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<span>Models</span> </div> </a> <button aria-controls="toc-Models-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>Toggle Models subsection</span> </button> <ul id="toc-Models-sublist" class="vector-toc-list"> <li id="toc-Sphere" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sphere"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Sphere</span> </div> </a> <ul id="toc-Sphere-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ellipsoid_of_revolution" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ellipsoid_of_revolution"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Ellipsoid of revolution</span> </div> </a> <ul id="toc-Ellipsoid_of_revolution-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Non-spheroidal_deviations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Non-spheroidal_deviations"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Non-spheroidal deviations</span> </div> </a> <ul id="toc-Non-spheroidal_deviations-sublist" class="vector-toc-list"> <li id="toc-Triaxiality_(equatorial_eccentricity)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Triaxiality_(equatorial_eccentricity)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.1</span> <span>Triaxiality (equatorial eccentricity)</span> </div> </a> <ul id="toc-Triaxiality_(equatorial_eccentricity)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Egg_or_pear_shape" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Egg_or_pear_shape"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.2</span> <span>Egg or pear shape</span> </div> </a> <ul id="toc-Egg_or_pear_shape-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Geoid" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Geoid"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Geoid</span> </div> </a> <ul id="toc-Geoid-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Local_approximations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Local_approximations"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Local approximations</span> </div> </a> <ul id="toc-Local_approximations-sublist" class="vector-toc-list"> <li id="toc-Local_tangent_plane" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Local_tangent_plane"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5.1</span> <span>Local tangent plane</span> </div> </a> <ul id="toc-Local_tangent_plane-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Osculating_sphere" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Osculating_sphere"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5.2</span> <span>Osculating sphere</span> </div> </a> <ul id="toc-Osculating_sphere-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Earth_rotation_and_Earth's_interior" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Earth_rotation_and_Earth's_interior"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Earth rotation and Earth's interior</span> </div> </a> <ul id="toc-Earth_rotation_and_Earth's_interior-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Global_and_regional_gravity_field" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Global_and_regional_gravity_field"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Global and regional gravity field</span> </div> </a> <ul id="toc-Global_and_regional_gravity_field-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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="Contents" 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="Toggle the table of contents" > <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">Toggle the table of contents</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">Figure of the Earth</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" 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Available in 23 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-23" 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">23 languages</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/%D8%B5%D9%88%D8%B1%D8%A9_%D8%A7%D9%84%D8%A3%D8%B1%D8%B6" title="صورة الأرض – Arabic" lang="ar" hreflang="ar" data-title="صورة الأرض" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A7%83%E0%A6%A5%E0%A6%BF%E0%A6%AC%E0%A7%80%E0%A6%B0_%E0%A6%86%E0%A6%95%E0%A6%BE%E0%A6%B0" title="পৃথিবীর আকার – Bangla" lang="bn" hreflang="bn" data-title="পৃথিবীর আকার" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A4%D1%96%D0%B3%D1%83%D1%80%D0%B0_%D0%97%D1%8F%D0%BC%D0%BB%D1%96" title="Фігура Зямлі – Belarusian" lang="be" hreflang="be" data-title="Фігура Зямлі" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A4%D0%BE%D1%80%D0%BC%D0%B0_%D0%BD%D0%B0_%D0%97%D0%B5%D0%BC%D1%8F%D1%82%D0%B0" title="Форма на Земята – Bulgarian" lang="bg" hreflang="bg" data-title="Форма на Земята" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Figura_de_la_Terra" title="Figura de la Terra – Catalan" lang="ca" hreflang="ca" data-title="Figura de la Terra" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Erdfigur" title="Erdfigur – German" lang="de" hreflang="de" data-title="Erdfigur" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Maa_kuju" title="Maa kuju – Estonian" lang="et" hreflang="et" data-title="Maa kuju" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Forma_de_la_Tierra" title="Forma de la Tierra – Spanish" lang="es" hreflang="es" data-title="Forma de la Tierra" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B4%DA%A9%D9%84_%D8%B3%DB%8C%D8%A7%D8%B1%D9%87_%D8%B2%D9%85%DB%8C%D9%86" title="شکل سیاره زمین – Persian" lang="fa" hreflang="fa" data-title="شکل سیاره زمین" data-language-autonym="فارسی" data-language-local-name="Persian" 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/Figure_de_la_Terre" title="Figure de la Terre – French" lang="fr" hreflang="fr" data-title="Figure de la Terre" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B5%D6%80%D5%AF%D6%80%D5%A1%D5%A3%D5%B6%D5%A4%D5%AB_%D5%B1%D6%87" title="Երկրագնդի ձև – Armenian" lang="hy" hreflang="hy" data-title="Երկրագնդի ձև" data-language-autonym="Հայերեն" data-language-local-name="Armenian" 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/Bentuk_Bumi" title="Bentuk Bumi – Indonesian" lang="id" hreflang="id" data-title="Bentuk Bumi" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Figura_della_Terra" title="Figura della Terra – Italian" lang="it" hreflang="it" data-title="Figura della Terra" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/A_F%C3%B6ld_alakja" title="A Föld alakja – Hungarian" lang="hu" hreflang="hu" data-title="A Föld alakja" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D0%B0%D1%82%D1%8C_%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86" title="Модать формац – Moksha" lang="mdf" hreflang="mdf" data-title="Модать формац" data-language-autonym="Мокшень" data-language-local-name="Moksha" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vorm_van_de_Aarde" title="Vorm van de Aarde – Dutch" lang="nl" hreflang="nl" data-title="Vorm van de Aarde" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Figura_da_Terra" title="Figura da Terra – Portuguese" lang="pt" hreflang="pt" data-title="Figura da Terra" data-language-autonym="Português" data-language-local-name="Portuguese" 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/Forma_P%C4%83m%C3%A2ntului" title="Forma Pământului – Romanian" lang="ro" hreflang="ro" data-title="Forma Pământului" data-language-autonym="Română" data-language-local-name="Romanian" 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%A4%D0%BE%D1%80%D0%BC%D0%B0_%D0%97%D0%B5%D0%BC%D0%BB%D0%B8" title="Форма Земли – Russian" lang="ru" hreflang="ru" data-title="Форма Земли" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Tvar_Zeme" title="Tvar Zeme – Slovak" lang="sk" hreflang="sk" data-title="Tvar Zeme" data-language-autonym="Slovenčina" data-language-local-name="Slovak" 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/Oblika_Zemlje" title="Oblika Zemlje – Slovenian" lang="sl" hreflang="sl" data-title="Oblika Zemlje" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/D%C3%BCnya%27n%C4%B1n_%C5%9Fekli" title="Dünya'nın şekli – Turkish" lang="tr" hreflang="tr" data-title="Dünya'nın şekli" data-language-autonym="Türkçe" data-language-local-name="Turkish" 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%A4%D1%96%D0%B3%D1%83%D1%80%D0%B0_%D0%97%D0%B5%D0%BC%D0%BB%D1%96" title="Фігура Землі – Ukrainian" lang="uk" hreflang="uk" data-title="Фігура Землі" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</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/Q437882#sitelinks-wikipedia" title="Edit 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class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Size and shape used to model the Earth for geodesy</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For the historical development of the concept, see <a href="/wiki/Spherical_Earth" title="Spherical Earth">Spherical Earth</a> and <a href="/wiki/Flat_Earth" title="Flat Earth">Flat Earth</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">For effects of and evidence for, see <a href="/wiki/Empirical_evidence_for_the_spherical_shape_of_Earth" title="Empirical evidence for the spherical shape of Earth">Empirical evidence for the spherical shape of Earth</a>.