\u003C/b\u003E на Викицитату.\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\n\u003Cdiv class=\"noticebanner\"\u003E\u003Cdiv class=\"plainlinks\" style=\"background-color: #FBEBEA; border-radius:5px; margin-top:10px; position:relative; border: 1px solid #aaa; font-family: \u0026#39;Helvetica\u0026#39;, \u0026#39;Arial\u0026#39;, sans-serif; line-height: 18px; box-shadow: 0 1px 1px rgba( 0, 0, 0, 0.15 ); overflow:hidden;\"\u003E\u003Cdiv style=\"display:block; top:4px; width:100%; text-align:center;;\"\u003E\u003Cdiv style=\"color:#000085; font-size:25px; line-height:25px\"\u003E\u003Cdiv style=\"padding-left:50px;\"\u003E\u003C/div\u003E\u003C/div\u003E\u003Cdiv style=\"padding-top:2px; color:#444; font-size:1.15em; line-height:1.5;\"\u003E\u003Cdiv style=\"padding-left:8px; padding-right:8px;\"\u003EПридружите се \u003Cb\u003E\u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%90%D0%BA%D1%86%D0%B8%D1%98%D0%B0_%D0%BF%D1%80%D0%BE%D1%88%D0%B8%D1%80%D0%B8%D0%B2%D0%B0%D1%9A%D0%B0_%D0%BA%D0%BB%D0%B8%D1%86%D0%B0\" title=\"Википедија:Акција проширивања клица\"\u003Eакцији проширивања клица\u003C/a\u003E\u003C/b\u003E.\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Сајт"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Садржај" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Садржај</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">помери на страну</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">сакриј</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Почетак</div> </a> </li> <li id="toc-Елипса" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Елипса"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Елипса</span> </div> </a> <ul id="toc-Елипса-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Хипербола" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Хипербола"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Хипербола</span> </div> </a> <ul id="toc-Хипербола-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Астрономија" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Астрономија"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Астрономија</span> </div> </a> <button aria-controls="toc-Астрономија-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Садржај одељка Астрономија</span> </button> <ul id="toc-Астрономија-sublist" class="vector-toc-list"> <li id="toc-Орбитални_период" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Орбитални_период"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Орбитални период</span> </div> </a> <ul id="toc-Орбитални_период-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Велике_и_полу-мале_осе_путања_планета" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Велике_и_полу-мале_осе_путања_планета"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Велике и полу-мале осе путања планета</span> </div> </a> <ul id="toc-Велике_и_полу-мале_осе_путања_планета-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Референце" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Референце"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Референце</span> </div> </a> <ul id="toc-Референце-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Литература" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Литература"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Литература</span> </div> </a> <ul id="toc-Литература-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Спољашње_везе" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Спољашње_везе"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Спољашње везе</span> </div> </a> <ul id="toc-Спољашње_везе-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="Садржај" 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="Прикажи/сакриј садржај" > <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">Прикажи/сакриј садржај</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">Велика полуоса</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="Чланак на другим језицима. Доступан на: 52" > <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-52" 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">52 језика</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar badge-Q70893996 mw-list-item" title=""><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B5%D9%81_%D8%A7%D9%84%D9%85%D8%AD%D9%88%D8%B1_%D8%A7%D9%84%D8%B1%D8%A6%D9%8A%D8%B3%D9%8A" title="نصف المحور الرئيسي — арапски" lang="ar" hreflang="ar" data-title="نصف المحور الرئيسي" data-language-autonym="العربية" data-language-local-name="арапски" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Semiexe_mayor" title="Semiexe mayor — астуријски" lang="ast" hreflang="ast" data-title="Semiexe mayor" data-language-autonym="Asturianu" data-language-local-name="астуријски" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Sumbu_semimayor" title="Sumbu semimayor — индонежански" lang="id" hreflang="id" data-title="Sumbu semimayor" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонежански" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Paksi_semimajor" title="Paksi semimajor — малајски" lang="ms" hreflang="ms" data-title="Paksi semimajor" data-language-autonym="Bahasa Melayu" data-language-local-name="малајски" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%93%D0%BE%D0%BB%D1%8F%D0%BC%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81" title="Голяма полуос — бугарски" lang="bg" hreflang="bg" data-title="Голяма полуос" data-language-autonym="Български" data-language-local-name="бугарски" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/K%C3%BAi-t%C5%8D_tn%CC%82g_p%C3%B2a%E2%81%BF-k%C3%A8ng" title="Kúi-tō tn̂g pòaⁿ-kèng — Minnan" lang="nan" hreflang="nan" data-title="Kúi-tō tn̂g pòaⁿ-kèng" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%92%D1%8F%D0%BB%D1%96%D0%BA%D0%B0%D1%8F_%D0%BF%D0%B0%D1%9E%D0%B2%D0%BE%D1%81%D1%8C" title="Вялікая паўвось — белоруски" lang="be" hreflang="be" data-title="Вялікая паўвось" data-language-autonym="Беларуская" data-language-local-name="белоруски" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%B0%E0%A6%BE%E0%A6%95%E0%A7%8D%E0%A6%B7" title="পরাক্ষ — бенгалски" lang="bn" hreflang="bn" data-title="পরাক্ষ" data-language-autonym="বাংলা" data-language-local-name="бенгалски" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Semieix_major" title="Semieix major — каталонски" lang="ca" hreflang="ca" data-title="Semieix major" data-language-autonym="Català" data-language-local-name="каталонски" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Velk%C3%A1_poloosa_dr%C3%A1hy" title="Velká poloosa dráhy — чешки" lang="cs" hreflang="cs" data-title="Velká poloosa dráhy" data-language-autonym="Čeština" data-language-local-name="чешки" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Gro%C3%9Fe_Halbachse" title="Große Halbachse — немачки" lang="de" hreflang="de" data-title="Große Halbachse" data-language-autonym="Deutsch" data-language-local-name="немачки" 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%97%CE%BC%CE%B9%CE%BC%CE%B5%CE%B3%CE%AC%CE%BB%CE%BF%CF%82_%CE%86%CE%BE%CE%BF%CE%BD%CE%B1%CF%82" title="Ημιμεγάλος Άξονας — грчки" lang="el" hreflang="el" data-title="Ημιμεγάλος Άξονας" data-language-autonym="Ελληνικά" data-language-local-name="грчки" 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/Semi-major_axis" title="Semi-major axis — енглески" lang="en" hreflang="en" data-title="Semi-major axis" data-language-autonym="English" data-language-local-name="енглески" 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/Semieje_mayor" title="Semieje mayor — шпански" lang="es" hreflang="es" data-title="Semieje mayor" data-language-autonym="Español" data-language-local-name="шпански" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Granda_duonakso" title="Granda duonakso — есперанто" lang="eo" hreflang="eo" data-title="Granda duonakso" data-language-autonym="Esperanto" data-language-local-name="есперанто" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Ardatzerdi_handi" title="Ardatzerdi handi — баскијски" lang="eu" hreflang="eu" data-title="Ardatzerdi handi" data-language-autonym="Euskara" data-language-local-name="баскијски" 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%86%DB%8C%D9%85%E2%80%8C%D9%82%D8%B7%D8%B1_%D8%A8%D8%B2%D8%B1%DA%AF" title="نیم‌قطر بزرگ — персијски" lang="fa" hreflang="fa" data-title="نیم‌قطر بزرگ" data-language-autonym="فارسی" data-language-local-name="персијски" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Grand_axe" title="Grand