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aria-label="Aspetto" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Aspetto</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_it.wikipedia.org&uselang=it" class=""><span>Fai una donazione</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speciale:CreaUtenza&returnto=Geoide" title="Si consiglia di registrarsi e di effettuare l'accesso, anche se non è obbligatorio" class=""><span>registrati</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Speciale:Entra&returnto=Geoide" title="Si consiglia di effettuare l'accesso, anche se non è obbligatorio [o]" accesskey="o" class=""><span>entra</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu 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mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pagine per utenti anonimi <a href="/wiki/Aiuto:Benvenuto" aria-label="Ulteriori informazioni sulla contribuzione"><span>ulteriori informazioni</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Speciale:MieiContributi" title="Un elenco delle modifiche fatte da questo indirizzo IP [y]" accesskey="y"><span>contributi</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Speciale:MieDiscussioni" title="Discussioni sulle modifiche fatte da questo indirizzo IP [n]" accesskey="n"><span>discussioni</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Sito"> <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="Indice" 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">Indice</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">nascondi</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">Inizio</div> </a> </li> <li id="toc-Descrizione" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Descrizione"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Descrizione</span> </div> </a> <ul id="toc-Descrizione-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Forma_della_Terra" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Forma_della_Terra"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Forma della Terra</span> </div> </a> <ul id="toc-Forma_della_Terra-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rappresentazione_per_armoniche_sferiche" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Rappresentazione_per_armoniche_sferiche"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Rappresentazione per armoniche sferiche</span> </div> </a> <ul id="toc-Rappresentazione_per_armoniche_sferiche-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voci_correlate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voci_correlate"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Voci correlate</span> </div> </a> <ul id="toc-Voci_correlate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Altri_progetti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Altri_progetti"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Altri progetti</span> </div> </a> <ul id="toc-Altri_progetti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Collegamenti_esterni" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Collegamenti_esterni"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Collegamenti esterni</span> </div> </a> <ul id="toc-Collegamenti_esterni-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="Indice" 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="Mostra/Nascondi l'indice" > <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">Mostra/Nascondi l'indice</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">Geoide</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="Vai a una voce in un'altra lingua. Disponibile in 65 lingue" > <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-65" 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">65 lingue</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AC%D8%B3%D9%85_%D8%A3%D8%B1%D8%B6%D9%8A" title="مجسم أرضي - arabo" lang="ar" hreflang="ar" data-title="مجسم أرضي" data-language-autonym="العربية" data-language-local-name="arabo" 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/Xeoide" title="Xeoide - asturiano" lang="ast" hreflang="ast" data-title="Xeoide" data-language-autonym="Asturianu" data-language-local-name="asturiano" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Geoid" title="Geoid - azerbaigiano" lang="az" hreflang="az" data-title="Geoid" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaigiano" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D1%96%D0%B4" title="Геоід - bielorusso" lang="be" hreflang="be" data-title="Геоід" data-language-autonym="Беларуская" data-language-local-name="bielorusso" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D1%96%D0%B4" title="Геоід - Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Геоід" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B8%D0%B4" title="Геоид - bulgaro" lang="bg" hreflang="bg" data-title="Геоид" data-language-autonym="Български" data-language-local-name="bulgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A5%85%E0%A4%87%E0%A4%A1" title="ज्याॅइड - Bhojpuri" lang="bh" hreflang="bh" data-title="ज्याॅइड" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AD%E0%A7%82%E0%A6%97%E0%A7%8B%E0%A6%B2%E0%A6%95" title="ভূগোলক - bengalese" lang="bn" hreflang="bn" data-title="ভূগোলক" data-language-autonym="বাংলা" data-language-local-name="bengalese" 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/Geoide" title="Geoide - catalano" lang="ca" hreflang="ca" data-title="Geoide" data-language-autonym="Català" data-language-local-name="catalano" 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/Geoid" title="Geoid - ceco" lang="cs" hreflang="cs" data-title="Geoid" data-language-autonym="Čeština" data-language-local-name="ceco" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Geoide" title="Geoide - danese" lang="da" hreflang="da" data-title="Geoide" data-language-autonym="Dansk" data-language-local-name="danese" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Geoid" title="Geoid - tedesco" lang="de" hreflang="de" data-title="Geoid" data-language-autonym="Deutsch" data-language-local-name="tedesco" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Geoid" title="Geoid - Zazaki" lang="diq" hreflang="diq" data-title="Geoid" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%89%CE%B5%CE%B9%CE%B4%CE%AD%CF%82" title="Γεωειδές - greco" lang="el" hreflang="el" data-title="Γεωειδές" data-language-autonym="Ελληνικά" data-language-local-name="greco" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Geoid" title="Geoid - inglese" lang="en" hreflang="en" data-title="Geoid" data-language-autonym="English" data-language-local-name="inglese" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Geoido" title="Geoido - esperanto" lang="eo" hreflang="eo" data-title="Geoido" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Geoide" title="Geoide - spagnolo" lang="es" hreflang="es" data-title="Geoide" data-language-autonym="Español" data-language-local-name="spagnolo" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Geoid" title="Geoid - estone" lang="et" hreflang="et" data-title="Geoid" data-language-autonym="Eesti" data-language-local-name="estone" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Geoide" title="Geoide - basco" lang="eu" hreflang="eu" data-title="Geoide" data-language-autonym="Euskara" data-language-local-name="basco" 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/%D8%B2%D9%85%DB%8C%D9%86%E2%80%8C%D9%88%D8%A7%D8%B1" title="زمین‌وار - persiano" lang="fa" hreflang="fa" data-title="زمین‌وار" data-language-autonym="فارسی" data-language-local-name="persiano" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Geoidi" title="Geoidi - finlandese" lang="fi" hreflang="fi" data-title="Geoidi" data-language-autonym="Suomi" data-language-local-name="finlandese" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/G%C3%A9o%C3%AFde" title="Géoïde - francese" lang="fr" hreflang="fr" data-title="Géoïde" data-language-autonym="Français" data-language-local-name="francese" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Xeoide" title="Xeoide - galiziano" lang="gl" hreflang="gl" data-title="Xeoide" data-language-autonym="Galego" data-language-local-name="galiziano" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%90%D7%95%D7%90%D7%99%D7%93" title="גאואיד - ebraico" lang="he" hreflang="he" data-title="גאואיד" data-language-autonym="עברית" data-language-local-name="ebraico" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Geoid" title="Geoid - croato" lang="hr" hreflang="hr" data-title="Geoid" data-language-autonym="Hrvatski" data-language-local-name="croato" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Geoid" title="Geoid - ungherese" lang="hu" hreflang="hu" data-title="Geoid" data-language-autonym="Magyar" data-language-local-name="ungherese" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B3%D5%A5%D5%B8%D5%AB%D5%A4" title="Գեոիդ - armeno" lang="hy" hreflang="hy" data-title="Գեոիդ" data-language-autonym="Հայերեն" data-language-local-name="armeno" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Geoid" title="Geoid - indonesiano" lang="id" hreflang="id" data-title="Geoid" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiano" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%B8%E3%82%AA%E3%82%A4%E3%83%89" title="ジオイド - giapponese" lang="ja" hreflang="ja" data-title="ジオイド" data-language-autonym="日本語" data-language-local-name="giapponese" 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%92%E1%83%94%E1%83%9D%E1%83%98%E1%83%93%E1%83%98" title="გეოიდი - georgiano" lang="ka" hreflang="ka" data-title="გეოიდი" data-language-autonym="ქართული" data-language-local-name="georgiano" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Geoid" title="Geoid - kara-kalpak" lang="kaa" hreflang="kaa" data-title="Geoid" data-language-autonym="Qaraqalpaqsha" data-language-local-name="kara-kalpak" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B8%D0%B4" title="Геоид - kazako" lang="kk" hreflang="kk" data-title="Геоид" data-language-autonym="Қазақша" data-language-local-name="kazako" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A7%80%EC%98%A4%EC%9D%B4%EB%93%9C" title="지오이드 - coreano" lang="ko" hreflang="ko" data-title="지오이드" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B8%D0%B4" title="Геоид - kirghiso" lang="ky" hreflang="ky" data-title="Геоид" data-language-autonym="Кыргызча" data-language-local-name="kirghiso" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Geoid" title="Geoid - lussemburghese" lang="lb" hreflang="lb" data-title="Geoid" data-language-autonym="Lëtzebuergesch" data-language-local-name="lussemburghese" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/%C4%A2eo%C4%ABds" title="Ģeoīds - lettone" lang="lv" hreflang="lv" data-title="Ģeoīds" data-language-autonym="Latviešu" data-language-local-name="lettone" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B8%D0%B4" title="Геоид - macedone" lang="mk" hreflang="mk" data-title="Геоид" data-language-autonym="Македонски" data-language-local-name="macedone" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%9C%E0%B4%BF%E0%B4%AF%E0%B5%8B%E0%B4%AF%E0%B4%BF%E0%B4%A1%E0%B5%8D" title="ജിയോയിഡ് - malayalam" lang="ml" hreflang="ml" data-title="ജിയോയിഡ്" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Geoid" title="Geoid - malese" lang="ms" hreflang="ms" data-title="Geoid" data-language-autonym="Bahasa Melayu" data-language-local-name="malese" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%B8%E0%A4%AE_%E0%A4%97%E0%A5%81%E0%A4%B0%E0%A5%81%E0%A4%A4%E0%A5%8D%E0%A4%B5_%E0%A4%B8%E0%A4%A4%E0%A4%B9_(%E0%A4%9C%E0%A4%BF%E0%A4%AF%E0%A5%8B%E0%A4%87%E0%A4%A1)" title="सम गुरुत्व सतह (जियोइड) - nepalese" lang="ne" hreflang="ne" data-title="सम गुरुत्व सतह (जियोइड)" data-language-autonym="नेपाली" data-language-local-name="nepalese" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Geo%C3%AFde" title="Geoïde - olandese" lang="nl" hreflang="nl" data-title="Geoïde" data-language-autonym="Nederlands" data-language-local-name="olandese" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Geoide" title="Geoide - norvegese nynorsk" lang="nn" hreflang="nn" data-title="Geoide" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegese nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Geoide" title="Geoide - norvegese bokmål" lang="nb" hreflang="nb" data-title="Geoide" data-language-autonym="Norsk bokmål" data-language-local-name="norvegese bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Geoida" title="Geoida - polacco" lang="pl" hreflang="pl" data-title="Geoida" data-language-autonym="Polski" data-language-local-name="polacco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Geoide" title="Geoide - portoghese" lang="pt" hreflang="pt" data-title="Geoide" data-language-autonym="Português" data-language-local-name="portoghese" 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/Geoid" title="Geoid - rumeno" lang="ro" hreflang="ro" data-title="Geoid" data-language-autonym="Română" data-language-local-name="rumeno" 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%93%D0%B5%D0%BE%D0%B8%D0%B4" title="Геоид - russo" lang="ru" hreflang="ru" data-title="Геоид" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B8%D0%B4" title="Геоид - ruteno" lang="rue" hreflang="rue" data-title="Геоид" data-language-autonym="Русиньскый" data-language-local-name="ruteno" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Geoid" title="Geoid - serbo-croato" lang="sh" hreflang="sh" data-title="Geoid" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croato" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Geoid" title="Geoid - Simple English" lang="en-simple" hreflang="en-simple" data-title="Geoid" 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/Geoid" title="Geoid - slovacco" lang="sk" hreflang="sk" data-title="Geoid" data-language-autonym="Slovenčina" data-language-local-name="slovacco" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Geoid" title="Geoid - sloveno" lang="sl" hreflang="sl" data-title="Geoid" data-language-autonym="Slovenščina" data-language-local-name="sloveno" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Gjeoidi" title="Gjeoidi - albanese" lang="sq" hreflang="sq" data-title="Gjeoidi" data-language-autonym="Shqip" data-language-local-name="albanese" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B8%D0%B4" title="Геоид - serbo" lang="sr" hreflang="sr" data-title="Геоид" data-language-autonym="Српски / srpski" data-language-local-name="serbo" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Geoid" title="Geoid - svedese" lang="sv" hreflang="sv" data-title="Geoid" data-language-autonym="Svenska" data-language-local-name="svedese" 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%AA%E0%AF%82%E0%AE%AE%E0%AE%BF%E0%AE%B5%E0%AE%9F%E0%AE%BF%E0%AE%B5%E0%AE%AE%E0%AF%8D" title="பூமிவடிவம் - tamil" lang="ta" hreflang="ta" data-title="பூமிவடிவம்" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%97%D0%B0%D0%BC%D0%B8%D0%BD%D0%B2%D0%BE%D1%80%D0%B0" title="Заминвора - tagico" lang="tg" hreflang="tg" data-title="Заминвора" data-language-autonym="Тоҷикӣ" data-language-local-name="tagico" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%88%E0%B8%B5%E0%B8%AD%E0%B8%AD%E0%B8%A2%E0%B8%94%E0%B9%8C" title="จีออยด์ - thailandese" lang="th" hreflang="th" data-title="จีออยด์" data-language-autonym="ไทย" data-language-local-name="thailandese" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Geoit" title="Geoit - turco" lang="tr" hreflang="tr" data-title="Geoit" data-language-autonym="Türkçe" data-language-local-name="turco" 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%93%D0%B5%D0%BE%D1%97%D0%B4" title="Геоїд - ucraino" lang="uk" hreflang="uk" data-title="Геоїд" data-language-autonym="Українська" data-language-local-name="ucraino" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Geoid" title="Geoid - uzbeco" lang="uz" hreflang="uz" data-title="Geoid" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeco" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Geoid" title="Geoid - vietnamita" lang="vi" hreflang="vi" data-title="Geoid" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%A4%A7%E5%9C%B0%E6%B0%B4%E5%87%86%E9%9D%A2" title="大地水准面 - wu" lang="wuu" hreflang="wuu" data-title="大地水准面" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A4%A7%E5%9C%B0%E6%B0%B4%E5%87%86%E9%9D%A2" title="大地水准面 - cinese" lang="zh" hreflang="zh" data-title="大地水准面" data-language-autonym="中文" data-language-local-name="cinese" 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%A4%A7%E5%9C%B0%E6%B0%B4%E6%BA%96%E9%9D%A2" title="大地水準面 - cantonese" lang="yue" hreflang="yue" data-title="大地水準面" data-language-autonym="粵語" data-language-local-name="cantonese" 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/Q185969#sitelinks-wikipedia" title="Modifica collegamenti interlinguistici" class="wbc-editpage">Modifica collegamenti</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespace"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Geoide" title="Vedi la voce [c]" accesskey="c"><span>Voce</span></a></li><li id="ca-talk" class="vector-tab-noicon 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vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Strumenti</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">nascondi</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Altre opzioni" > <div class="vector-menu-heading"> Azioni </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Geoide"><span>Leggi</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Geoide&veaction=edit" title="Modifica questa pagina [v]" accesskey="v"><span>Modifica</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Geoide&action=edit" title="Modifica il wikitesto di questa pagina [e]" accesskey="e"><span>Modifica wikitesto</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Geoide&action=history"><span>Cronologia</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Generale </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speciale:PuntanoQui/Geoide" title="Elenco di tutte le pagine che sono collegate a questa [j]" accesskey="j"><span>Puntano qui</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speciale:ModificheCorrelate/Geoide" rel="nofollow" title="Elenco delle ultime modifiche alle pagine collegate a questa [k]" accesskey="k"><span>Modifiche correlate</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Speciale:PagineSpeciali" title="Elenco di tutte le pagine speciali [q]" accesskey="q"><span>Pagine speciali</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Geoide&oldid=141510522" title="Collegamento permanente a questa versione di questa pagina"><span>Link permanente</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Geoide&action=info" title="Ulteriori informazioni su questa pagina"><span>Informazioni pagina</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speciale:Cita&page=Geoide&id=141510522&wpFormIdentifier=titleform" title="Informazioni su come citare questa pagina"><span>Cita questa voce</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speciale:UrlShortener&url=https%3A%2F%2Fit.wikipedia.org%2Fwiki%2FGeoide"><span>Ottieni URL breve</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speciale:QrCode&url=https%3A%2F%2Fit.wikipedia.org%2Fwiki%2FGeoide"><span>Scarica codice QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Stampa/esporta </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Speciale:Libro&bookcmd=book_creator&referer=Geoide"><span>Crea un libro</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speciale:DownloadAsPdf&page=Geoide&action=show-download-screen"><span>Scarica come PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Geoide&printable=yes" title="Versione stampabile di questa pagina [p]" accesskey="p"><span>Versione stampabile</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In altri progetti </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Geoid" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q185969" title="Collegamento all'elemento connesso dell'archivio dati [g]" accesskey="g"><span>Elemento Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Strumenti pagine"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspetto"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aspetto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">nascondi</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Da Wikipedia, l'enciclopedia libera.