</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1129693374">.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 .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist 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title="Geoid">Geoid</a></li> <li><a class="mw-selflink selflink">Figure of the Earth</a> <small>(<a href="/wiki/Earth_radius" title="Earth radius">radius</a> and <a href="/wiki/Earth%27s_circumference" title="Earth's circumference">circumference</a>)</small></li> <li><a href="/wiki/Geodetic_coordinates" title="Geodetic coordinates">Geodetic coordinates</a></li> <li><a href="/wiki/Geodetic_datum" title="Geodetic datum">Geodetic datum</a></li> <li><a href="/wiki/Geodesic" title="Geodesic">Geodesic</a></li> <li><a href="/wiki/Horizontal_position_representation" title="Horizontal position representation">Horizontal position representation</a></li> <li><span class="nowrap"><a href="/wiki/Latitude" title="Latitude">Latitude</a> / <a href="/wiki/Longitude" title="Longitude">Longitude</a></span></li> <li><a href="/wiki/Map_projection" title="Map projection">Map projection</a></li> <li><a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">Reference ellipsoid</a></li> <li><a href="/wiki/Satellite_geodesy" title="Satellite geodesy">Satellite geodesy</a></li> <li><a href="/wiki/Spatial_reference_system" title="Spatial reference system">Spatial reference system</a></li> <li><a href="/wiki/Spatial_relation" title="Spatial relation">Spatial relations</a></li> <li><a href="/wiki/Vertical_position" title="Vertical position">Vertical positions</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Technologies</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Satellite_navigation" title="Satellite navigation">Global Nav. Sat. Systems (GNSSs)</a></li> <li><a href="/wiki/Global_Positioning_System" title="Global Positioning System">Global Pos. System (GPS)</a></li> <li><a href="/wiki/GLONASS" title="GLONASS">GLONASS <span style="font-size:85%;">(Russia)</span></a></li> <li><a href="/wiki/BeiDou" title="BeiDou">BeiDou (BDS) <span style="font-size:85%;">(China)</span></a></li> <li><a href="/wiki/Galileo_(satellite_navigation)" title="Galileo (satellite navigation)">Galileo <span style="font-size:85%;">(Europe)</span></a></li> <li><a href="/wiki/Indian_Regional_Navigation_Satellite_System" title="Indian Regional Navigation Satellite System">NAVIC <span style="font-size:85%;">(India)</span></a></li> <li><a href="/wiki/Quasi-Zenith_Satellite_System" title="Quasi-Zenith Satellite System">Quasi-Zenith Sat. Sys. (QZSS) <span style="font-size:85%;">(Japan)</span></a></li> <li><a href="/wiki/Discrete_Global_Grid" class="mw-redirect" title="Discrete Global Grid">Discrete Global Grid and Geocoding</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed plainlist"><div class="sidebar-list-title" style="color: var(--color-base)">Standards (history)</div><div class="sidebar-list-content mw-collapsible-content hlist"><table class="nowrap" style="width:100%;border-collapse:collapse;border-spacing:0px 0px;border:none;line-height:1.2em;"><tbody><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/Sea_Level_Datum_of_1929" class="mw-redirect" title="Sea Level Datum of 1929">NGVD 29</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Sea Level Datum 1929</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/OSGB36" class="mw-redirect" title="OSGB36">OSGB36</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Ordnance Survey Great Britain 1936</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/SK-42_reference_system" title="SK-42 reference system">SK-42</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Systema Koordinat 1942 goda</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/ED50" title="ED50">ED50</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> European Datum 1950</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/South_American_Datum#SAD69" title="South American Datum">SAD69</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> South American Datum 1969</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/GRS_80" class="mw-redirect" title="GRS 80">GRS 80</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Geodetic Reference System 1980</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/ISO_6709" title="ISO 6709">ISO 6709</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Geographic point coord. 1983</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/North_American_Datum#North_American_Datum_of_1983" title="North American Datum">NAD 83</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> North American Datum 1983</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/World_Geodetic_System" title="World Geodetic System">WGS 84</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> World Geodetic System 1984</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/North_American_Vertical_Datum_of_1988" title="North American Vertical Datum of 1988">NAVD 88</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> N. American Vertical Datum 1988</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/European_Terrestrial_Reference_System_1989" title="European Terrestrial Reference System 1989">ETRS89</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> European Terrestrial Ref. Sys. 1989</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/Restrictions_on_geographic_data_in_China" title="Restrictions on geographic data in China">GCJ-02</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Chinese obfuscated datum 2002</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/Geo_URI_scheme" title="Geo URI scheme">Geo URI</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Internet link to a point 2010</td></tr></tbody></table> <ul><li><a href="/wiki/International_Terrestrial_Reference_System" class="mw-redirect" title="International Terrestrial Reference System">International Terrestrial Reference System</a></li> <li><a href="/wiki/SRID" class="mw-redirect" title="SRID">Spatial Reference System Identifier (SRID)</a></li> <li><a href="/wiki/Universal_Transverse_Mercator_coordinate_system" title="Universal Transverse Mercator coordinate system">Universal Transverse Mercator (UTM)</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Geodesy" title="Template:Geodesy"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Geodesy" title="Template talk:Geodesy"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Geodesy" title="Special:EditPage/Template:Geodesy"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>In <a href="/wiki/Geodesy" title="Geodesy">geodesy</a>, the <b>figure of the Earth</b> is the size and shape used to model planet <a href="/wiki/Earth" title="Earth">Earth</a>. The kind of <a href="/wiki/Figure_(geometry)" class="mw-redirect" title="Figure (geometry)">figure</a> depends on application, including the precision needed for the model. A <a href="/wiki/Spherical_Earth" title="Spherical Earth">spherical Earth</a> is a well-known historical approximation that is satisfactory for <a href="/wiki/Geography" title="Geography">geography</a>, <a href="/wiki/Astronomy" title="Astronomy">astronomy</a> and many other purposes. Several models with greater accuracy (including <a href="/wiki/Earth_ellipsoid" title="Earth ellipsoid">ellipsoid</a>) have been developed so that <a href="/wiki/Geographic_coordinate_system" title="Geographic coordinate system">coordinate systems</a> can serve the precise needs of <a href="/wiki/Navigation" title="Navigation">navigation</a>, <a href="/wiki/Surveying" title="Surveying">surveying</a>, <a href="/wiki/Cadastre" title="Cadastre">cadastre</a>, <a href="/wiki/Land_use" title="Land use">land use</a>, and various other concerns. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Motivation">Motivation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=1" title="Edit section: Motivation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Earth's <a href="/wiki/Topography" title="Topography">topographic</a> surface is apparent with its variety of land forms and water areas. This topographic surface is generally the concern of topographers, <a href="/wiki/Hydrography" title="Hydrography">hydrographers</a>, and <a href="/wiki/Geophysics" title="Geophysics">geophysicists</a>. While it is the surface on which Earth measurements are made, mathematically modeling it while taking the irregularities into account would be extremely complicated. </p><p>The <a href="/wiki/Pythagoreanism" title="Pythagoreanism">Pythagorean</a> concept of a <a href="/wiki/Spherical_Earth" title="Spherical Earth">spherical Earth</a> offers a simple surface that is easy to deal with mathematically. Many astronomical and navigational computations use a <a href="/wiki/Sphere" title="Sphere">sphere</a> to model the Earth as a close approximation. However, a more accurate figure is needed for measuring distances and areas on the scale beyond the purely local. Better approximations can be made by modeling the entire surface as an <a href="/wiki/Oblate_spheroid" class="mw-redirect" title="Oblate spheroid">oblate spheroid</a>, using <a href="/wiki/Spherical_harmonic" class="mw-redirect" title="Spherical harmonic">spherical harmonics</a> to approximate the <a href="/wiki/Geoid" title="Geoid">geoid</a>, or modeling a region with a best-fit <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">reference ellipsoid</a>. </p><p>For surveys of small areas, a planar (flat) model of Earth's surface suffices because the local topography overwhelms the curvature. <a href="/wiki/Plane-table" class="mw-redirect" title="Plane-table">Plane-table</a> surveys are made for relatively small areas without considering the size and shape of the entire Earth. A survey of a city, for example, might be conducted this way. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Earth2014shape_SouthAmerica_small.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Earth2014shape_SouthAmerica_small.jpg/220px-Earth2014shape_SouthAmerica_small.jpg" decoding="async" width="220" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Earth2014shape_SouthAmerica_small.jpg/330px-Earth2014shape_SouthAmerica_small.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/Earth2014shape_SouthAmerica_small.jpg/440px-Earth2014shape_SouthAmerica_small.jpg 2x" data-file-width="1500" data-file-height="1362" /></a><figcaption>Topographic view of Earth relative to Earth's center (instead of to <a href="/wiki/Mean_sea_level" class="mw-redirect" title="Mean sea level">mean sea level</a>, as in common topographic maps)</figcaption></figure> <p>By the late 1600s, serious effort was devoted to modeling the Earth as an ellipsoid, beginning with French astronomer <a href="/wiki/Jean_Picard" title="Jean Picard">Jean Picard</a>'s measurement of a degree of arc along the <a href="/wiki/Paris_meridian" title="Paris meridian">Paris meridian</a>. Improved maps and better measurement of distances and areas of national territories motivated these early attempts. Surveying instrumentation and techniques improved over the ensuing centuries. Models for the figure of the Earth improved in step. </p><p>In the mid- to late 20th century, research across the <a href="/wiki/Earth_science" title="Earth science">geosciences</a> contributed to drastic improvements in the accuracy of the figure of the Earth. The primary utility of this improved accuracy was to provide geographical and gravitational data for the <a href="/wiki/Inertial_guidance_system" class="mw-redirect" title="Inertial guidance system">inertial guidance systems</a> of <a href="/wiki/Ballistic_missile" title="Ballistic missile">ballistic missiles</a>. This funding also drove the expansion of geoscientific disciplines, fostering the creation and growth of various geoscience departments at many universities.<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> These developments benefited many civilian pursuits as well, such as weather and communication <a href="/wiki/Satellite" title="Satellite">satellite</a> control and <a href="/wiki/GPS" class="mw-redirect" title="GPS">GPS</a> location-finding, which would be impossible without highly accurate models for the figure of the Earth. </p> <div class="mw-heading mw-heading2"><h2 id="Models">Models</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=2" title="Edit section: Models"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The models for the figure of the Earth vary in the way they are used, in their complexity, and in the accuracy with which they represent the size and shape of the Earth. </p> <div class="mw-heading mw-heading3"><h3 id="Sphere">Sphere</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=3" title="Edit section: Sphere"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Spherical_Earth" title="Spherical Earth">Spherical Earth</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Earth_radius" title="Earth radius">Earth radius</a> and <a href="/wiki/Earth%27s_circumference" title="Earth's circumference">Earth's circumference</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Horizon,_Valencia_(Spain).JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Horizon%2C_Valencia_%28Spain%29.JPG/260px-Horizon%2C_Valencia_%28Spain%29.JPG" decoding="async" width="260" height="195" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Horizon%2C_Valencia_%28Spain%29.JPG/390px-Horizon%2C_Valencia_%28Spain%29.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/Horizon%2C_Valencia_%28Spain%29.JPG/520px-Horizon%2C_Valencia_%28Spain%29.JPG 2x" data-file-width="2592" data-file-height="1944" /></a><figcaption>A view across a 20-km-wide bay in the coast of <a href="/wiki/Spain" title="Spain">Spain</a>. The curvature of the Earth is evident in the <a href="/wiki/Horizon" title="Horizon">horizon</a> across the image, and the bases of the buildings on the far shore are below that horizon and hidden by the sea.</figcaption></figure> <p>The simplest model for the shape of the entire Earth is a sphere. The Earth's <a href="/wiki/Radius" title="Radius">radius</a> is the <a href="/wiki/Distance" title="Distance">distance</a> from Earth's center to its surface, about 6,371 km (3,959 mi). While "radius" normally is a characteristic of perfect spheres, the Earth deviates from spherical by only a third of a percent, sufficiently close to treat it as a sphere in many contexts and justifying the term "the radius of the Earth". </p><p>The concept of a spherical Earth dates back to around the <a href="/wiki/6th_century_BC" title="6th century BC">6th century BC</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> but remained a matter of philosophical speculation until the <a href="/wiki/3rd_century_BC" title="3rd century BC">3rd century BC</a>. The first scientific estimation of the radius of the Earth was given by <a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a> about 240 BC, with estimates of the accuracy of Eratosthenes's measurement ranging from −1% to 15%. </p><p>The Earth is only approximately spherical, so no single value serves as its natural radius. Distances from points on the surface to the center range from 6,353 km (3,948 mi) to 6,384 km (3,967 mi). Several different ways of modeling the Earth as a sphere each yield a mean radius of 6,371 km (3,959 mi). Regardless of the model, any radius falls between the polar minimum of about 6,357 km (3,950 mi) and the equatorial maximum of about 6,378 km (3,963 mi). The difference 21 km (13 mi) correspond to the polar radius being approximately 0.3% shorter than the equatorial radius. </p> <div class="mw-heading mw-heading3"><h3 id="Ellipsoid_of_revolution">Ellipsoid of revolution</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=4" title="Edit section: Ellipsoid of revolution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:OblateSpheroid.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/OblateSpheroid.PNG/220px-OblateSpheroid.PNG" decoding="async" width="220" height="186" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/OblateSpheroid.PNG/330px-OblateSpheroid.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b5/OblateSpheroid.PNG/440px-OblateSpheroid.PNG 2x" data-file-width="503" data-file-height="426" /></a><figcaption>An <a href="/wiki/Oblate_spheroid" class="mw-redirect" title="Oblate spheroid">oblate spheroid</a>, highly exaggerated relative to the actual Earth</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Earth_oblateness_to_scale.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Earth_oblateness_to_scale.svg/220px-Earth_oblateness_to_scale.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Earth_oblateness_to_scale.svg/330px-Earth_oblateness_to_scale.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Earth_oblateness_to_scale.svg/440px-Earth_oblateness_to_scale.