axe — француски" lang="fr" hreflang="fr" data-title="Grand axe" data-language-autonym="Français" data-language-local-name="француски" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Ais_leathmh%C3%B3r" title="Ais leathmhór — ирски" lang="ga" hreflang="ga" data-title="Ais leathmhór" data-language-autonym="Gaeilge" data-language-local-name="ирски" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Semieixo_maior" title="Semieixo maior — галицијски" lang="gl" hreflang="gl" data-title="Semieixo maior" data-language-autonym="Galego" data-language-local-name="галицијски" 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%85%E0%A4%B0%E0%A5%8D%E0%A4%A7_%E0%A4%A6%E0%A5%80%E0%A4%B0%E0%A5%8D%E0%A4%98_%E0%A4%85%E0%A4%95%E0%A5%8D%E0%A4%B7" title="अर्ध दीर्घ अक्ष — хинди" lang="hi" hreflang="hi" data-title="अर्ध दीर्घ अक्ष" data-language-autonym="हिन्दी" data-language-local-name="хинди" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A5%D5%AE_%D5%AF%D5%AB%D5%BD%D5%A1%D5%A1%D5%BC%D5%A1%D5%B6%D6%81%D6%84" title="Մեծ կիսաառանցք — јерменски" lang="hy" hreflang="hy" data-title="Մեծ կիսաառանցք" data-language-autonym="Հայերեն" data-language-local-name="јерменски" 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/Semiasse_maggiore" title="Semiasse maggiore — италијански" lang="it" hreflang="it" data-title="Semiasse maggiore" data-language-autonym="Italiano" data-language-local-name="италијански" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%BB%8C%E9%81%93%E9%95%B7%E5%8D%8A%E5%BE%84" title="軌道長半径 — јапански" lang="ja" hreflang="ja" data-title="軌道長半径" data-language-autonym="日本語" data-language-local-name="јапански" 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%93%E1%83%98%E1%83%93%E1%83%98_%E1%83%9C%E1%83%90%E1%83%AE%E1%83%94%E1%83%95%E1%83%90%E1%83%A0%E1%83%A6%E1%83%94%E1%83%A0%E1%83%AB%E1%83%98" title="დიდი ნახევარღერძი — грузијски" lang="ka" hreflang="ka" data-title="დიდი ნახევარღერძი" data-language-autonym="ქართული" data-language-local-name="грузијски" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B8%B4%EB%B0%98%EC%A7%80%EB%A6%84" title="긴반지름 — корејски" lang="ko" hreflang="ko" data-title="긴반지름" data-language-autonym="한국어" data-language-local-name="корејски" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Semiaxis_maior" title="Semiaxis maior — латински" lang="la" hreflang="la" data-title="Semiaxis maior" data-language-autonym="Latina" data-language-local-name="латински" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Orb%C4%ABtas_liel%C4%81_pusass" title="Orbītas lielā pusass — летонски" lang="lv" hreflang="lv" data-title="Orbītas lielā pusass" data-language-autonym="Latviešu" data-language-local-name="летонски" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/F%C3%A9l_nagytengely" title="Fél nagytengely — мађарски" lang="hu" hreflang="hu" data-title="Fél nagytengely" data-language-autonym="Magyar" data-language-local-name="мађарски" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%93%D0%BE%D0%BB%D0%B5%D0%BC%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%BA%D0%B0" title="Голема полуоска — македонски" lang="mk" hreflang="mk" data-title="Голема полуоска" data-language-autonym="Македонски" data-language-local-name="македонски" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%85%E0%A4%B0%E0%A5%8D%E0%A4%A7%E0%A4%A6%E0%A5%80%E0%A4%B0%E0%A5%8D%E0%A4%98_%E0%A4%85%E0%A4%95%E0%A5%8D%E0%A4%B7" title="अर्धदीर्घ अक्ष — марати" lang="mr" hreflang="mr" data-title="अर्धदीर्घ अक्ष" data-language-autonym="मराठी" data-language-local-name="марати" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Store_halvakse" title="Store halvakse — норвешки букмол" lang="nb" hreflang="nb" data-title="Store halvakse" data-language-autonym="Norsk bokmål" data-language-local-name="норвешки букмол" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Stor_halvakse" title="Stor halvakse — норвешки нинорск" lang="nn" hreflang="nn" data-title="Stor halvakse" data-language-autonym="Norsk nynorsk" data-language-local-name="норвешки нинорск" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Semiaxe_major" title="Semiaxe major — окситански" lang="oc" hreflang="oc" data-title="Semiaxe major" data-language-autonym="Occitan" data-language-local-name="окситански" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/P%C3%B3%C5%82o%C5%9B_wielka" title="Półoś wielka — пољски" lang="pl" hreflang="pl" data-title="Półoś wielka" data-language-autonym="Polski" data-language-local-name="пољски" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt badge-Q70893996 mw-list-item" title=""><a href="https://pt.wikipedia.org/wiki/Semieixo_maior" title="Semieixo maior — португалски" lang="pt" hreflang="pt" data-title="Semieixo maior" data-language-autonym="Português" data-language-local-name="португалски" 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/Semiaxa_mare" title="Semiaxa mare — румунски" lang="ro" hreflang="ro" data-title="Semiaxa mare" data-language-autonym="Română" data-language-local-name="румунски" 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%91%D0%BE%D0%BB%D1%8C%D1%88%D0%B0%D1%8F_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D1%8C" title="Большая полуось — руски" lang="ru" hreflang="ru" data-title="Большая полуось" data-language-autonym="Русский" data-language-local-name="руски" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%85%E0%B6%A9-%E0%B6%B8%E0%B7%84%E0%B7%8F_%E0%B6%85%E0%B6%9A%E0%B7%8A%E0%B7%82%E0%B6%BA" title="අඩ-මහා අක්ෂය — синхалешки" lang="si" hreflang="si" data-title="අඩ-මහා අක්ෂය" data-language-autonym="සිංහල" data-language-local-name="синхалешки" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple badge-Q70893996 mw-list-item" title=""><a href="https://simple.wikipedia.org/wiki/Semi-major_axis" title="Semi-major axis — Simple English" lang="en-simple" hreflang="en-simple" data-title="Semi-major axis" 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/Ve%C4%BEk%C3%A1_polos" title="Veľká polos — словачки" lang="sk" hreflang="sk" data-title="Veľká polos" data-language-autonym="Slovenčina" data-language-local-name="словачки" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Velika_poluosa" title="Velika poluosa — српскохрватски" lang="sh" hreflang="sh" data-title="Velika poluosa" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="српскохрватски" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Sumbu_semi-mayor" title="Sumbu semi-mayor — сундански" lang="su" hreflang="su" data-title="Sumbu semi-mayor" data-language-autonym="Sunda" data-language-local-name="сундански" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Radan_isoakselin_puolikas" title="Radan isoakselin puolikas — фински" lang="fi" hreflang="fi" data-title="Radan isoakselin puolikas" data-language-autonym="Suomi" data-language-local-name="фински" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Halv_storaxel" title="Halv storaxel — шведски" lang="sv" hreflang="sv" data-title="Halv storaxel" data-language-autonym="Svenska" data-language-local-name="шведски" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%B0%E0%AF%88%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%87%E0%AE%B0%E0%AE%9A%E0%AF%8D%E0%AE%9A%E0%AF%81" title="அரைப்பேரச்சு — тамилски" lang="ta" hreflang="ta" data-title="அரைப்பேரச்சு" data-language-autonym="தமிழ்" data-language-local-name="тамилски" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B6%E0%B9%88%E0%B8%87%E0%B9%81%E0%B8%81%E0%B8%99%E0%B9%80%E0%B8%AD%E0%B8%81" title="กึ่งแกนเอก — тајски" lang="th" hreflang="th" data-title="กึ่งแกนเอก" data-language-autonym="ไทย" data-language-local-name="тајски" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/B%C3%A1n_tr%E1%BB%A5c_l%E1%BB%9Bn" title="Bán trục lớn — вијетнамски" lang="vi" hreflang="vi" data-title="Bán trục lớn" data-language-autonym="Tiếng Việt" data-language-local-name="вијетнамски" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Ana_eksen" title="Ana eksen — турски" lang="tr" hreflang="tr" data-title="Ana eksen" data-language-autonym="Türkçe" data-language-local-name="турски" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D1%96%D0%B2%D0%B2%D1%96%D1%81%D1%8C" title="Велика піввісь — украјински" lang="uk" hreflang="uk" data-title="Велика піввісь" data-language-autonym="Українська" data-language-local-name="украјински" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8D%8A%E9%95%B7%E8%BB%B8" title="半長軸 — кинески" lang="zh" hreflang="zh" data-title="半長軸" data-language-autonym="中文" data-language-local-name="кинески" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%8D%8A%E9%95%B7%E8%BB%B8" title="半長軸 — кантонски" lang="yue" hreflang="yue" data-title="半長軸" data-language-autonym="粵語" data-language-local-name="кантонски" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q171594#sitelinks-wikipedia" title="Уреди међујезичке везе" class="wbc-editpage">Уреди везе</a></span></div> </div> </div> </div> </header> 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<div class="mw-indicators"> </div> <div id="siteSub" class="noprint">С Википедије, слободне енциклопедије</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="sr" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%D0%94%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Ellipse_semi-major_and_minor_axes.