</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="it" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Geoid_height_red_blue.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Geoid_height_red_blue.png/350px-Geoid_height_red_blue.png" decoding="async" width="350" height="242" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Geoid_height_red_blue.png/525px-Geoid_height_red_blue.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/08/Geoid_height_red_blue.png/700px-Geoid_height_red_blue.png 2x" data-file-width="1686" data-file-height="1166" /></a><figcaption>Mappa dell'ondulazione del geoide, in metri (basata sul modello di gravità <a href="/wiki/EGM96" title="EGM96">EGM96</a> e sull'ellissoide di riferimento <a href="/wiki/WGS84" title="WGS84">WGS84</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></figcaption></figure> <p>Con il termine <b>geoide</b> si indica la <a href="/wiki/Superficie_equipotenziale" title="Superficie equipotenziale">superficie equipotenziale</a> del <a href="/wiki/Campo_gravitazionale_terrestre" title="Campo gravitazionale terrestre">campo gravitazionale terrestre</a>, che coincide con il <a href="/wiki/Livello_del_mare" title="Livello del mare">livello medio del mare</a>; si ottiene considerando una superficie sempre perpendicolare a un filo a piombo, cioè alla direzione della forza di gravità. Il geoide tiene conto delle irregolarità gravitazionali prodotte dalla presenza di montagne (maggior gravità dovuta alla massa) o di materiali meno densi come l'acqua degli oceani (quindi minor gravità). Il geoide è un modello fisico in quanto descrive il profilo della superficie terrestre al livello del mare rispetto al quale si misura l'altezza ed è anche un costrutto matematico in quanto tiene conto delle variazioni di gravità. </p><p>È il solido la cui superficie in ogni suo punto è perpendicolare al filo al piombo, tenendo presente che si dispone sulla verticale fisica e non su quella geocentrica. </p><p><style data-mw-deduplicate="TemplateStyles:r140554517">.mw-parser-output .chiarimento{background:#ffeaea;color:#444444}.mw-parser-output .chiarimento-apice{color:#EE0700}@media screen{html.skin-theme-clientpref-night .mw-parser-output .chiarimento{background:rgba(179,36,36,0.21);color:inherit}html.skin-theme-clientpref-night .mw-parser-output .chiarimento-apice{color:#b32424}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .chiarimento{background:rgba(179,36,36,0.21);color:inherit}html.skin-theme-clientpref-os .mw-parser-output .chiarimento-apice{color:#b32424}}</style><span class="chiarimento" title="Queste informazioni non sono comprovate da fonti attendibili.">Se la Terra fosse costituita da materiali perfettamente omogenei, l'ellissoide e il geoide coinciderebbero; in realtà essi risultano sfasati di alcune decine di metri.</span><sup class="noprint chiarimento-apice" title="Queste informazioni non sono comprovate da fonti attendibili.">[<i><a href="/wiki/Wikipedia:Uso_delle_fonti" title="Wikipedia:Uso delle fonti">senza fonte</a></i>]</sup> Poiché attualmente non esiste un modello matematico unificato che renda ragione sia delle proprietà globali sia di quelle locali della Terra, i due modelli sono entrambi necessari per definire un sistema di riferimento geodetico e per effettuare misurazioni corrette nelle tre dimensioni: sferoide, ellissoide e geoide. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Descrizione">Descrizione</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geoide&veaction=edit&section=1" title="Modifica la sezione Descrizione" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Geoide&action=edit&section=1" title="Edit section's source code: Descrizione"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Geoida.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Geoida.svg/350px-Geoida.svg.png" decoding="async" width="350" height="162" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Geoida.svg/525px-Geoida.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Geoida.svg/700px-Geoida.svg.png 2x" data-file-width="730" data-file-height="338" /></a><figcaption>1. <a href="/wiki/Oceano" title="Oceano">Oceano</a><br />2. <a href="/wiki/Ellissoide_di_riferimento" title="Ellissoide di riferimento">Ellissoide di riferimento</a><br />3. <a href="/wiki/Filo_a_piombo" title="Filo a piombo">Filo a piombo</a> locale<br />4. <a href="/wiki/Continente" title="Continente">Continente</a><br />5. Geoide</figcaption></figure> <p>Un geoide è una superficie perpendicolare in ogni punto alla direzione della verticale, cioè alla direzione della <a href="/wiki/Forza_di_gravit%C3%A0" class="mw-redirect" title="Forza di gravità">forza di gravità</a>. Questa è la superficie che meglio descrive la superficie media degli oceani (a meno dell'influenza di <a href="/wiki/Marea" title="Marea">maree</a>, correnti ed effetti meteorologici) e, quindi, la superficie media della Terra. Esso, infatti, è definibile come la <a href="/wiki/Superficie_equipotenziale" title="Superficie equipotenziale">superficie equipotenziale</a> (in cui, cioè, il <a href="/wiki/Potenziale_gravitazionale" class="mw-redirect" title="Potenziale gravitazionale">potenziale gravitazionale</a> ha valore uguale) che presenta i minimi scostamenti dal <a href="/wiki/Livello_del_mare" title="Livello del mare">livello medio del mare</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> </p><p>Dal punto di vista <a href="/wiki/Cartografia" title="Cartografia">cartografico</a> il geoide non può essere utilizzato per la determinazione <a href="/wiki/Planimetria" title="Planimetria">planimetrica</a> di una porzione di terreno perché, se anche si riuscisse a mettere in corrispondenza i punti della superficie fisica della Terra con quelli del geoide, non si potrebbe poi mettere in corrispondenza i punti del geoide con un sistema cartesiano piano. In pratica non è possibile utilizzare il geoide per la creazione di <a href="/wiki/Pianta_(architettura)" title="Pianta (architettura)">piante</a> perché i dati derivanti dalla proiezione sul geoide della superficie terrestre non possono essere descritti su un piano. Di conseguenza questa superficie viene utilizzata solo in riferimento alle quote. </p><p>Questo