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>A scale diagram of the <a href="/wiki/Flattening" title="Flattening">oblateness</a> of the 2003 <a href="/wiki/IERS" class="mw-redirect" title="IERS">IERS</a> <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">reference ellipsoid</a>, with north at the top. The outer edge of the dark blue line is an <a href="/wiki/Ellipse" title="Ellipse">ellipse</a> with the same <a href="/wiki/Eccentricity_(mathematics)#Ellipses" title="Eccentricity (mathematics)">eccentricity</a> as that of Earth. For comparison, the light blue circle within has a diameter equal to the ellipse's <a href="/wiki/Minor_axis" class="mw-redirect" title="Minor axis">minor axis</a>. The red curve represents the <a href="/wiki/Karman_line" class="mw-redirect" title="Karman line">Karman line</a> 100 km (62 mi) above <a href="/wiki/Sea_level" title="Sea level">sea level</a>, while the yellow band denotes the <a href="/wiki/Apsis" title="Apsis">altitude</a> range of the <a href="/wiki/International_Space_Station" title="International Space Station">ISS</a> in <a href="/wiki/Low_Earth_orbit" title="Low Earth orbit">low Earth orbit</a>.</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Earth_ellipsoid" title="Earth ellipsoid">Earth ellipsoid</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">Reference ellipsoid</a></div> <p>As theorized by <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> and <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens</a>,<sup id="cite_ref-DMA_3-0" class="reference"><a href="#cite_note-DMA-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 4">: 4 </span></sup> the Earth is <a href="/wiki/Flattening" title="Flattening">flattened</a> at the poles and <a href="/wiki/Equatorial_bulge" title="Equatorial bulge">bulged</a> at the <a href="/wiki/Equator" title="Equator">equator</a>. Thus, <a href="/wiki/Geodesy" title="Geodesy">geodesy</a> represents the figure of the Earth as an oblate <a href="/wiki/Spheroid" title="Spheroid">spheroid</a>. The oblate spheroid, or <a href="/wiki/Oblate_ellipsoid" class="mw-redirect" title="Oblate ellipsoid">oblate ellipsoid</a>, is an <a href="/wiki/Ellipsoid_of_revolution" class="mw-redirect" title="Ellipsoid of revolution">ellipsoid of revolution</a> obtained by rotating an ellipse about its shorter axis. It is the regular <a href="/wiki/Geometric" class="mw-redirect" title="Geometric">geometric</a> shape that most nearly approximates the shape of the Earth. A spheroid describing the figure of the Earth or other <a href="/wiki/Celestial_body" class="mw-redirect" title="Celestial body">celestial body</a> is called a <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">reference ellipsoid</a>. The reference ellipsoid for Earth is called an <i>Earth ellipsoid</i>. </p><p>An ellipsoid of revolution is uniquely defined by two quantities. Several conventions for expressing the two quantities are used in geodesy, but they are all equivalent to and convertible with each other: </p> <ul><li>Equatorial radius <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> (called <i>semimajor axis</i>), and polar radius <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> (called <i>semiminor axis</i>);</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 a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> and <a href="/wiki/Eccentricity_(mathematics)" title="Eccentricity (mathematics)">eccentricity</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 e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}"></span>;</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 a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> and flattening <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 f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span>.</li></ul> <p>Eccentricity and flattening are different ways of expressing how squashed the ellipsoid is. When flattening appears as one of the defining quantities in geodesy, generally it is expressed by its reciprocal. For example, in the <a href="/wiki/World_Geodetic_System#WGS84" title="World Geodetic System">WGS 84</a> spheroid used by today's GPS systems, the reciprocal of the flattening <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1/f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9cd0e60c02ddf533da2abed825389fe5a94b7d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.603ex; height:2.843ex;" alt="{\displaystyle 1/f}"></span> is set to be exactly <span style="white-space:nowrap">298.257<span style="margin-left:0.25em">223</span><span style="margin-left:0.25em">563</span></span>. </p><p>The difference between a sphere and a reference ellipsoid for Earth is small, only about one part in 300. Historically, flattening was computed from <a href="/wiki/Grade_measurement" class="mw-redirect" title="Grade measurement">grade measurements</a>. Nowadays, geodetic networks and <a href="/wiki/Satellite_geodesy" title="Satellite geodesy">satellite geodesy</a> are used. In practice, many reference ellipsoids have been developed over the centuries from different surveys. The flattening value varies slightly from one reference ellipsoid to another, reflecting local conditions and whether the reference ellipsoid is intended to model the entire Earth or only some portion of it. </p><p>A sphere has a single <a href="/wiki/Radius_of_curvature_(applications)" class="mw-redirect" title="Radius of curvature (applications)">radius of curvature</a>, which is simply the radius of the sphere. More complex surfaces have radii of curvature that vary over the surface. The radius of curvature describes the radius of the sphere that best approximates the surface at that point. Oblate ellipsoids have a constant radius of curvature east to west along <a href="/wiki/Parallel_(latitude)" class="mw-redirect" title="Parallel (latitude)">parallels</a>, if a <a href="/wiki/Geographic_coordinate_system" title="Geographic coordinate system">graticule</a> is drawn on the surface, but varying curvature in any other direction. For an oblate ellipsoid, the polar radius of curvature <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_{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d02ec163fac8837ac757005d783b375e52808b97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.108ex; height:2.343ex;" alt="{\displaystyle r_{p}}"></span> is larger than the equatorial </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{p}={\frac {a^{2}}{b}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>b</mi> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{p}={\frac {a^{2}}{b}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e51f65461181d5c178d61abfaef681a2df326e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.973ex; height:5.843ex;" alt="{\displaystyle r_{p}={\frac {a^{2}}{b}},}"></span></dd></dl> <p>because the pole is flattened: the flatter the surface, the larger the sphere must be to approximate it. Conversely, the ellipsoid's north–south radius of curvature at the equator <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_{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c652979f43cb2855b9a028560d7e228aa2f9bb1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.047ex; height:2.009ex;" alt="{\displaystyle r_{e}}"></span> is smaller than the polar </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r_{e}={\frac {b^{2}}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{e}={\frac {b^{2}}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4bcb822ca7b2a745f348db5c9aa30a90949df136" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.033ex; height:5.676ex;" alt="{\displaystyle r_{e}={\frac {b^{2}}{a}}}"></span></dd></dl> <p>where <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> is the distance from the center of the ellipsoid to the equator (semi-major axis), and <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> is the distance from the center to the pole. (semi-minor axis) </p> <div class="mw-heading mw-heading3"><h3 id="Non-spheroidal_deviations">Non-spheroidal deviations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=5" title="Edit section: Non-spheroidal deviations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Triaxiality_(equatorial_eccentricity)"><span id="Triaxiality_.28equatorial_eccentricity.29"></span>Triaxiality (equatorial eccentricity) <span class="anchor" id="Triaxiality"></span><span class="anchor" id="Equatorial_eccentricity"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=6" title="Edit section: Triaxiality (equatorial eccentricity)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The possibility that the Earth's equator is better characterized as an ellipse rather than a circle and therefore that the ellipsoid is triaxial has been a matter of scientific inquiry for many years.<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><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> Modern technological developments have furnished new and rapid methods for data collection and, since the launch of <a href="/wiki/Sputnik_1" title="Sputnik 1">Sputnik 1</a>, orbital data have been used to investigate the theory of ellipticity.