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Ellipse_semi-major_and_minor_axes.svg/260px-Ellipse_semi-major_and_minor_axes.svg.png" decoding="async" width="260" height="159" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Ellipse_semi-major_and_minor_axes.svg/390px-Ellipse_semi-major_and_minor_axes.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Ellipse_semi-major_and_minor_axes.svg/520px-Ellipse_semi-major_and_minor_axes.svg.png 2x" data-file-width="720" data-file-height="440" /></a><figcaption>Велика (<i>a</i>) и мала полуоса (<i>b</i>б) елипсе</figcaption></figure> <p><b>Велика полуоса</b> у геометрији служи да опише димензије <a href="/wiki/%D0%95%D0%BB%D0%B8%D0%BF%D1%81%D0%B0" title="Елипса">елипсе</a> или <a href="/wiki/%D0%A5%D0%B8%D0%BF%D0%B5%D1%80%D0%B1%D0%BE%D0%BB%D0%B0" title="Хипербола">хиперболе</a>.<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> У <a href="/wiki/Geometry" class="mw-redirect" title="Geometry">геометрији</a>, <i>главна оса</i> <a href="/wiki/Ellipse" class="mw-redirect" title="Ellipse">елипсе</a> је њен најдужи <a href="/wiki/Diameter" class="mw-redirect" title="Diameter">пречник</a>: <a href="/wiki/Line_segment" class="mw-redirect" title="Line segment">сегмент линије</a> који пролази кроз центар и оба <a href="/w/index.php?title=Focus_(geometry)&action=edit&redlink=1" class="new" title="Focus (geometry) (страница не постоји)">фокуса</a>, са крајевима у две најшире одвојене тачке <a href="/wiki/Perimeter" class="mw-redirect" title="Perimeter">периметра</a>. <i>Велика полуоса</i> је најдужи <a href="/w/index.php?title=Semidiameter&action=edit&redlink=1" class="new" title="Semidiameter (страница не постоји)">полупречник</a> или једна половина велике осе, и тако иде од центра, кроз фокус и до периметра. <i>Мала полуоса</i> елипсе или <a href="/wiki/Hyperbola" class="mw-redirect" title="Hyperbola">хиперболе</a> је сегмент праве који је под <a href="/wiki/Right_angle" class="mw-redirect" title="Right angle">правим углом</a> са великом полуосом и има један крај у центру <a href="/wiki/Conic_section" class="mw-redirect" title="Conic section">конусног пресека</a>. За посебан случај круга, дужине полуосе су једнаке <a href="/wiki/Radius" class="mw-redirect" title="Radius">полупречнику</a> круга. </p><p>Дужина велике полуосе <span class="texhtml mvar" style="font-style:italic;">a</span> елипсе повезана је са дужином мале полуосе <span class="texhtml mvar" style="font-style:italic;">b</span> кроз <a href="/wiki/Eccentricity_(mathematics)" class="mw-redirect" title="Eccentricity (mathematics)">ексцентрицитет</a> <span class="texhtml mvar" style="font-style:italic;">e</span> и <a href="/wiki/Semi-latus_rectum" class="mw-redirect" title="Semi-latus rectum">полу-латус ректум</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 \ell }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ℓ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f066e981e530bacc07efc6a10fa82deee985929e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.97ex; height:2.176ex;" alt="{\displaystyle \ell }"></span>, на следећи начин: </p> <style data-mw-deduplicate="TemplateStyles:r23521346">.mw-parser-output .block-indent{padding-left:3em;padding-right:0;overflow:hidden}</style><div class="block-indent"><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 {\begin{aligned}b&=a{\sqrt {1-e^{2}}},\\\ell &=a(1-e^{2}),\\a\ell &=b^{2}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>b</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>ℓ</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>a</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>a</mi> <mi>ℓ</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}b&=a{\sqrt {1-e^{2}}},\\\ell &=a(1-e^{2}),\\a\ell &=b^{2}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed50a264eee7832d931b7b3a15590649ecfeac1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:16.39ex; height:9.843ex;" alt="{\displaystyle {\begin{aligned}b&=a{\sqrt {1-e^{2}}},\\\ell &=a(1-e^{2}),\\a\ell &=b^{2}.\end{aligned}}}"></span></div> <p>Велика полуоса <a href="/wiki/Hyperbola" class="mw-redirect" title="Hyperbola">хиперболе</a> је, у зависности од конвенције, плус или минус половина растојања између две гране. Дакле, то је растојање од центра до било ког <a href="/w/index.php?title=Vertex_(curve)&action=edit&redlink=1" class="new" title="Vertex (curve) (страница не постоји)">врха</a> хиперболе. </p><p><a href="/wiki/%D0%9F%D0%B0%D1%80%D0%B0%D0%B1%D0%BE%D0%BB%D0%B0" title="Парабола">Парабола</a> се може добити као граница низа елипса где је један фокус фиксиран док је другом дозвољено да се помера произвољно далеко у једном правцу, држећи <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 \ell }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ℓ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f066e981e530bacc07efc6a10fa82deee985929e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.97ex; height:2.176ex;" alt="{\displaystyle \ell }"></span> фиксним. Тако <span class="texhtml mvar" style="font-style:italic;">a</span> и <span class="texhtml mvar" style="font-style:italic;">b</span> теже бесконачности, <span class="texhtml mvar" style="font-style:italic;">a</span> брже од <span class="texhtml mvar" style="font-style:italic;">b</span>. </p><p>Велика и мала оса су <a href="/w/index.php?title=Axis_of_symmetry&action=edit&redlink=1" class="new" title="Axis of symmetry (страница не постоји)">оса симетрије</a> за криву: у елипси, мала оса је краћа; код хиперболе је она која не сече хиперболу. </p><p>У <a href="/wiki/%D0%90%D1%81%D1%82%D1%80%D0%BE%D0%BD%D0%BE%D0%BC%D0%B8%D1%98%D0%B0" title="Астрономија">астрономији</a> велика полуоса је један од шест <a href="/wiki/%D0%9E%D1%80%D0%B1%D0%B8%D1%82%D0%B0%D0%BB%D0%BD%D0%B8_%D0%B5%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B8" title="Орбитални елементи">орбиталних елемената</a> који описују <a href="/wiki/%D0%9E%D1%80%D0%B1%D0%B8%D1%82%D0%B0" title="Орбита">путању</a> једног тела. Велика полуоса код елиптичне путање је половина веће осе <a href="/wiki/%D0%95%D0%BB%D0%B8%D0%BF%D1%81%D0%B0" title="Елипса">елипсе</a>, и представља, како би се могло рећи просечно растојање објекта од Сунца, ако се ради о елиптичној путањи где је Сунце у једној од <a href="/wiki/%D0%A4%D0%BE%D0%BA%D1%83%D1%81_(%D0%BE%D0%BF%D1%82%D0%B8%D0%BA%D0%B0)" title="Фокус (оптика)">жижа</a>. <a href="/wiki/%D0%9E%D1%80%D0%B1%D0%B8%D1%82%D0%B0%D0%BB%D0%BD%D0%B8_%D0%BF%D0%B5%D1%80%D0%B8%D0%BE%D0%B4" title="Орбитални период">Орбитални период</a> објекта се у односу на велику осу, о чему говори <a href="/wiki/%D0%A2%D1%80%D0%B5%D1%9B%D0%B8_%D0%9A%D0%B5%D0%BF%D0%BB%D0%B5%D1%80%D0%BE%D0%B2_%D0%B7%D0%B0%D0%BA%D0%BE%D0%BD" class="mw-redirect" title="Трећи Кеплеров закон">трећи Кеплеров закон</a>,<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><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> односи као: <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^{2}\propto a^{3}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>∝</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T^{2}\propto a^{3}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26438d70943ab7944d3eca7efb032f5e22e97880" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.544ex; height:2.676ex;" alt="{\displaystyle T^{2}\propto a^{3}\,}"></span> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Елипса"><span id=".D0.95.D0.BB.D0.B8.D0.BF.D1.81.D0.B0"></span>Елипса</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&veaction=edit&section=1" title="Уредите одељак „Елипса”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&action=edit&section=1" title="Уреди