accade perché non è possibile descrivere il geoide con una formula matematica risolvibile: per conoscere l'andamento del geoide, infatti, sarebbe necessario conoscere in ogni punto della superficie terrestre la direzione della forza di gravità, la quale a sua volta dipende dalla <a href="/wiki/Densit%C3%A0" title="Densità">densità</a> che la Terra assume in ogni punto. Questo, tuttavia, è impossibile da conoscere senza una certa <a href="/wiki/Incertezza_di_misura" title="Incertezza di misura">approssimazione</a>, rendendo poco operativa dal punto di vista <a href="/wiki/Matematica" title="Matematica">matematico</a> la definizione di geoide. </p><p>Assumendo certe semplificazioni è però possibile ricavare delle superfici utili nella topografia. Ipotizzando infatti la densità simmetrica rispetto all'asse di rotazione si definisce lo sferoide, mentre ipotizzando la densità costante, oltre che simmetrica rispetto all'asse di rotazione, si definisce l'ellissoide. </p><p>È necessario porre molta attenzione sulle differenze che intercorrono tra il geoide e l'<a href="/wiki/Ellissoide_di_riferimento" title="Ellissoide di riferimento">ellissoide di riferimento</a> (utilizzato nella creazione di carte <a href="/wiki/Topografia" title="Topografia">topografiche</a>): mentre il primo ha una rigorosa definizione fisica ma non è descrivibile matematicamente, il secondo ha una ben definita equazione matematica che lo descrive ma non ha alcun significato fisico per quanto riguarda la superficie terrestre. Inoltre esiste una certa <a href="/wiki/Deviazione_della_verticale" title="Deviazione della verticale">deviazione della verticale</a> tra le due superfici. </p> <div class="mw-heading mw-heading2"><h2 id="Forma_della_Terra">Forma della Terra</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geoide&veaction=edit&section=2" title="Modifica la sezione Forma della Terra" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Geoide&action=edit&section=2" title="Edit section's source code: Forma della Terra"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Il termine geoide è utilizzato anche per indicare la forma della Terra a <a href="/wiki/Ellissoide" title="Ellissoide">ellissoide</a>, che è una <a href="/wiki/Sfera" title="Sfera">sfera</a> schiacciata ai poli, ottenuta dalla rotazione di un'<a href="/wiki/Ellisse" title="Ellisse">ellisse</a> intorno al suo asse minore. Il raggio terrestre in corrispondenza dei poli risulta di circa <span class="nowrap"><span data-sort-value="7004210000000000000♠"></span>21 <a href="/wiki/Chilometro" title="Chilometro">km</a></span> inferiore al raggio medio terrestre, pari a circa <span class="nowrap"><span data-sort-value="7006637100000000000♠"></span>6<span style="margin-left:.25em;">371</span> <a href="/wiki/Chilometro" title="Chilometro">km</a></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Rappresentazione_per_armoniche_sferiche">Rappresentazione per armoniche sferiche</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geoide&veaction=edit&section=3" title="Modifica la sezione Rappresentazione per armoniche sferiche" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Geoide&action=edit&section=3" title="Edit section's source code: Rappresentazione per armoniche sferiche"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:GRACE_globe_animation.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/GRACE_globe_animation.gif/220px-GRACE_globe_animation.gif" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/GRACE_globe_animation.gif/330px-GRACE_globe_animation.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/78/GRACE_globe_animation.gif/440px-GRACE_globe_animation.gif 2x" data-file-width="455" data-file-height="455" /></a><figcaption>Animazione del geoide ottenuto grazie alle misurazioni dei satelliti <a href="/wiki/Gravity_Recovery_and_Climate_Experiment" title="Gravity Recovery and Climate Experiment">GRACE</a></figcaption></figure> <p>Le <a href="/wiki/Armoniche_sferiche" title="Armoniche sferiche">armoniche sferiche</a> sono spesso usate per approssimare la forma del geoide. Il miglior insieme di coefficienti migliori per le armoniche sferiche è l'<a href="/wiki/EGM96" title="EGM96">EGM96</a><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>, determinati nel progetto di collaborazione internazionale guidato dalla NIMA.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>La descrizione matematica della parte non rotante <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> della funzione potenziale del modello è:<sup id="cite_ref-noaa.gov_5-0" class="reference"><a href="#cite_note-noaa.gov-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {GM}{r}}\left(1+{\sum _{n=2}^{n_{\text{max}}}}\left({\frac {a}{r}}\right)^{n}\cdot {\sum _{m=0}^{n}}{\overline {P}}_{nm}(\cos \phi )\cdot \left[{\overline {C}}_{nm}\cdot \cos(m\cdot \lambda )+{\overline {S}}_{nm}\cdot \sin(m\cdot \lambda )\right]\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>G</mi> <mi>M</mi> </mrow> <mi>r</mi> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>max</mtext> </mrow> </msub> </mrow> </munderover> </mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>r</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>P</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>m</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>cos</mi> <mo>⁡</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mrow> <mo>[</mo> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>m</mi> </mrow> </msub> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>⋅</mo> <mi>λ</mi> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>m</mi> </mrow> </msub> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>⋅</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {GM}{r}}\left(1+{\sum _{n=2}^{n_{\text{max}}}}\left({\frac {a}{r}}\right)^{n}\cdot {\sum _{m=0}^{n}}{\overline {P}}_{nm}(\cos \phi )\cdot \left[{\overline {C}}_{nm}\cdot \cos(m\cdot \lambda )+{\overline {S}}_{nm}\cdot \sin(m\cdot \lambda )\right]\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0876be5a4b9e549ad64894280c8f7335ef40f3a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:84.133ex; height:7.509ex;" alt="{\displaystyle V={\frac {GM}{r}}\left(1+{\sum _{n=2}^{n_{\text{max}}}}\left({\frac {a}{r}}\right)^{n}\cdot {\sum _{m=0}^{n}}{\overline {P}}_{nm}(\cos \phi )\cdot \left[{\overline {C}}_{nm}\cdot \cos(m\cdot \lambda )+{\overline {S}}_{nm}\cdot \sin(m\cdot \lambda )\right]\right),}"></span></dd></dl> <p>dove: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle GM=(3986004,418\pm 0,008)\times 10^{8}\ m^{3}/s^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mi>M</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>3986004</mn> <mo>,</mo> <mn>418</mn> <mo>±</mo> <mn>0</mn> <mo>,</mo> <mn>008</mn> <mo stretchy="false">)</mo> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mtext> </mtext> <msup> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle GM=(3986004,418\pm 0,008)\times 10^{8}\ m^{3}/s^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b8394119a97ab199b80ce4b662d4fd463adf4e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:43.561ex; height:3.176ex;" alt="{\displaystyle GM=(3986004,418\pm 0,008)\times 10^{8}\ m^{3}/s^{2}}"></span> è la costante di gravitazione terrestre;<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></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi \ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi \ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4c7f7052f131b0858274cdd86e38a4119fbb28b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.966ex; height:2.509ex;" alt="{\displaystyle \phi \ }"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda \ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda \ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7098afc76a9c0a8bc5079e98cf4aad3a4f9face7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.936ex; height:2.176ex;" alt="{\displaystyle \lambda \ }"></span> sono rispettivamente la latitudine e longitudine geocentriche;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\overline {P}}_{nm}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>P</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\overline {P}}_{nm}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7c66cf6bbafe970e74323fb957cce592eb5d783" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.686ex; height:3.343ex;" alt="{\textstyle {\overline {P}}_{nm}}"></span> sono i <a href="/wiki/Polinomi_associati_di_Legendre" class="mw-redirect" title="Polinomi associati di Legendre">polinomi associati di Legendre</a> completamente normalizzati di grado n e ordine m;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle {\overline {C}}_{nm}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\overline {C}}_{nm}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d66dacacd4e5288c79b304e598f217afd15ee20b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.611ex; height:3.343ex;" alt="{\textstyle {\overline {C}}_{nm}}"></span> e <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="{\textstyle {\overline {S}}_{nm}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\overline {S}}_{nm}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f898536edb7b9ef6b34f80e105cb6757426c789e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.324ex; height:3.343ex;" alt="{\textstyle {\overline {S}}_{nm}}"></span> sono i coefficienti numerici del modello basati sui dati misurati.</li></ul> <p>Si noti che l'equazione descrive il potenziale gravitazionale <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span>, non il geoide in sé nel punto <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="{\textstyle (\phi ,\;\lambda ,\;r,\ )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo>,</mo> <mspace width="thickmathspace" /> <mi>λ</mi> <mo>,</mo> <mspace width="thickmathspace" /> <mi>r</mi> <mo>,</mo> <mtext> </mtext> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle (\phi ,\;\lambda ,\;r,\ )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6baeedd03ae894655db77315f53b803d64b87ea8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.571ex; height:2.843ex;" alt="{\textstyle (\phi ,\;\lambda ,\;r,\ )}"></span>, essendo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> il raggio dal centro terrestre. </p><p>Il geoide è una particolare superficie potenziale, complicata da calcolare. Il gradiente di questo potenziale fornisce anche un modello per l'accelerazione gravitazionale. L'EGM96 contiene un insieme completo di coefficienti fino al grado e ordine 360, descrivendo il geoide con un dettaglio di <span class="nowrap">± 55 km</span>. Il numero di coefficienti <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="{\textstyle {\overline {C}}_{nm}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\overline {C}}_{nm}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d66dacacd4e5288c79b304e598f217afd15ee20b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.611ex; height:3.343ex;" alt="{\textstyle {\overline {C}}_{nm}}"></span> e <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="{\textstyle {\overline {S}}_{nm}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo accent="false">¯</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle {\overline {S}}_{nm}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f898536edb7b9ef6b34f80e105cb6757426c789e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.324ex; height:3.343ex;" alt="{\textstyle {\overline {S}}_{nm}}"></span>, può essere ottenuto osservando che nell'equazione di <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> per ogni <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> ci sono due coefficienti per ogni <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 m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> a eccezione di <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 m=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e57f21007575fd03e3be0da20af34d25829cc9a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.301ex; height:2.176ex;" alt="{\displaystyle m=0}"></span>, in cui ce n'è solo uno. </p><p>Di conseguenza, siccome <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="{\textstyle \sum _{I=1}^{L}I=L(L+1)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>I</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </munderover> <mi>I</mi> <mo>=</mo> <mi>L</mi> <mo stretchy="false">(</mo> <mi>L</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \sum _{I=1}^{L}I=L(L+1)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9a9e9d5c3775edfdcca1be12d0eabc30e7f2365" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:21.575ex; height:3.509ex;" alt="{\textstyle \sum _{I=1}^{L}I=L(L+1)/2}"></span>, il numero totale di coefficienti, per <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{max}=360}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>360</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{max}=360}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5703940504f3b681ed6fbeeb6632717d51ca0fd4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.465ex; height:2.509ex;" alt="{\displaystyle n_{max}=360}"></span>, è: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{n=2}^{n_{\text{max}}}(2n+1)=n_{\text{max}}(n_{\text{max}}+1)+n_{\text{max}}-3=130\,317}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>max</mtext> </mrow> </msub> </mrow> </munderover> <mo