<sup id="cite_ref-DMA_3-1" class="reference"><a href="#cite_note-DMA-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> More recent results indicate a 70 m difference between the two equatorial major and minor axes of inertia, with the larger semidiameter pointing to 15° W longitude (and also 180-degree away).<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><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> </p><p><span class="anchor" id="Pear_shape"></span> </p> <div class="mw-heading mw-heading4"><h4 id="Egg_or_pear_shape">Egg or pear shape</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=7" title="Edit section: Egg or pear shape"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Following work by Picard, Italian polymath <a href="/wiki/Giovanni_Domenico_Cassini" title="Giovanni Domenico Cassini">Giovanni Domenico Cassini</a> found that the length of a degree was apparently shorter north of Paris than to the south, implying the Earth to be <a href="/wiki/Egg" title="Egg">egg</a>-shaped.<sup id="cite_ref-DMA_3-2" class="reference"><a href="#cite_note-DMA-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 4">: 4 </span></sup> In 1498, <a href="/wiki/Christopher_Columbus" title="Christopher Columbus">Christopher Columbus</a> dubiously suggested that the Earth was pear-shaped based on his disparate mobile readings of the angle of the <a href="/wiki/North_Star" class="mw-redirect" title="North Star">North Star</a>, which he incorrectly interpreted as having varying <a href="/wiki/Diurnal_motion" title="Diurnal motion">diurnal motion</a>.<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><p>The theory of a slightly pear-shaped Earth arose when data was received from the U.S.'s artificial satellite <a href="/wiki/Vanguard_1" title="Vanguard 1">Vanguard 1</a> in 1958. It was found to vary in its long periodic orbit, with the Southern Hemisphere exhibiting higher gravitational attraction than the Northern Hemisphere. This indicated a flattening at the <a href="/wiki/South_Pole" title="South Pole">South Pole</a> and a bulge of the same degree at the <a href="/wiki/North_Pole" title="North Pole">North Pole</a>, with the <a href="/wiki/Sea_level" title="Sea level">sea level</a> increased about 9 m (30 ft) at the latter.<sup id="cite_ref-:0_9-0" class="reference"><a href="#cite_note-:0-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_10-0" class="reference"><a href="#cite_note-:1-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-DMA_3-3" class="reference"><a href="#cite_note-DMA-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 9">: 9 </span></sup> This theory implies the northern middle <a href="/wiki/Latitudes" class="mw-redirect" title="Latitudes">latitudes</a> to be slightly flattened and the southern middle latitudes correspondingly bulged.<sup id="cite_ref-DMA_3-4" class="reference"><a href="#cite_note-DMA-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 9">: 9 </span></sup> Potential factors involved in this aberration include <a href="/wiki/Tide" title="Tide">tides</a> and <a href="/wiki/Internal_structure_of_Earth" title="Internal structure of Earth">subcrustal</a> motion (e.g. <a href="/wiki/Plate_tectonics" title="Plate tectonics">plate tectonics</a>).<sup id="cite_ref-:0_9-1" class="reference"><a href="#cite_note-:0-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_10-1" class="reference"><a href="#cite_note-:1-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/John_A._O%27Keefe_(astronomer)" title="John A. O'Keefe (astronomer)">John A. O'Keefe</a> and co-authors are credited with the discovery that the Earth had a significant third degree <a href="/wiki/Zonal_spherical_harmonic" class="mw-redirect" title="Zonal spherical harmonic">zonal spherical harmonic</a> in its <a href="/wiki/Earth%27s_gravity" class="mw-redirect" title="Earth's gravity">gravitational field</a> using Vanguard 1 satellite data.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Based on further <a href="/wiki/Satellite_geodesy" title="Satellite geodesy">satellite geodesy</a> data, <a href="/wiki/Desmond_King-Hele" title="Desmond King-Hele">Desmond King-Hele</a> refined the estimate to a 45 m (148 ft) difference between north and south polar radii, owing to a 19 m (62 ft) "stem" rising in the North Pole and a 26 m (85 ft) depression in the South Pole.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> The polar asymmetry is about a thousand times smaller than the Earth's flattening and even smaller than its <a href="/wiki/Geoidal_undulation" class="mw-redirect" title="Geoidal undulation">geoidal undulation</a> in some regions.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Geoid">Geoid</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=8" title="Edit section: Geoid"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Geoid" title="Geoid">Geoid</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Earth_Gravitational_Model_1996.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Earth_Gravitational_Model_1996.png/330px-Earth_Gravitational_Model_1996.png" decoding="async" width="330" height="208" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Earth_Gravitational_Model_1996.png/495px-Earth_Gravitational_Model_1996.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Earth_Gravitational_Model_1996.png/660px-Earth_Gravitational_Model_1996.png 2x" data-file-width="742" data-file-height="468" /></a><figcaption>Map of the undulation of the geoid in meters (based on the <a href="/wiki/EGM96" class="mw-redirect" title="EGM96">EGM96</a> gravity model and the <a href="/wiki/WGS84" class="mw-redirect" title="WGS84">WGS84</a> reference ellipsoid).</figcaption></figure> <p>Modern geodesy tends to retain the ellipsoid of revolution as a <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">reference ellipsoid</a> and treat triaxiality and pear shape as a part of the <a href="/wiki/Geoid" title="Geoid">geoid</a> figure: they are represented by the spherical harmonic coefficients <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 C_{22},S_{22}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>22</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>22</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{22},S_{22}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b72658f13ab6ee103442a2d66bcc1f0ac8fe364c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.873ex; height:2.509ex;" alt="{\displaystyle C_{22},S_{22}}"></span> and <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 C_{30}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>30</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{30}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33c1c71ece6cf8dc641c8a903f002337e7df12be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.538ex; height:2.509ex;" alt="{\displaystyle C_{30}}"></span>, respectively, corresponding to degree and order numbers 2.2 for the triaxiality and 3.0 for the pear shape. </p><p>It was stated earlier that measurements are made on the apparent or topographic surface of the Earth and it has just been explained that computations are performed on an ellipsoid. One other surface is involved in geodetic measurement: the geoid. In geodetic surveying, the computation of the <a href="/wiki/Geodetic_coordinates" title="Geodetic coordinates">geodetic coordinates</a> of points is commonly performed on a <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">reference ellipsoid</a> closely approximating the size and shape of the Earth in the area of the survey. The actual measurements made on the surface of the Earth with certain instruments are however referred to the geoid. The ellipsoid is a mathematically defined regular surface with specific dimensions. The geoid, on the other hand, coincides with that surface to which the oceans would conform over the entire Earth if free to adjust to the combined effect of the Earth's mass attraction (<a href="/wiki/Gravitation" class="mw-redirect" title="Gravitation">gravitation</a>) and the centrifugal force of the <a href="/wiki/Earth%27s_rotation" title="Earth's rotation">Earth's rotation</a>. As a result of the uneven distribution of the Earth's mass, the geoidal surface is irregular and, since the ellipsoid is a regular surface, the separations between the two, referred to as <a href="/wiki/Geoid_undulation" class="mw-redirect" title="Geoid undulation">geoid undulations</a>, geoid heights, or geoid separations, will be irregular as well. </p><p>The geoid is a surface along which the gravity <a href="/wiki/Equipotential" title="Equipotential">potential is equal</a> everywhere and to which the direction of gravity is always perpendicular. The latter is particularly important because optical instruments containing gravity-reference leveling devices are commonly used to make geodetic measurements. When properly adjusted, the vertical axis of the instrument coincides with the direction of gravity and is, therefore, perpendicular to the geoid. The angle between the <a href="/wiki/Plumb_line" class="mw-redirect" title="Plumb line">plumb line</a> which is perpendicular to the geoid (sometimes called "the vertical") and the perpendicular to the ellipsoid (sometimes called "the ellipsoidal normal") is defined as the <a href="/wiki/Vertical_deflection" title="Vertical deflection">deflection of the vertical</a>. It has two components: an east–west and a north–south component.