извор одељка: Елипса"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Једначина елипсе је </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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 {\frac {(x-h)^{2}}{a^{2}}}+{\frac {(y-k)^{2}}{b^{2}}}=1,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>h</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>y</mi> <mo>−</mo> <mi>k</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {(x-h)^{2}}{a^{2}}}+{\frac {(y-k)^{2}}{b^{2}}}=1,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60608b4a2a8c795ba807697cbfe30e915d11ee26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:25.864ex; height:6.176ex;" alt="{\displaystyle {\frac {(x-h)^{2}}{a^{2}}}+{\frac {(y-k)^{2}}{b^{2}}}=1,}"></span></div> <p>где је (<i>h</i>, <i>k</i>) центар елипсе у <a href="/wiki/Coordinates_(elementary_mathematics)" class="mw-redirect" title="Coordinates (elementary mathematics)">Декартовим координатама</a>, у којој је произвољна тачка дата са (<i>x</i>, <i>y</i>). </p><p>Главна полуоса је средња вредност максималног и минималног растојања: <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_{\text{max}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>max</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{\text{max}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73a6ee225c851851556a8dd1fbfdac372c78025a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.34ex; height:2.009ex;" alt="{\displaystyle r_{\text{max}}}"></span> и <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_{\text{min}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>min</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{\text{min}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c2982e4fb1cdc5592601df96022a32c76b0b8f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.021ex; height:2.009ex;" alt="{\displaystyle r_{\text{min}}}"></span> елипсе из фокуса — то јест, растојања од фокуса до крајњих тачака главне осе </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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={\frac {r_{\text{max}}+r_{\text{min}}}{2}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>max</mtext> </mrow> </msub> <mo>+</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>min</mtext> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a={\frac {r_{\text{max}}+r_{\text{min}}}{2}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10ed6d4463383abe7efce16fb5c47d837ef8ac5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.012ex; height:5.009ex;" alt="{\displaystyle a={\frac {r_{\text{max}}+r_{\text{min}}}{2}}.}"></span></div> <p>У астрономији ове екстремне тачке се називају <a href="/wiki/Apsis" class="mw-redirect" title="Apsis">апсиде</a>.<sup id="cite_ref-lissauer2019_4-0" class="reference"><a href="#cite_note-lissauer2019-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Мала полуоса елипсе је <a href="/wiki/Geometric_mean" class="mw-redirect" title="Geometric mean">геометријска средина</a> ових растојања: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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 b={\sqrt {r_{\text{max}}r_{\text{min}}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>max</mtext> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>min</mtext> </mrow> </msub> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b={\sqrt {r_{\text{max}}r_{\text{min}}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24298cc74de2185914634ea24af7db1cd283b0e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:15.04ex; height:3.009ex;" alt="{\displaystyle b={\sqrt {r_{\text{max}}r_{\text{min}}}}.}"></span></div> <p><a href="/wiki/Eccentricity_(mathematics)" class="mw-redirect" title="Eccentricity (mathematics)">Ексцентрицитет</a> елипсе се дефинише као </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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 e={\sqrt {1-{\frac {b^{2}}{a^{2}}}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e={\sqrt {1-{\frac {b^{2}}{a^{2}}}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b29cc155528dda40ce3f4acfac37a998259f11b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:14.276ex; height:7.509ex;" alt="{\displaystyle e={\sqrt {1-{\frac {b^{2}}{a^{2}}}}},}"></span></div> <p>те је </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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_{\text{min}}=a(1-e),\quad r_{\text{max}}=a(1+e).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>min</mtext> </mrow> </msub> <mo>=</mo> <mi>a</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>e</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="1em" /> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>max</mtext> </mrow> </msub> <mo>=</mo> <mi>a</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>e</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{\text{min}}=a(1-e),\quad r_{\text{max}}=a(1+e).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c837e2fe4b724069aa1fd027137bc0b5ff128a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.812ex; height:2.843ex;" alt="{\displaystyle r_{\text{min}}=a(1-e),\quad r_{\text{max}}=a(1+e).}"></span></div> <p>Сада размотрино једначину у <a href="/wiki/Polar_coordinate_system" class="mw-redirect" title="Polar coordinate system">поларним координатама</a>, са једним фокусом на исходишту, а другим у правцу <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 \theta =\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>=</mo> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta =\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab4db588619489e27efb50a1d0d5aa016c49ce15" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.521ex; height:2.176ex;" alt="{\displaystyle \theta =\pi }"></span>: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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+e\cos \theta )=\ell .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>e</mi> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ℓ</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r(1+e\cos \theta )=\ell .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/376419b1bdb80e4d677e01692e5513eac760d5c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.635ex; height:2.843ex;" alt="{\displaystyle r(1+e\cos \theta )=\ell .}"></span></div> <p>Средња вредност од <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=\ell /(1-e)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>e</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=\ell /(1-e)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96659b5179e951346d7ce5eb75bd89b5318243aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.175ex; height:2.843ex;" alt="{\displaystyle r=\ell /(1-e)}"></span> и <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=\ell /(1+e)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>e</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=\ell /(1+e)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/190ef1cc6e2156aaf9b572db0b651e3c17dab086" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.175ex; height:2.843ex;" alt="{\displaystyle r=\ell /(1+e)}"></span>, за <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 \theta =\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>=</mo> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta =\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab4db588619489e27efb50a1d0d5aa016c49ce15" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.521ex; height:2.176ex;" alt="{\displaystyle \theta =\pi }"></span> и <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 \theta =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a7bc6e34b53e0e8a8815159c356b1acccf7ea24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.351ex; height:2.176ex;" alt="{\displaystyle \theta =0}"></span> је </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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={\frac {\ell }{1-e^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ℓ</mi> <mrow> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a={\frac {\ell }{1-e^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2789e37cd50fd5edc6be243e1f797279632038b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.952ex; height:5.843ex;" alt="{\displaystyle a={\frac {\ell }{1-e^{2}}}.