stretchy="false">(</mo> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>max</mtext> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>max</mtext> </mrow> </msub> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>max</mtext> </mrow> </msub> <mo>−</mo> <mn>3</mn> <mo>=</mo> <mn>130</mn> <mspace width="thinmathspace" /> <mn>317</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{n=2}^{n_{\text{max}}}(2n+1)=n_{\text{max}}(n_{\text{max}}+1)+n_{\text{max}}-3=130\,317}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17479737197a006afc24f21b4125d0e87bbc56b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:52.275ex; height:7.009ex;" alt="{\displaystyle \sum _{n=2}^{n_{\text{max}}}(2n+1)=n_{\text{max}}(n_{\text{max}}+1)+n_{\text{max}}-3=130\,317}"></span></dd></dl> <p>Per molte applicazione la serie completa non è necessaria e ci si ferma a pochi termini. Sono in sviluppo nuovi modelli a più alta risoluzione, diversi autori dell'EGM96 stanno lavorando a un modello aggiornato<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> che dovrebbe contenere i nuovi dati gravitazionali ottenuti dai satelliti, e dovrebbe prevedere fino a 2 160 gradi e ordini. </p><p>La <a href="/wiki/National_Geospatial-Intelligence_Agency" title="National Geospatial-Intelligence Agency">National Geospatial-Intelligence Agency</a> ha annunciato la disponibilità del EGM2008, con 2 159 gradi che contiene dei coefficienti addizionali che estendono i gradi a 2 190.<sup id="cite_ref-nga.mil_8-0" class="reference"><a href="#cite_note-nga.mil-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geoide&veaction=edit&section=4" title="Modifica la sezione Note" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Geoide&action=edit&section=4" title="Edit section's source code: Note"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1"><b>^</b></a> <span class="reference-text"><cite class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://earth-info.nga.mil/index.php?dir=wgs84&action=wgs84"><span style="font-style:italic;">NGA Geomatics - WGS 84</span></a>, su <span style="font-style:italic;">earth-info.nga.mil</span>. <small>URL consultato il 2 luglio 2023</small>.</cite></span> </li> <li id="cite_note-2"><a href="#cite_ref-2"><b>^</b></a> <span class="reference-text"><cite class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Clint Conrad, <a rel="nofollow" class="external text" href="http://www.soest.hawaii.edu/GG/FACULTY/conrad/classes/GG612_S11/Lecture_03.pdf"><span style="font-style:italic;">Lezione 3: La forma della Terra, gravità, e geoide</span></a> (<span style="font-weight: bolder; font-size:80%"><abbr title="documento in formato PDF">PDF</abbr></span>), su <span style="font-style:italic;">soest.hawaii.edu</span>, Università delle Hawaii, 2 gennaio 2011. <small>URL consultato il 12 agosto 2015</small>.</cite></span> </li> <li id="cite_note-3"><a href="#cite_ref-3"><b>^</b></a> <span class="reference-text">Earth Gravity Model 1996</span> </li> <li id="cite_note-4"><a href="#cite_ref-4"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFNIMA_(2000)">NIMA (2000)</a></cite>.</span> </li> <li id="cite_note-noaa.gov-5"><a href="#cite_ref-noaa.gov_5-0"><b>^</b></a> <span class="reference-text"><cite class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="http://www.ngs.noaa.gov/PUBS_LIB/EGM96_GEOID_PAPER/egm96_geoid_paper.html"><span style="font-style:italic;">There is no such thing as "The" EGM96 geoid: Subtle points on the use of a global geopotential model.</span></a>, su <span style="font-style:italic;">noaa.gov</span>.</cite></span> </li> <li id="cite_note-6"><a href="#cite_ref-6"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFNIMA_(2000)">NIMA (2000)</a>, p. 3-3</cite>.</span> </li> <li id="cite_note-7"><a href="#cite_ref-7"><b>^</b></a> <span class="reference-text">Pavlis, N.K., S.A. Holmes. S. Kenyon, D. Schmit, R. Trimmer, "Gravitational potential expansion to degree 2160", <i>IAG International Symposium, gravity, geoid and Space Mission GGSM2004</i>, Porto, Portugal, 2004.</span> </li> <li id="cite_note-nga.mil-8"><a href="#cite_ref-nga.mil_8-0"><b>^</b></a> <span class="reference-text"><cite class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100508002312/http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008/index.html"><span style="font-style:italic;">Earth Gravitational Model 2008 (EGM2008)</span></a>, su <span style="font-style:italic;">nga.mil</span>. <small>URL consultato il 12 agosto 2015</small> <small>(archiviato dall'<abbr title="http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008/index.html">url originale</abbr> l'8 maggio 2010)</small>.</cite></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geoide&veaction=edit&section=5" title="Modifica la sezione Bibliografia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Geoide&action=edit&section=5" title="Edit section's source code: Bibliografia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite id="CITEREFNIMA_(2000)" class="citation pubblicazione" style="font-style:normal"> National Imagery and Mapping Agency, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170709014930/http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf"><span style="font-style:italic;">Department of Defense World Geodetic System 1984 - Its definitions and relationships with local geodetic systems</span></a> (<span style="font-weight: bolder; font-size:80%"><abbr title="documento in formato PDF">PDF</abbr></span>), in <span style="font-style:italic;">Technical report</span>, 2000 <small>(archiviato dall'<abbr title="http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf">url originale</abbr> il 9 luglio 2017)</small>.