<sup id="cite_ref-DMA_3-5" class="reference"><a href="#cite_note-DMA-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Local_approximations">Local approximations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=9" title="Edit section: Local approximations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Simpler local approximations are possible. </p> <div class="mw-heading mw-heading4"><h4 id="Local_tangent_plane">Local tangent plane</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=10" title="Edit section: Local tangent plane"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:ECEF_ENU_Longitude_Latitude_relationships.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/ECEF_ENU_Longitude_Latitude_relationships.svg/220px-ECEF_ENU_Longitude_Latitude_relationships.svg.png" decoding="async" width="220" height="212" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/ECEF_ENU_Longitude_Latitude_relationships.svg/330px-ECEF_ENU_Longitude_Latitude_relationships.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/ECEF_ENU_Longitude_Latitude_relationships.svg/440px-ECEF_ENU_Longitude_Latitude_relationships.svg.png 2x" data-file-width="520" data-file-height="500" /></a><figcaption><a href="/wiki/Local_tangent_plane" class="mw-redirect" title="Local tangent plane">Local tangent plane</a>.</figcaption></figure> <p>The <a href="/wiki/Local_tangent_plane" class="mw-redirect" title="Local tangent plane">local tangent plane</a> is appropriate for analysis across small distances. </p> <div class="mw-heading mw-heading4"><h4 id="Osculating_sphere">Osculating sphere</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=11" title="Edit section: Osculating sphere"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Referenzellipsoid_im_x-z-Schnitt_mit_Kruemmungskreis.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Referenzellipsoid_im_x-z-Schnitt_mit_Kruemmungskreis.svg/220px-Referenzellipsoid_im_x-z-Schnitt_mit_Kruemmungskreis.svg.png" decoding="async" width="220" height="161" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Referenzellipsoid_im_x-z-Schnitt_mit_Kruemmungskreis.svg/330px-Referenzellipsoid_im_x-z-Schnitt_mit_Kruemmungskreis.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Referenzellipsoid_im_x-z-Schnitt_mit_Kruemmungskreis.svg/440px-Referenzellipsoid_im_x-z-Schnitt_mit_Kruemmungskreis.svg.png 2x" data-file-width="985" data-file-height="723" /></a><figcaption>Ellipsoid and osculating sphere</figcaption></figure> <p>The best local spherical approximation to the ellipsoid in the vicinity of a given point is the <i>Earth's <a href="/wiki/Osculating_circle" title="Osculating circle">osculating</a> sphere</i>. Its radius equals <a href="/wiki/Earth_radius#Gaussian_radius_of_curvature" title="Earth radius">Earth's Gaussian radius of curvature</a>, and its radial direction coincides with the <a href="/wiki/Geodetic_normal" class="mw-redirect" title="Geodetic normal">geodetic normal</a> direction. The center of the osculating sphere is offset from the center of the ellipsoid, but is at the <a href="/wiki/Center_of_curvature" title="Center of curvature">center of curvature</a> for the given point on the ellipsoid surface. This concept aids the interpretation of terrestrial and planetary <a href="/wiki/Radio_occultation" title="Radio occultation">radio occultation</a> <a href="/wiki/Refraction" title="Refraction">refraction</a> measurements and in some navigation and surveillance applications.<sup id="cite_ref-Williams_15-0" class="reference"><a href="#cite_note-Williams-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Razin_16-0" class="reference"><a href="#cite_note-Razin-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:left;" class=""></div> <div class="mw-heading mw-heading2"><h2 id="Earth_rotation_and_Earth's_interior"><span id="Earth_rotation_and_Earth.27s_interior"></span>Earth rotation and Earth's interior</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=12" title="Edit section: Earth rotation and Earth's interior"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Clairaut%27s_theorem" class="mw-redirect" title="Clairaut's theorem">Clairaut's theorem</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Structure_of_Earth" class="mw-redirect" title="Structure of Earth">Structure of Earth</a> and <a href="/wiki/Theoretical_gravity" title="Theoretical gravity">Theoretical gravity</a></div> <p>Determining the exact figure of the Earth is not only a geometric task of geodesy, but also has <a href="/wiki/Geophysical" class="mw-redirect" title="Geophysical">geophysical</a> considerations. According to theoretical arguments by Newton, <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a>, and others, a body having a uniform density of 5,515 kg/m<sup>3</sup> that rotates like the Earth should have a flattening of 1:229. This can be concluded without any information about the composition of <a href="/wiki/Earth%27s_interior" class="mw-redirect" title="Earth's interior">Earth's interior</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> However, the measured flattening is 1:298.25, which is closer to a sphere and a strong argument that <a href="/wiki/Structure_of_the_Earth" class="mw-redirect" title="Structure of the Earth">Earth's core</a> is extremely compact. Therefore, the <a href="/wiki/Density" title="Density">density</a> must be a function of the depth, ranging from 2,600 kg/m<sup>3</sup> at the surface (rock density of <a href="/wiki/Granite" title="Granite">granite</a>, etc.), up to 13,000 kg/m<sup>3</sup> within the inner core.<sup id="cite_ref-PREM_18-0" class="reference"><a href="#cite_note-PREM-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Global_and_regional_gravity_field">Global and regional gravity field</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=13" title="Edit section: Global and regional gravity field"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Gravity_of_Earth" title="Gravity of Earth">Gravity of Earth</a></div> <p>Also with implications for the physical exploration of the Earth's interior is the <a href="/wiki/Gravitational_field" title="Gravitational field">gravitational field</a>, which is the net effect of gravitation (due to mass attraction) and centrifugal force (due to rotation). It can be measured very accurately at the surface and remotely by satellites. True <a href="/wiki/Vertical_direction" class="mw-redirect" title="Vertical direction">vertical</a> generally does not correspond to theoretical vertical (<a href="/wiki/Deflection_(physics)" title="Deflection (physics)">deflection</a> ranges up to 50") because <a href="/wiki/Topography" title="Topography">topography</a> and all <i>geological masses</i> disturb the gravitational field. Therefore, the gross structure of the <a href="/wiki/Earth%27s_crust" title="Earth's crust">Earth's crust</a> and mantle can be determined by geodetic-geophysical models of the subsurface. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=14" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Clairaut%27s_theorem" class="mw-redirect" title="Clairaut's theorem">Clairaut's theorem</a></li> <li><a href="/wiki/EGM96" class="mw-redirect" title="EGM96">EGM96</a></li> <li><a href="/wiki/Gravity_formula" class="mw-redirect" title="Gravity formula">Gravity formula</a></li> <li>Horizon §§ <a href="/wiki/Horizon#Distance" title="Horizon">Distance</a> and <a href="/wiki/Horizon#Curvature" title="Horizon">Curvature</a></li> <li><a href="/wiki/Meridian_arc" title="Meridian arc">Meridian arc</a></li></ul> <dl><dt>History</dt> <dd></dd></dl> <ul><li><a href="/wiki/Pierre_Bouguer" title="Pierre Bouguer">Pierre Bouguer</a></li> <li><a href="/wiki/Earth%27s_circumference#History" title="Earth's circumference">Earth's circumference#History</a></li> <li><a href="/wiki/Earth%27s_radius#History" class="mw-redirect" title="Earth's radius">Earth's radius#History</a></li> <li><a href="/wiki/Flat_Earth" title="Flat Earth">Flat Earth</a></li> <li><a href="/wiki/Friedrich_Robert_Helmert" title="Friedrich Robert Helmert">Friedrich Robert Helmert</a></li> <li><a href="/wiki/History_of_geodesy" title="History of geodesy">History of geodesy</a></li> <li><a href="/wiki/History_of_the_metre" title="History of the metre">History of the metre</a></li> <li><a href="/wiki/Meridian_arc#History" title="Meridian arc">Meridian arc#History</a></li> <li><a href="/wiki/Seconds_pendulum" title="Seconds pendulum">Seconds pendulum</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=15" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.