}"></span></div> <p>У елипси, велика полуоса је <a href="/wiki/Geometric_mean" class="mw-redirect" title="Geometric mean">геометријска средина</a> удаљености од центра до било ког фокуса и растојања од центра до било које директрисе. </p><p>Мала полуоса елипсе иде од центра елипсе (тачка на пола пута између и на линији која пролази између <a href="/w/index.php?title=Focus_(geometry)&action=edit&redlink=1" class="new" title="Focus (geometry) (страница не постоји)">жаришта</a>) до ивице елипсе. Мала полу-оса је половина мале осе. Мала оса је најдужи линијски сегмент нормалан на главну осу који спаја две тачке на ивици елипсе. </p><p>Мала полуоса <span class="texhtml mvar" style="font-style:italic;">b</span> је повезана са великом полуосом <span class="texhtml mvar" style="font-style:italic;">a</span> кроз ексцентрицитет <span class="texhtml mvar" style="font-style:italic;">e</span> и <a href="/wiki/Semi-latus_rectum" class="mw-redirect" title="Semi-latus rectum">полулатус ректум</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 \ell }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ℓ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f066e981e530bacc07efc6a10fa82deee985929e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.97ex; height:2.176ex;" alt="{\displaystyle \ell }"></span>, на следећи начин: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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 {\begin{aligned}b&=a{\sqrt {1-e^{2}}},\\a\ell &=b^{2}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>b</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi>a</mi> <mi>ℓ</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}b&=a{\sqrt {1-e^{2}}},\\a\ell &=b^{2}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/026c1776fbe4da82b8642cc51b6a3b5676d7c51d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:16.39ex; height:6.509ex;" alt="{\displaystyle {\begin{aligned}b&=a{\sqrt {1-e^{2}}},\\a\ell &=b^{2}.\end{aligned}}}"></span></div> <p><a href="/wiki/%D0%9F%D0%B0%D1%80%D0%B0%D0%B1%D0%BE%D0%BB%D0%B0" title="Парабола">Парабола</a> се може добити као граница низа елипси где је један фокус фиксиран док је другом дозвољено да се помера произвољно далеко у једном правцу, држећи <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 \ell }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ℓ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f066e981e530bacc07efc6a10fa82deee985929e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.97ex; height:2.176ex;" alt="{\displaystyle \ell }"></span> фиксним. Тако <span class="texhtml mvar" style="font-style:italic;">a</span> и <span class="texhtml mvar" style="font-style:italic;">b</span> теже бесконачности, <span class="texhtml mvar" style="font-style:italic;">a</span> брже од <span class="texhtml mvar" style="font-style:italic;">b</span>. </p><p>Дужина мале полуосе се такође може наћи помоћу следеће формуле:<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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 2b={\sqrt {(p+q)^{2}-f^{2}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <mi>p</mi> <mo>+</mo> <mi>q</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2b={\sqrt {(p+q)^{2}-f^{2}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/faf59442233adfefdb991d6b8e696c7fa54555cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:21.387ex; height:4.843ex;" alt="{\displaystyle 2b={\sqrt {(p+q)^{2}-f^{2}}},}"></span></div> <p>где је <span class="texhtml mvar" style="font-style:italic;">f</span> растојање између фокуса, <span class="texhtml mvar" style="font-style:italic;">p</span> и <span class="texhtml mvar" style="font-style:italic;">q</span> су растојања од сваког фокуса до било које тачке у елипси. </p> <div class="mw-heading mw-heading2"><h2 id="Хипербола"><span id=".D0.A5.D0.B8.D0.BF.D0.B5.D1.80.D0.B1.D0.BE.D0.BB.D0.B0"></span>Хипербола</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&veaction=edit&section=2" title="Уредите одељак „Хипербола”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&action=edit&section=2" title="Уреди извор одељка: Хипербола"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Велика полуоса <a href="/wiki/Hyperbola" class="mw-redirect" title="Hyperbola">хиперболе</a> је, у зависности од конвенције, плус или минус половина растојања између две гране; ако је ово <span class="texhtml mvar" style="font-style:italic;">a</span> у x-смеру, једначина је: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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 {\frac {\left(x-h\right)^{2}}{a^{2}}}-{\frac {\left(y-k\right)^{2}}{b^{2}}}=1.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>−</mo> <mi>h</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow> <mo>(</mo> <mrow> <mi>y</mi> <mo>−</mo> <mi>k</mi> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mn>1.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\left(x-h\right)^{2}}{a^{2}}}-{\frac {\left(y-k\right)^{2}}{b^{2}}}=1.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf506e71968b40dc09ff048698fe51c9832dc088" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:25.864ex; height:6.343ex;" alt="{\displaystyle {\frac {\left(x-h\right)^{2}}{a^{2}}}-{\frac {\left(y-k\right)^{2}}{b^{2}}}=1.}"></span></div> <p>У погледу семи-латус ректума и ексцентричности које важи </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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={\ell \over e^{2}-1}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ℓ</mi> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a={\ell \over e^{2}-1}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e8e65e9f2f133eae9c9616111fb0a5fe77e7e68" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.952ex; height:5.843ex;" alt="{\displaystyle a={\ell \over e^{2}-1}.}"></span></div> <p>Попречна оса хиперболе поклапа се са великом осом.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>У хиперболи, коњугирана оса или мала оса дужине <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 2b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3da45af0250645a54cab2ef45483c4399e4a40df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.16ex; height:2.176ex;" alt="{\displaystyle 2b}"></span>, која одговара малој оси елипсе, може се повући окомито на попречну осу или главну осу, која повезује два <a href="/w/index.php?title=Vertex_(curve)&action=edit&redlink=1" class="new" title="Vertex (curve) (страница не постоји)">врха</a> (прекретнице) хиперболе, са две осе које се секу у центру хиперболе. Крајње тачке <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 (0,\pm b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mo>±</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (0,\pm b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4a4b6f543f2c7d7fbb812baa5306a5a9ced8c21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.811ex; height:2.843ex;" alt="{\displaystyle (0,\pm b)}"></span> мале осе леже у висини асимптота изнад/испод врхова хиперболе. Било која половина мале осе се назива полумала оса, дужине <span class="texhtml mvar" style="font-style:italic;">b</span>. Означавајући дужину велике полуосе (удаљеност од центра до темена) као <span class="texhtml mvar" style="font-style:italic;">a</span>, дужине мале и велике полуосе се појављују у једначини хиперболе у односу на ове осе на следећи начин: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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 {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mn>1.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1dca7da192772ac6dca32d5bdc3782d59955a319" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.019ex; height:6.009ex;" alt="{\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1.}"></span></div> <p>Мала полуоса је такође растојање од једног од фокуса хиперболе до асимптоте. Често звана <a href="/w/index.php?title=Impact_parameter&action=edit&redlink=1" class="new" title="Impact parameter (страница не постоји)">параметар удара</a>, она је важна у физици и астрономији и изражава раздаљину на којој ће честица промашити фокус ако тело у фокусу не омета њено путовање. </p><p>Мала полуоса и велика полуоса су повезане кроз ексцентрицитет, на следећи начин: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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 b=a{\sqrt {e^{2}-1}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b=a{\sqrt {e^{2}-1}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6edd082f68fec0c2955becbad4f23f47560524c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.437ex; height:3.509ex;" alt="{\displaystyle b=a{\sqrt {e^{2}-1}}.