</cite></li></ul> <div class="mw-heading mw-heading2"><h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geoide&veaction=edit&section=6" title="Modifica la sezione Voci correlate" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Geoide&action=edit&section=6" title="Edit section's source code: Voci correlate"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Normalnull" title="Normalnull">Normalnull</a></li> <li><a href="/wiki/Altimetria" title="Altimetria">Altimetria</a></li> <li><a href="/wiki/Livello_del_mare" title="Livello del mare">Livello del mare</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Altri_progetti">Altri progetti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geoide&veaction=edit&section=7" title="Modifica la sezione Altri progetti" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Geoide&action=edit&section=7" title="Edit section's source code: Altri progetti"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="interProject" class="toccolours" style="display: none; clear: both; margin-top: 2em"><p id="sisterProjects" style="background-color: #efefef; color: black; font-weight: bold; margin: 0"><span>Altri progetti</span></p><ul title="Collegamenti verso gli altri progetti Wikimedia"> <li class="" title=""><a href="https://it.wiktionary.org/wiki/geoide" class="extiw" title="wikt:geoide">Wikizionario</a></li> <li class="" title=""><span class="plainlinks" title="commons:Category:Geoid"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Geoid?uselang=it">Wikimedia Commons</a></span></li></ul></div> <ul><li><span typeof="mw:File"><a href="https://it.wiktionary.org/wiki/" title="Collabora a Wikizionario"><img alt="Collabora a Wikizionario" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/18px-Wiktionary_small.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/27px-Wiktionary_small.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/36px-Wiktionary_small.svg.png 2x" data-file-width="350" data-file-height="350" /></a></span> <a href="https://it.wiktionary.org/wiki/" class="extiw" title="wikt:">Wikizionario</a> contiene il lemma di dizionario «<b><a href="https://it.wiktionary.org/wiki/geoide" class="extiw" title="wikt:geoide">geoide</a></b>»</li> <li><span typeof="mw:File"><a href="https://commons.wikimedia.org/wiki/?uselang=it" title="Collabora a Wikimedia Commons"><img alt="Collabora a Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png" decoding="async" width="18" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/27px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/36px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/?uselang=it">Wikimedia Commons</a></span> contiene immagini o altri file su <b><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Geoid?uselang=it">geoide</a></span></b></li></ul> <div class="mw-heading mw-heading2"><h2 id="Collegamenti_esterni">Collegamenti esterni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geoide&veaction=edit&section=8" title="Modifica la sezione Collegamenti esterni" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Geoide&action=edit&section=8" title="Edit section's source code: Collegamenti esterni"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li class="mw-empty-elt"></li> <li><cite id="CITEREFTreccani.it" class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://www.treccani.it/enciclopedia/geoide"><span style="font-style:italic;">geoide</span></a>, su <span style="font-style:italic;">Treccani.it – Enciclopedie on line</span>, <a href="/wiki/Istituto_dell%27Enciclopedia_Italiana" title="Istituto dell'Enciclopedia Italiana">Istituto dell'Enciclopedia Italiana</a>.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q185969#P3365" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFDizionario_delle_scienze_fisiche" class="citation libro" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://www.treccani.it/enciclopedia/geoide_(Dizionario-delle-Scienze-Fisiche)/"><span style="font-style:italic;">geoide</span></a>, in <span style="font-style:italic;">Dizionario delle scienze fisiche</span>, <a href="/wiki/Istituto_dell%27Enciclopedia_Italiana" title="Istituto dell'Enciclopedia Italiana">Istituto dell'Enciclopedia Italiana</a>, 1996.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q185969#P10017" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFVocabolario_Treccani" class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://www.treccani.it/vocabolario/geoide"><span style="font-style:italic;">geòide</span></a>, su <span style="font-style:italic;"><a href="/wiki/Vocabolario_Treccani" title="Vocabolario Treccani">Vocabolario Treccani</a></span>, <a href="/wiki/Istituto_dell%27Enciclopedia_Italiana" title="Istituto dell'Enciclopedia Italiana">Istituto dell'Enciclopedia Italiana</a>.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q185969#P5844" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFSapere.it" class="citation web" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://www.sapere.it/enciclopedia/geòide.html"><span style="font-style:italic;">geòide</span></a>, su <span style="font-style:italic;">sapere.it</span>, <a href="/wiki/De_Agostini" title="De Agostini">De Agostini</a>.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q185969#P6706" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFEnciclopedia_della_Matematica" class="citation libro" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://www.treccani.it/enciclopedia/geoide_(Enciclopedia-della-Matematica)/"><span style="font-style:italic;">geoide</span></a>, in <span style="font-style:italic;">Enciclopedia della Matematica</span>, <a href="/wiki/Istituto_dell%27Enciclopedia_Italiana" title="Istituto dell'Enciclopedia Italiana">Istituto dell'Enciclopedia Italiana</a>, 2013.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q185969#P9621" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFBritannica.com" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Urho A. Uotila e George D. Garland, <a rel="nofollow" class="external text" href="https://www.britannica.com/science/geoid"><span style="font-style:italic;">geoid</span></a>, su <span style="font-style:italic;"><a href="/wiki/Enciclopedia_Britannica" title="Enciclopedia Britannica">Enciclopedia Britannica</a></span>, Encyclopædia Britannica, Inc.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q185969#P1417" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r140554510">.mw-parser-output .CdA{border:1px solid #aaa;width:100%;margin:auto;font-size:90%;padding:2px}.mw-parser-output .CdA th{background-color:#f2f2f2;font-weight:bold;width:20%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .CdA{border-color:#54595D}html.skin-theme-clientpref-night .mw-parser-output .CdA th{background-color:#202122}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .CdA{border-color:#54595D}html.skin-theme-clientpref-os .mw-parser-output .CdA th{background-color:#202122}}</style><table class="CdA"><tbody><tr><th><a href="/wiki/Aiuto:Controllo_di_autorit%C3%A0" title="Aiuto:Controllo di autorità">Controllo di autorità</a></th><td><a href="/wiki/Nuovo_soggettario" title="Nuovo soggettario">Thesaurus BNCF</a> <span class="uid"><a rel="nofollow" class="external text" href="https://thes.bncf.firenze.sbn.it/termine.php?id=33760">33760</a></span><span style="font-weight:bold;"> ·</span> <a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a> <span class="uid">(<span style="font-weight:bolder; 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