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 mw-references-columns"><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"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFCloud2000" class="citation journal cs1">Cloud, John (2000). "Crossing the Olentangy River: The Figure of the Earth and the Military-Industrial-Academic Complex, 1947–1972". <i>Studies in History and Philosophy of Modern Physics</i>. <b>31</b> (3): 371–404. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000SHPMP..31..371C">2000SHPMP..31..371C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS1355-2198%2800%2900017-4">10.1016/S1355-2198(00)00017-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Studies+in+History+and+Philosophy+of+Modern+Physics&rft.atitle=Crossing+the+Olentangy+River%3A+The+Figure+of+the+Earth+and+the+Military-Industrial-Academic+Complex%2C+1947%E2%80%931972&rft.volume=31&rft.issue=3&rft.pages=371-404&rft.date=2000&rft_id=info%3Adoi%2F10.1016%2FS1355-2198%2800%2900017-4&rft_id=info%3Abibcode%2F2000SHPMP..31..371C&rft.aulast=Cloud&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDicks1970" class="citation book cs1">Dicks, D.R. (1970). <a rel="nofollow" class="external text" href="https://archive.org/details/earlygreekastron0000dick/page/72"><i>Early Greek Astronomy to Aristotle</i></a>. Ithaca, N.Y.: <a href="/wiki/Cornell_University_Press" title="Cornell University Press">Cornell University Press</a>. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/earlygreekastron0000dick/page/72">72–198</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8014-0561-7" title="Special:BookSources/978-0-8014-0561-7"><bdi>978-0-8014-0561-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Early+Greek+Astronomy+to+Aristotle&rft.place=Ithaca%2C+N.Y.&rft.pages=72-198&rft.pub=Cornell+University+Press&rft.date=1970&rft.isbn=978-0-8014-0561-7&rft.aulast=Dicks&rft.aufirst=D.R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fearlygreekastron0000dick%2Fpage%2F72&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> <li id="cite_note-DMA-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-DMA_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-DMA_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-DMA_3-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-DMA_3-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-DMA_3-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-DMA_3-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDefense_Mapping_Agency1983" class="citation report cs1">Defense Mapping Agency (1983). <a rel="nofollow" class="external text" href="https://apps.dtic.mil/sti/citations/ADA142764">Geodesy for the Layman</a> (Report) (4th ed.). United States Air Force.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=Geodesy+for+the+Layman&rft.edition=4th&rft.pub=United+States+Air+Force&rft.date=1983&rft.au=Defense+Mapping+Agency&rft_id=https%3A%2F%2Fapps.dtic.mil%2Fsti%2Fcitations%2FADA142764&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeiskanen1962" class="citation journal cs1">Heiskanen, W. A. (1962). "Is the Earth a triaxial ellipsoid?". <i>Journal of Geophysical Research</i>. <b>67</b> (1): 321–327. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1962JGR....67..321H">1962JGR....67..321H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1029%2FJZ067i001p00321">10.1029/JZ067i001p00321</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Geophysical+Research&rft.atitle=Is+the+Earth+a+triaxial+ellipsoid%3F&rft.volume=67&rft.issue=1&rft.pages=321-327&rft.date=1962&rft_id=info%3Adoi%2F10.1029%2FJZ067i001p00321&rft_id=info%3Abibcode%2F1962JGR....67..321H&rft.aulast=Heiskanen&rft.aufirst=W.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBurša1993" class="citation journal cs1">Burša, Milan (1993). "Parameters of the Earth's tri-axial level ellipsoid". <i>Studia Geophysica et Geodaetica</i>. <b>37</b> (1): 1–13. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1993StGG...37....1B">1993StGG...37....1B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01613918">10.1007/BF01613918</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:128674427">128674427</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Studia+Geophysica+et+Geodaetica&rft.atitle=Parameters+of+the+Earth%27s+tri-axial+level+ellipsoid&rft.volume=37&rft.issue=1&rft.pages=1-13&rft.date=1993&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A128674427%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF01613918&rft_id=info%3Abibcode%2F1993StGG...37....1B&rft.aulast=Bur%C5%A1a&rft.aufirst=Milan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Torge & Müller (2012) Geodesy, De Gruyter, p.100</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Marchenko, A.N. (2009): Current estimation of the Earth’s mechanical and geometrical para meters. In Sideris, M.G., ed. (2009): Observing our changing Earth. IAG Symp. Proceed. 133., pp. 473–481. DOI:10.1007/978-3-540-85426-5_57</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMorison1991" class="citation book cs1"><a href="/wiki/Samuel_Eliot_Morison" title="Samuel Eliot Morison">Morison, Samuel Eliot</a> (1991) [1942]. <i>Admiral of the Ocean Sea: A Life of Christopher Columbus</i>. Boston: Little, Brown and Company. p. 557. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-316-58478-4" title="Special:BookSources/978-0-316-58478-4"><bdi>978-0-316-58478-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1154365097">1154365097</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Admiral+of+the+Ocean+Sea%3A+A+Life+of+Christopher+Columbus&rft.place=Boston&rft.pages=557&rft.pub=Little%2C+Brown+and+Company&rft.date=1991&rft_id=info%3Aoclcnum%2F1154365097&rft.isbn=978-0-316-58478-4&rft.aulast=Morison&rft.aufirst=Samuel+Eliot&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> <li id="cite_note-:0-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTyson2007" class="citation book cs1"><a href="/wiki/Neil_deGrasse_Tyson" title="Neil deGrasse Tyson">Tyson, Neil deGrasse</a> (2007). <a rel="nofollow" class="external text" href="https://archive.org/details/NeilDeGrasseTysonDeathByBlackHoleAndOtherCosmicQuandaries/page/n61/mode/2up"><i>Death By Black Hole: And Other Cosmic Quandaries</i></a> (1st ed.). New York: W. W. Norton. p. 61. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-393-11378-5" title="Special:BookSources/978-0-393-11378-5"><bdi>978-0-393-11378-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Death+By+Black+Hole%3A+And+Other+Cosmic+Quandaries&rft.place=New+York&rft.pages=61&rft.edition=1st&rft.pub=W.+W.+Norton&rft.date=2007&rft.isbn=978-0-393-11378-5&rft.aulast=Tyson&rft.aufirst=Neil+deGrasse&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2FNeilDeGrasseTysonDeathByBlackHoleAndOtherCosmicQuandaries%2Fpage%2Fn61%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> <li id="cite_note-:1-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_10-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHawkins1969" class="citation book cs1"><a href="/wiki/Gerald_Hawkins" title="Gerald Hawkins">Hawkins, Gerald S.</a> (1969) [1961]. <a rel="nofollow" class="external text" href="https://archive.org/details/splendorinsky00hawk/page/242/mode/2up"><i>Splendor in the Sky</i></a>. New York: Harper & Row. p. 242.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Splendor+in+the+Sky&rft.place=New+York&rft.pages=242&rft.pub=Harper+%26+Row&rft.date=1969&rft.aulast=Hawkins&rft.aufirst=Gerald+S.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsplendorinsky00hawk%2Fpage%2F242%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">O’Keefe, J. A., Eckeis, A., and Squires, R. K. (1959). "Vanguard Measurements Give Pear-Shaped Component of Earth’s Figure". <i>Science</i>, 129(3348), 565–566. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.129.3348.565">10.1126/science.129.3348.565</a>.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKing-HeleCook1973" class="citation journal cs1">King-Hele, D. G.; Cook, G. E. (1973). "Refining the Earth's Pear Shape". <i>Nature</i>. <b>246</b> (5428). Springer Nature: 86–88. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1973Natur.246...86K">1973Natur.246...86K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F246086a0">10.1038/246086a0</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0028-0836">0028-0836</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4260099">4260099</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Refining+the+Earth%27s+Pear+Shape&rft.volume=246&rft.issue=5428&rft.pages=86-88&rft.date=1973&rft_id=info%3Adoi%2F10.1038%2F246086a0&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4260099%23id-name%3DS2CID&rft.issn=0028-0836&rft_id=info%3Abibcode%2F1973Natur.246...86K&rft.aulast=King-Hele&rft.aufirst=D.+G.&rft.au=Cook%2C+G.+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKing-Hele1967" class="citation journal cs1">King-Hele, Desmond (1967). "The Shape of the Earth". <i>Scientific American</i>. <b>217</b> (4): 67–80. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fscientificamerican1067-67">10.1038/scientificamerican1067-67</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/24926147">24926147</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+American&rft.atitle=The+Shape+of+the+Earth&rft.volume=217&rft.issue=4&rft.pages=67-80&rft.date=1967&rft_id=info%3Adoi%2F10.1038%2Fscientificamerican1067-67&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F24926147%23id-name%3DJSTOR&rft.aulast=King-Hele&rft.aufirst=Desmond&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">Günter Seeber (2008), <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=qZTS6OI9NGoC&dq=geoid%20j3%20pear&pg=PA517">Satellite Geodesy</a></i>, Walter de Gruyter.</span> </li> <li id="cite_note-Williams-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Williams_15-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWilliamsLast2003" class="citation conference cs1">Williams, Paul; Last, David (3–7 November 2003). <a rel="nofollow" class="external text" href="https://loran.org/proceedings/Meeting2003/Session9/WmsLastILA03TD2LL.pdf"><i>On Loran-C Time-Difference to Co-ordinate Converters</i></a> <span class="cs1-format">(PDF)</span>. <a rel="nofollow" class="external text" href="https://loran.org/proceedings/Meeting2003/ProceedingsIndex.htm">International Loran Association (ILA) – 32nd Annual Convention and Technical Symposium</a>. Boulder, Colorado. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.594.6212">10.1.1.594.6212</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=On+Loran-C+Time-Difference+to+Co-ordinate+Converters&rft.place=Boulder%2C+Colorado&rft.date=2003-11-03%2F2003-11-07&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.594.6212%23id-name%3DCiteSeerX&rft.aulast=Williams&rft.aufirst=Paul&rft.au=Last%2C+David&rft_id=https%3A%2F%2Floran.org%2Fproceedings%2FMeeting2003%2FSession9%2FWmsLastILA03TD2LL.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> <li id="cite_note-Razin-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-Razin_16-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRazin1967" class="citation journal cs1">Razin, Sheldon (Fall 1967). "Explicit (Noniterative) Loran Solution". <i>Navigation: Journal of the Institute of Navigation</i>. <b>14</b> (3): 265–269. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fj.2161-4296.1967.tb02208.x">10.1002/j.2161-4296.1967.tb02208.x</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Navigation%3A+Journal+of+the+Institute+of+Navigation&rft.atitle=Explicit+%28Noniterative%29+Loran+Solution&rft.ssn=fall&rft.volume=14&rft.issue=3&rft.pages=265-269&rft.date=1967&rft_id=info%3Adoi%2F10.1002%2Fj.2161-4296.1967.tb02208.x&rft.aulast=Razin&rft.aufirst=Sheldon&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHeine2013" class="citation journal cs1">Heine, George (2013). <a rel="nofollow" class="external text" href="http://digitaleditions.walsworthprintgroup.com/publication/?i=172875&article_id=1491473&view=articleBrowser&ver=html5#{%22issue_id%22:172875,%22view%22:%22articleBrowser%22,%22article_id%22:%221491473%22}">"Euler and the Flattening of the Earth"</a>. <i>Math Horizons</i>. <b>21</b> (1). Mathematical Association of America: 25–29. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4169%2Fmathhorizons.21.1.25">10.4169/mathhorizons.21.1.25</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:126412032">126412032</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Math+Horizons&rft.atitle=Euler+and+the+Flattening+of+the+Earth&rft.volume=21&rft.issue=1&rft.pages=25-29&rft.date=2013&rft_id=info%3Adoi%2F10.4169%2Fmathhorizons.21.1.25&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A126412032%23id-name%3DS2CID&rft.aulast=Heine&rft.aufirst=George&rft_id=http%3A%2F%2Fdigitaleditions.walsworthprintgroup.com%2Fpublication%2F%3Fi%3D172875%26article_id%3D1491473%26view%3DarticleBrowser%26ver%3Dhtml5%23%7B%2522issue_id%2522%3A172875%2C%2522view%2522%3A%2522articleBrowser%2522%2C%2522article_id%2522%3A%25221491473%2522%7D&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> <li id="cite_note-PREM-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-PREM_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDziewonskiAnderson1981" class="citation cs2">Dziewonski, A. M.; Anderson, D. L. (1981), <a rel="nofollow" class="external text" href="https://www.cfa.harvard.edu/~lzeng/papers/PREM.pdf">"Preliminary reference Earth model"</a> <span class="cs1-format">(PDF)</span>, <i>Physics of the Earth and Planetary Interiors</i>, <b>25</b> (4): 297–356, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1981PEPI...25..297D">1981PEPI...25..297D</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0031-9201%2881%2990046-7">10.1016/0031-9201(81)90046-7</a>, <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0031-9201">0031-9201</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+of+the+Earth+and+Planetary+Interiors&rft.atitle=Preliminary+reference+Earth+model&rft.volume=25&rft.issue=4&rft.pages=297-356&rft.date=1981&rft.issn=0031-9201&rft_id=info%3Adoi%2F10.1016%2F0031-9201%2881%2990046-7&rft_id=info%3Abibcode%2F1981PEPI...25..297D&rft.aulast=Dziewonski&rft.aufirst=A.+M.&rft.au=Anderson%2C+D.+L.&rft_id=https%3A%2F%2Fwww.cfa.harvard.edu%2F~lzeng%2Fpapers%2FPREM.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span></span> </li> </ol></div></div> <dl><dt>Attribution</dt></dl> <p><span class="noviewer" typeof="mw:File"><span><img alt="Public Domain" src="//upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/12px-PD-icon.svg.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/18px-PD-icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/24px-PD-icon.svg.png 2x" data-file-width="196" data-file-height="196" /></span></span> This article incorporates text from this source, which is in the <a href="/wiki/Public_domain" title="Public domain">public domain</a>: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDefense_Mapping_Agency1983" class="citation report cs1">Defense Mapping Agency (1983). <a rel="nofollow" class="external text" href="https://apps.dtic.mil/sti/citations/ADA142764">Geodesy for the Layman</a> (Report). United States Air Force.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=Geodesy+for+the+Layman&rft.pub=United+States+Air+Force&rft.date=1983&rft.au=Defense+Mapping+Agency&rft_id=https%3A%2F%2Fapps.dtic.mil%2Fsti%2Fcitations%2FADA142764&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFigure+of+the+Earth" class="Z3988"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=16" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Guy_Bomford" title="Guy Bomford">Guy Bomford</a>, <i><a href="/wiki/Geodesy_(book)" title="Geodesy (book)">Geodesy</a></i>, Oxford 1952 and 1980.</li> <li>Guy Bomford, <i>Determination of the European geoid by means of <a href="/wiki/Vertical_deflection" title="Vertical deflection">vertical deflections</a></i>. Rpt of Comm. 14, <a href="/wiki/IUGG" class="mw-redirect" title="IUGG">IUGG</a> 10th Gen. Ass., Rome 1954.</li> <li><a href="/wiki/Karl_Ledersteger" title="Karl Ledersteger">Karl Ledersteger</a> and <a href="/w/index.php?title=Gottfried_Gerstbach&action=edit&redlink=1" class="new" title="Gottfried Gerstbach (page does not exist)">Gottfried Gerstbach</a>, <i>Die horizontale <a href="/wiki/Isostasy" title="Isostasy">Isostasie</a> / Das isostatische Geoid 31. Ordnung</i>. Geowissenschaftliche Mitteilungen Band 5, <a href="/wiki/TU_Wien" title="TU Wien">TU Wien</a> 1975.</li> <li><a href="/wiki/Helmut_Moritz" title="Helmut Moritz">Helmut Moritz</a> and <a href="/w/index.php?title=Bernhard_Hofmann-Wellenhof&action=edit&redlink=1" class="new" title="Bernhard Hofmann-Wellenhof (page does not exist)">Bernhard Hofmann</a>, <i>Physical Geodesy</i>. <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer</a>, Wien & New York 2005.</li> <li><i>Geodesy for the Layman</i>, <a href="/wiki/Defense_Mapping_Agency" class="mw-redirect" title="Defense Mapping Agency">Defense Mapping Agency</a>, St. Louis, 1983.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Figure_of_the_Earth&action=edit&section=17" title="Edit section: External links"><span>edit</span></a><span 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