}"></span><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></div> <p>Треба имати на уму да у хиперболи <span class="texhtml mvar" style="font-style:italic;">b</span> може бити веће од <span class="texhtml mvar" style="font-style:italic;">a</span>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Астрономија"><span id=".D0.90.D1.81.D1.82.D1.80.D0.BE.D0.BD.D0.BE.D0.BC.D0.B8.D1.98.D0.B0"></span>Астрономија</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&veaction=edit&section=3" title="Уредите одељак „Астрономија”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&action=edit&section=3" title="Уреди извор одељка: Астрономија"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Орбитални_период"><span id=".D0.9E.D1.80.D0.B1.D0.B8.D1.82.D0.B0.D0.BB.D0.BD.D0.B8_.D0.BF.D0.B5.D1.80.D0.B8.D0.BE.D0.B4"></span>Орбитални период</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&veaction=edit&section=4" title="Уредите одељак „Орбитални период”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&action=edit&section=4" title="Уреди извор одељка: Орбитални период"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>У <a href="/wiki/Astrodynamics" class="mw-redirect" title="Astrodynamics">астродинамици</a> <a href="/wiki/Orbital_period" class="mw-redirect" title="Orbital period">орбитални период</a> <span class="texhtml mvar" style="font-style:italic;">T</span> малог тела које кружи око централног тела у кружној или елиптичној орбити је:<sup id="cite_ref-lissauer2019_4-1" class="reference"><a href="#cite_note-lissauer2019-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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=2\pi {\sqrt {\frac {a^{3}}{\mu }}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mi>μ</mi> </mfrac> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T=2\pi {\sqrt {\frac {a^{3}}{\mu }}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e563bb9968d8428b2747af41f3c1a2f1815a3b6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:13.32ex; height:7.676ex;" alt="{\displaystyle T=2\pi {\sqrt {\frac {a^{3}}{\mu }}},}"></span></div> <p>где је: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><span class="texhtml mvar" style="font-style:italic;">a</span> дужина велике полуосе орбите,</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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> </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/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> је <a href="/w/index.php?title=Standard_gravitational_parameter&action=edit&redlink=1" class="new" title="Standard gravitational parameter (страница не постоји)">стандардни гравитациони параметар</a> централног тела.</div> <p>Све елипсе са датом великом полуосом имају исти орбитални период, без обзира на њихов ексцентрицитет. </p><p><a href="/w/index.php?title=Specific_relative_angular_momentum&action=edit&redlink=1" class="new" title="Specific relative angular momentum (страница не постоји)">Специфични угаони момент</a> <span class="texhtml mvar" style="font-style:italic;">h</span> малог тела које кружи око централног тела у кружној или елиптичној орбити је<sup id="cite_ref-lissauer2019_4-2" class="reference"><a href="#cite_note-lissauer2019-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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={\sqrt {a\mu (1-e^{2})}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>a</mi> <mi>μ</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h={\sqrt {a\mu (1-e^{2})}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c60aea24c047c5665110812cb5c4ff328362a3a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:17.989ex; height:4.843ex;" alt="{\displaystyle h={\sqrt {a\mu (1-e^{2})}},}"></span></div> <p>где је: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><span class="texhtml mvar" style="font-style:italic;">a</span> и <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> </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/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> су као што је горе дефинисано,</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><span class="texhtml mvar" style="font-style:italic;">e</span> је ексцентрицитет орбите.</div> <p>У <a href="/wiki/Astronomy" class="mw-redirect" title="Astronomy">астрономији</a>, велика полуоса је један од најважнијих <a href="/wiki/Orbital_elements" class="mw-redirect" title="Orbital elements">орбиталних елемената</a> <a href="/wiki/Orbit" class="mw-redirect" title="Orbit">орбите</a>, заједно са њеним <a href="/wiki/Orbital_period" class="mw-redirect" title="Orbital period">орбиталним периодом</a>. За објекте <a href="/wiki/Solar_System" class="mw-redirect" title="Solar System">Сунчевог система</a>, велика полуоса је повезана са периодом орбите по <a href="/wiki/Kepler%27s_laws_of_planetary_motion" class="mw-redirect" title="Kepler's laws of planetary motion">Кеплеровом трећем закону</a> (првобитно <a href="/w/index.php?title=Empirical&action=edit&redlink=1" class="new" title="Empirical (страница не постоји)">емпиријски</a> изведеном):<sup id="cite_ref-lissauer2019_4-3" class="reference"><a href="#cite_note-lissauer2019-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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^{2}\propto a^{3},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>∝</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T^{2}\propto a^{3},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d339f81d403ae23a32d04963aa2596ad30efda2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.804ex; height:3.009ex;" alt="{\displaystyle T^{2}\propto a^{3},}"></span></div> <p>где је <span class="texhtml mvar" style="font-style:italic;">T</span> период, а <span class="texhtml mvar" style="font-style:italic;">a</span> велика полуоса. Испоставило се да је овај облик поједностављење опште форме за <a href="/wiki/Two-body_problem" class="mw-redirect" title="Two-body problem">проблем два тела</a>, како је одредио <a href="/wiki/Isaac_Newton" class="mw-redirect" title="Isaac Newton">Њутн</a>:<sup id="cite_ref-lissauer2019_4-4" class="reference"><a href="#cite_note-lissauer2019-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r23521346"><div class="block-indent"><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^{2}={\frac {4\pi ^{2}}{G(M+m)}}a^{3},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>G</mi> <mo stretchy="false">(</mo> <mi>M</mi> <mo>+</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T^{2}={\frac {4\pi ^{2}}{G(M+m)}}a^{3},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c91bf0b3fb7fbf28fdde676c374680da1a494ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:20.599ex; height:6.509ex;" alt="{\displaystyle T^{2}={\frac {4\pi ^{2}}{G(M+m)}}a^{3},}"></span></div> <p>где је <span class="texhtml mvar" style="font-style:italic;">G</span> <a href="/wiki/Gravitational_constant" class="mw-redirect" title="Gravitational constant">гравитациона константа</a>, <span class="texhtml mvar" style="font-style:italic;">M</span> <a href="/wiki/%D0%9C%D0%B0%D1%81%D0%B0" title="Маса">маса</a> централног тела, а <span class="texhtml mvar" style="font-style:italic;">m</span> маса тела у орбити. Типично, маса централног тела је толико већа од масе тела у орбити, да се <span class="texhtml mvar" style="font-style:italic;">m</span> може занемарити. Изношење те претпоставке и коришћење типичних астрономских јединица резултира једноставнијим обликом који је Кеплер открио </p> <div class="mw-heading mw-heading3"><h3 id="Велике_и_полу-мале_осе_путања_планета"><span id=".D0.92.D0.B5.D0.BB.D0.B8.D0.BA.D0.B5_.D0.B8_.D0.BF.D0.BE.D0.BB.D1.83-.D0.BC.D0.B0.D0.BB.D0.B5_.D0.BE.D1.81.D0.B5_.D0.BF.D1.83.D1.82.D0.B0.D1.9A.D0.B0_.D0.BF.D0.BB.D0.B0.D0.BD.D0.B5.D1.82.D0.B0"></span>Велике и полу-мале осе путања планета</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&veaction=edit&section=5" title="Уредите одељак „Велике и полу-мале осе путања планета”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&action=edit&section=5" title="Уреди извор одељка: Велике и полу-мале осе путања планета"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Орбите планета се увек наводе као главни примери елипса (<a href="/wiki/Kepler%27s_laws_of_planetary_motion" class="mw-redirect" title="Kepler's laws of planetary motion">Кеплеров први закон</a>). Међутим, минимална разлика између велике и полумале осе показује да су оне практично кружног изгледа. Та разлика (или однос) је заснована на ексцентрицитету и израчунава се као <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 {\frac {a}{b}}={\frac {1}{\sqrt {1-e^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {a}{b}}={\frac {1}{\sqrt {1-e^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbd1a6988e45aaa4ebfe432a63f20d853c891578" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:14.465ex; height:6.509ex;" alt="{\displaystyle {\frac {a}{b}}={\frac {1}{\sqrt {1-e^{2}}}}}"></span>, што за типичне ексцентричности планета даје веома мале резултати. </p><p>Разлог за претпоставку о истакнутим елиптичним орбитама вероватно лежи у много већој разлици између афела и перихела. Та разлика (или однос) се такође заснива на ексцентрицитету и израчунава се као <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 {\frac {r_{\text{a}}}{r_{\text{p}}}}={\frac {1+e}{1-e}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>e</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mi>e</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {r_{\text{a}}}{r_{\text{p}}}}={\frac {1+e}{1-e}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4df02be48a1e24965dbe7776b034bd80fe3074b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:12.052ex; height:5.843ex;" alt="{\displaystyle {\frac {r_{\text{a}}}{r_{\text{p}}}}={\frac {1+e}{1-e}}}"></span>. Због велике разлике између афела и перихела, <a href="/wiki/Kepler%27s_laws_of_planetary_motion" class="mw-redirect" title="Kepler's laws of planetary motion">Кеплеров други закон</a> се лако визуелизује. </p> <table class="wikitable sortable" style="margin: 1em auto; text-align: center;"> <tbody><tr> <th class="unsortable"> </th> <th><a href="/wiki/Orbital_eccentricity" class="mw-redirect" title="Orbital eccentricity">Ексцентрицитет</a> </th> <th>Велика полуоса <i>a</i> (<a href="/wiki/Astronomical_unit" class="mw-redirect" title="Astronomical unit">AU</a>) </th> <th>Мала полуоса <i>b</i> (<a href="/wiki/Astronomical_unit" class="mw-redirect" title="Astronomical unit">AU</a>) </th> <th>Разлика (%) </th> <th><a href="/wiki/Perihelion" class="mw-redirect" title="Perihelion">Перихел</a> (<a href="/wiki/Astronomical_unit" class="mw-redirect" title="Astronomical unit">AU</a>) </th> <th><a href="/wiki/Aphelion" class="mw-redirect" title="Aphelion">Афел</a> (<a href="/wiki/Astronomical_unit" class="mw-redirect" title="Astronomical unit">AU</a>) </th> <th>Разлика (%) </th></tr> <tr> <th><a href="/wiki/Mercury_(planet)" class="mw-redirect" title="Mercury (planet)">Меркур</a> </th> <td>0,206 </td> <td>0,38700 </td> <td>0,37870 </td> <td>2,2 </td> <td>0,307 </td> <td>0,467 </td> <td>52 </td></tr> <tr> <th><a href="/wiki/Venus" class="mw-redirect" title="Venus">Венера</a> </th> <td>0,007 </td> <td>0,72300 </td> <td>0,72298 </td> <td>0,002 </td> <td>0,718 </td> <td>0,728 </td> <td>1,4 </td></tr> <tr> <th><a href="/wiki/Earth" class="mw-redirect" title="Earth">Земља</a> </th> <td>0,017 </td> <td>1,00000 </td> <td>0,99986 </td> <td>0,014 </td> <td>0,983 </td> <td>1,017 </td> <td>3,5 </td></tr> <tr> <th><a href="/wiki/%D0%9C%D0%B0%D1%80%D1%81" title="Марс">Марс</a> </th> <td>0,093 </td> <td>1,52400 </td> <td>1,51740 </td> <td>0,44 </td> <td>1,382 </td> <td>1,666 </td> <td>21 </td></tr> <tr> <th><a href="/wiki/%D0%88%D1%83%D0%BF%D0%B8%D1%82%D0%B5%D1%80" title="Јупитер">Јупитер</a> </th> <td>0,049 </td> <td>5,20440 </td> <td>5,19820 </td> <td>0,12 </td> <td>4,950 </td> <td>5,459 </td> <td>10 </td></tr> <tr> <th><a href="/wiki/%D0%A1%D0%B0%D1%82%D1%83%D1%80%D0%BD" title="Сатурн">Сатурн</a> </th> <td>0,057 </td> <td>9,58260 </td> <td>9,56730 </td> <td>0,16 </td> <td>9,041 </td> <td>10,124 </td> <td>12 </td></tr> <tr> <th><a href="/wiki/Uranus" class="mw-redirect" title="Uranus">Уран</a> </th> <td>0,046 </td> <td>19,21840 </td> <td>19,19770 </td> <td>0,11 </td> <td>18,330 </td> <td>20,110 </td> <td>9,7 </td></tr> <tr> <th><a href="/wiki/Neptune" class="mw-redirect" title="Neptune">Нептун</a> </th> <td>0,010 </td> <td>30,11000 </td> <td>30,10870 </td> <td>0,004 </td> <td>29,820 </td> <td>30,400 </td> <td>1,9 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Референце"><span id=".D0.A0.D0.B5.D1.84.D0.B5.D1.80.D0.B5.D0.BD.D1.86.D0.B5"></span>Референце</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&veaction=edit&section=6" title="Уредите одељак „Референце”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&action=edit&section=6" title="Уреди извор одељка: Референце"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r28440201">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20021014232553/http://www.amsat.org/amsat/keps/kepmodel.html">„Tutorial”</a>. <i><a href="/w/index.php?title=AMSAT&action=edit&redlink=1" class="new" title="AMSAT (страница не постоји)">AMSAT</a></i>. 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Приступљено <span class="nowrap">05. 07. 2022</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.btitle=7.1+Alternative+Characterization&rft.genre=unknown&rft_id=http%3A%2F%2Fwww.geom.uiuc.edu%2Fdocs%2Freference%2FCRC-formulas%2Fnode27.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Литература"><span id=".D0.9B.D0.B8.D1.82.D0.B5.D1.80.D0.B0.D1.82.D1.83.D1.80.D0.B0"></span>Литература</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&veaction=edit&section=7" title="Уредите одељак „Литература”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&action=edit&section=7" title="Уреди извор одељка: Литература"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r28440192">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li>Р. Грин: „Астрономија: Класика у новом руху“, Веста, 1998.</li> <li>З. Бркић и Б. Шеварлић: „Општа астрономија“, <a href="/wiki/%D0%9D%D0%B0%D1%83%D1%87%D0%BD%D0%B0_%D0%BA%D1%9A%D0%B8%D0%B3%D0%B0" title="Научна књига">Научна књига</a>, 1981.</li> <li><cite class="citation journal">Gurfil, Pini (2005). „Euler parameters as nonsingular orbital elements in Near-Equatorial Orbits”. <i>J. Guid. Contrl. Dynamics</i>. <b>28</b> (5): 1079—1084. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a>:<a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/2005JGCD...28.1079G">2005JGCD...28.1079G</a>. <a href="/wiki/Digitalni_identifikator_objekta" title="Digitalni identifikator objekta">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2514%2F1.14760">10.2514/1.14760</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.atitle=Euler+parameters+as+nonsingular+orbital+elements+in+Near-Equatorial+Orbits&rft.aufirst=Pini&rft.aulast=Gurfil&rft.date=2005&rft.genre=article&rft.issue=5&rft.jtitle=J.+Guid.+Contrl.+Dynamics&rft.pages=1079-1084&rft.volume=28&rft_id=info%3Abibcode%2F2005JGCD...28.1079G&rft_id=info%3Adoi%2F10.2514%2F1.14760&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation report"><a rel="nofollow" class="external text" href="https://www.celestrak.com/NORAD/documentation/spacetrk.pdf">Report No. 3</a> <span style="font-size:85%;">(PDF)</span>. <i>celestrak</i> (Извештај). Spacetrack. <a href="/w/index.php?title=North_American_Aerospace_Defense_Command&action=edit&redlink=1" class="new" title="North American Aerospace Defense Command (страница не постоји)">North American Aerospace Defense Command</a> (NORAD).</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.btitle=Report+No.+3&rft.genre=report&rft.pub=North+American+Aerospace+Defense+Command+%28NORAD%29&rft.series=Spacetrack&rft_id=https%3A%2F%2Fwww.celestrak.com%2FNORAD%2Fdocumentation%2Fspacetrk.pdf&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span> – a serious treatment of orbital elements</li> <li><cite class="citation web"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160326061740/http://celestrak.com/columns/v04n03/">„FAQ”</a>. <i>Celestrak</i>. Two-Line Elements. Архивирано из <a rel="nofollow" class="external text" href="http://celestrak.com/columns/v04n03/">оригинала</a> 2016-03-26. г.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.atitle=FAQ&rft.genre=unknown&rft.jtitle=Celestrak&rft_id=http%3A%2F%2Fcelestrak.com%2Fcolumns%2Fv04n03%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book">Besant, W.H. (1907). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=TRJLAAAAYAAJ&pg=PA50">„Chapter III. The Ellipse”</a>. <i>Conic Sections</i>. London: George Bell and Sons. стр. 50.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.atitle=Chapter+III.+The+Ellipse&rft.aufirst=W.H.&rft.aulast=Besant&rft.btitle=Conic+Sections&rft.date=1907&rft.genre=bookitem&rft.pages=50&rft.place=London&rft.pub=George+Bell+and+Sons&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DTRJLAAAAYAAJ%26pg%3DPA50&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book">Coxeter, H.S.M. (1969). <span class="plainlinks"><a rel="nofollow" class="external text" href="https://archive.org/details/introductiontoge0002coxe"><i>Introduction to <span class="nowrap">Geometry<span style="padding-left:0.15em"><span typeof="mw:File"><span title="Неопходна слободна регистрација"><img alt="Неопходна слободна регистрација" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Lock-blue-alt-2.svg/9px-Lock-blue-alt-2.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Lock-blue-alt-2.svg/14px-Lock-blue-alt-2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Lock-blue-alt-2.svg/18px-Lock-blue-alt-2.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span></span></span></i></a></span> (2nd изд.). New York: Wiley. стр. <a rel="nofollow" class="external text" href="https://archive.org/details/introductiontoge0002coxe/page/115">115–9</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.au=Coxeter%2C+H.S.M.&rft.btitle=Introduction+to+Geometry&rft.date=1969&rft.edition=2nd&rft.genre=book&rft.pages=115-9&rft.place=New+York&rft.pub=Wiley&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroductiontoge0002coxe&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite id="CITEREFMeserve1983" class="citation">Meserve, Bruce E. (1983) [1959], <i>Fundamental Concepts of Geometry</i>, Dover Publications, <a href="/wiki/Me%C4%91unarodni_standardni_broj_knjige" title="Međunarodni standardni broj knjige">ISBN</a> <a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0%D0%BC%D0%BF%D0%B0%D0%BD%D0%B8_%D0%B8%D0%B7%D0%B2%D0%BE%D1%80%D0%B8/978-0-486-63415-9" title="Посебно:Штампани извори/978-0-486-63415-9">978-0-486-63415-9</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.aufirst=Bruce+E.&rft.aulast=Meserve&rft.btitle=Fundamental+Concepts+of+Geometry&rft.date=1983&rft.genre=book&rft.isbn=978-0-486-63415-9&rft.pub=Dover+Publications&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book">Miller, Charles D.; Lial, Margaret L.; Schneider, David I. (1990). <a rel="nofollow" class="external text" href="https://archive.org/details/fundamentalsofco0000mill_g1q3/page/381"><i>Fundamentals of College Algebra</i></a> (3rd изд.). Scott Foresman/Little. стр. <a rel="nofollow" class="external text" href="https://archive.org/details/fundamentalsofco0000mill_g1q3/page/381">381</a>. <a href="/wiki/Me%C4%91unarodni_standardni_broj_knjige" title="Međunarodni standardni broj knjige">ISBN</a> <a href="/wiki/%D0%9F%D0%BE%D1%81%D0%B5%D0%B1%D0%BD%D0%BE:%D0%A8%D1%82%D0%B0%D0%BC%D0%BF%D0%B0%D0%BD%D0%B8_%D0%B8%D0%B7%D0%B2%D0%BE%D1%80%D0%B8/978-0-673-38638-0" title="Посебно:Штампани извори/978-0-673-38638-0">978-0-673-38638-0</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.au=Lial%2C+Margaret+L.&rft.au=Miller%2C+Charles+D.&rft.au=Schneider%2C+David+I.&rft.btitle=Fundamentals+of+College+Algebra&rft.date=1990&rft.edition=3rd&rft.genre=book&rft.isbn=978-0-673-38638-0&rft.pages=381&rft.pub=Scott+Foresman%2FLittle&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffundamentalsofco0000mill_g1q3%2Fpage%2F381&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite id="CITEREFProtterMorrey1970" class="citation">Protter, Murray H.; Morrey, Charles B. Jr. (1970), <i>College Calculus with Analytic Geometry</i> (2nd изд.), Reading: <a href="/w/index.php?title=Addison-Wesley&action=edit&redlink=1" class="new" title="Addison-Wesley (страница не постоји)">Addison-Wesley</a>, <a href="/wiki/Kontrolni_broj_Kongresne_biblioteke" title="Kontrolni broj Kongresne biblioteke">LCCN</a> <a rel="nofollow" class="external text" href="//lccn.loc.gov/76087042">76087042</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.au=Morrey%2C+Charles+B.+Jr.&rft.aufirst=Murray+H.&rft.aulast=Protter&rft.btitle=College+Calculus+with+Analytic+Geometry&rft.date=1970&rft.edition=2nd&rft.genre=book&rft.place=Reading&rft.pub=Addison-Wesley&rft_id=info%3Alccn%2F76087042&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Спољашње_везе"><span id=".D0.A1.D0.BF.D0.BE.D1.99.D0.B0.D1.88.D1.9A.D0.B5_.D0.B2.D0.B5.D0.B7.D0.B5"></span>Спољашње везе</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&veaction=edit&section=8" title="Уредите одељак „Спољашње везе”" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0_%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&action=edit&section=8" title="Уреди извор одељка: Спољашње везе"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r25554621">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9;display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r25554968">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist"><span style="font-weight:bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Orbital_elements" class="extiw" title="commons:Category:Orbital elements">Велика полуоса</a></span> на <a href="https://commons.wikimedia.org/wiki/%D0%93%D0%BB%D0%B0%D0%B2%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B0" class="extiw" title="commons:Главна страна">Викимедијиној остави</a>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.mathopenref.com/ellipsesemiaxes.html">Semi-major and semi-minor axes of an ellipse</a> With interactive animation</li> <li><cite class="citation web"><a rel="nofollow" class="external text" href="https://ssd.jpl.nasa.gov/?horizons">„The JPL HORIZONS online ephemeris”</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.btitle=The+JPL+HORIZONS+online+ephemeris&rft.genre=unknown&rft_id=https%3A%2F%2Fssd.jpl.nasa.gov%2F%3Fhorizons&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span> – also furnishes orbital elements for a large number of solar system objects</li></ul> <ul><li><cite class="citation web"><a rel="nofollow" class="external text" href="https://ssd.jpl.nasa.gov/?sat_elem">„Mean orbital parameters”</a>. <i>ssd.jpl.nasa.gov</i>. Planetary satellites. JPL / NASA.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.atitle=Mean+orbital+parameters&rft.genre=unknown&rft.jtitle=ssd.jpl.nasa.gov&rft_id=https%3A%2F%2Fssd.jpl.nasa.gov%2F%3Fsat_elem&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li></ul> <ul><li><cite class="citation web"><a rel="nofollow" class="external text" href="ftp://ssd.jpl.nasa.gov/pub/eph/planets/README.txt">„Introduction to exporting”</a>. <i>ssd.jpl.nasa.gov</i>. JPL planetary and lunar ephemerides. JPL / NASA.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.atitle=Introduction+to+exporting&rft.genre=unknown&rft.jtitle=ssd.jpl.nasa.gov&rft_id=ftp%3A%2F%2Fssd.jpl.nasa.gov%2Fpub%2Feph%2Fplanets%2FREADME.txt&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li></ul> <ul><li><cite class="citation web"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160303213938/http://www.mindspring.com/~n2wwd/html/body_state_vectors.html">„State vectors: VEC2TLE”</a>. <i>MindSpring</i> (software). Архивирано из <a rel="nofollow" class="external text" href="http://www.mindspring.com/~n2wwd/html/body_state_vectors.html">оригинала</a> 2016-03-03. г.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.atitle=State+vectors%3A+VEC2TLE&rft.genre=unknown&rft.jtitle=MindSpring&rft_id=http%3A%2F%2Fwww.mindspring.com%2F~n2wwd%2Fhtml%2Fbody_state_vectors.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span> – access to VEC2TLE software</li></ul> <ul><li><cite class="citation web"><a rel="nofollow" class="external text" href="http://www.iausofa.org/2016_0503_C/sofa/plan94.c">„Function 'iauPlan94<span style="padding-right:0.2em;">'</span>”</a> (<a href="/wiki/C_programming_language" class="mw-redirect" title="C programming language">C software source</a>). IAU SOFA C Library.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fsr.wikipedia.org%3A%D0%92%D0%B5%D0%BB%D0%B8%D0%BA%D0%B0+%D0%BF%D0%BE%D0%BB%D1%83%D0%BE%D1%81%D0%B0&rft.btitle=Function+%27iauPlan94%27&rft.genre=unknown&rft.series=IAU+SOFA+C+Library&rft_id=http%3A%2F%2Fwww.iausofa.org%2F2016_0503_C%2Fsofa%2Fplan94.c&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span> – orbital elements of the major planets</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r25469611">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output 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