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<span>Definition</span> </div> </a> <ul id="toc-Definition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geoid_and_reference_ellipsoid" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Geoid_and_reference_ellipsoid"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Geoid and reference ellipsoid</span> </div> </a> <ul id="toc-Geoid_and_reference_ellipsoid-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Coordinate_systems_in_space" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Coordinate_systems_in_space"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Coordinate systems in space</span> </div> </a> <button aria-controls="toc-Coordinate_systems_in_space-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 Coordinate systems in space subsection</span> </button> <ul id="toc-Coordinate_systems_in_space-sublist" class="vector-toc-list"> <li id="toc-Coordinate_systems_in_the_plane" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Coordinate_systems_in_the_plane"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Coordinate systems in the plane</span> </div> </a> <ul id="toc-Coordinate_systems_in_the_plane-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Heights" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Heights"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Heights</span> </div> </a> <ul id="toc-Heights-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geodetic_datums" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Geodetic_datums"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Geodetic datums</span> </div> </a> <ul id="toc-Geodetic_datums-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Positioning" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Positioning"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Positioning</span> </div> </a> <ul id="toc-Positioning-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geodetic_problems" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Geodetic_problems"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Geodetic problems</span> </div> </a> <ul id="toc-Geodetic_problems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Observational_concepts" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Observational_concepts"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Observational concepts</span> </div> </a> <ul id="toc-Observational_concepts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Measurements" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Measurements"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Measurements</span> </div> </a> <ul id="toc-Measurements-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Units_and_measures_on_the_ellipsoid" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Units_and_measures_on_the_ellipsoid"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Units and measures on the ellipsoid</span> </div> </a> <ul id="toc-Units_and_measures_on_the_ellipsoid-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Temporal_changes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Temporal_changes"> <div class="vector-toc-text"> <span class="vector-toc-numb">12</span> <span>Temporal changes</span> </div> </a> <ul id="toc-Temporal_changes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notable_geodesists" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notable_geodesists"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>Notable geodesists</span> </div> </a> <ul id="toc-Notable_geodesists-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">14</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">15</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">16</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">17</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" title="Table of Contents" > <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">Geodesy</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 86 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-86" 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">86 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Aardmeetkunde" title="Aardmeetkunde – Afrikaans" lang="af" hreflang="af" data-title="Aardmeetkunde" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B3%D8%AD_%D8%A7%D9%84%D8%A3%D8%B1%D8%B6" title="مسح الأرض – Arabic" lang="ar" hreflang="ar" data-title="مسح الأرض" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Xeodesia" title="Xeodesia – Asturian" lang="ast" hreflang="ast" data-title="Xeodesia" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Geodeziya" title="Geodeziya – Azerbaijani" lang="az" hreflang="az" data-title="Geodeziya" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AD%E0%A7%82%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="ভূগণিত – Bangla" lang="bn" hreflang="bn" data-title="ভূগণিত" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D1%8F" title="Геодезия – Bashkir" lang="ba" hreflang="ba" data-title="Геодезия" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%93%D0%B5%D0%B0%D0%B4%D1%8D%D0%B7%D1%96%D1%8F" title="Геадэзія – Belarusian" lang="be" hreflang="be" data-title="Геадэзія" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%93%D0%B5%D0%B0%D0%B4%D1%8D%D0%B7%D1%96%D1%8F" title="Геадэзія – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Геадэзія" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D1%8F" title="Геодезия – Bulgarian" lang="bg" hreflang="bg" data-title="Геодезия" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Geodezija" title="Geodezija – Bosnian" lang="bs" hreflang="bs" data-title="Geodezija" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Geod%C3%A8sia" title="Geodèsia – Catalan" lang="ca" hreflang="ca" data-title="Geodèsia" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8" title="Геодези – Chuvash" lang="cv" hreflang="cv" data-title="Геодези" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Geod%C3%A9zie" title="Geodézie – Czech" lang="cs" hreflang="cs" data-title="Geodézie" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Jekanyika" title="Jekanyika – Shona" lang="sn" hreflang="sn" data-title="Jekanyika" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Geodedd" title="Geodedd – Welsh" lang="cy" hreflang="cy" data-title="Geodedd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Geod%C3%A6si" title="Geodæsi – Danish" lang="da" hreflang="da" data-title="Geodæsi" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Geod%C3%A4sie" title="Geodäsie – German" lang="de" hreflang="de" data-title="Geodäsie" 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/Geodeesia" title="Geodeesia – Estonian" lang="et" hreflang="et" data-title="Geodeesia" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%89%CE%B4%CE%B1%CE%B9%CF%83%CE%AF%CE%B1" title="Γεωδαισία – Greek" lang="el" hreflang="el" data-title="Γεωδαισία" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Geodesia" title="Geodesia – Spanish" lang="es" hreflang="es" data-title="Geodesia" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Geodezio" title="Geodezio – Esperanto" lang="eo" hreflang="eo" data-title="Geodezio" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Geodesia" title="Geodesia – Basque" lang="eu" hreflang="eu" data-title="Geodesia" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B2%D9%85%DB%8C%D9%86%E2%80%8C%D8%B3%D9%86%D8%AC%DB%8C" title="زمین‌سنجی – Persian" lang="fa" hreflang="fa" data-title="زمین‌سنجی" 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/G%C3%A9od%C3%A9sie" title="Géodésie – French" lang="fr" hreflang="fr" data-title="Géodésie" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Geodasa%C3%ADocht" title="Geodasaíocht – Irish" lang="ga" hreflang="ga" data-title="Geodasaíocht" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Xeodesia" title="Xeodesia – Galician" lang="gl" hreflang="gl" data-title="Xeodesia" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%B8%A1%EC%A7%80%ED%95%99" title="측지학 – Korean" lang="ko" hreflang="ko" data-title="측지학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B3%D5%A5%D5%B8%D5%A4%D5%A5%D5%A6%D5%AB%D5%A1" title="Գեոդեզիա – Armenian" lang="hy" hreflang="hy" data-title="Գեոդեզիա" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AD%E0%A5%82%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="भूगणित – Hindi" lang="hi" hreflang="hi" data-title="भूगणित" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Geodezija" title="Geodezija – Croatian" lang="hr" hreflang="hr" data-title="Geodezija" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Geodezio" title="Geodezio – Ido" lang="io" hreflang="io" data-title="Geodezio" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Geodesi" title="Geodesi – Indonesian" lang="id" hreflang="id" data-title="Geodesi" 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/Geodesia" title="Geodesia – Italian" lang="it" hreflang="it" data-title="Geodesia" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%90%D7%95%D7%93%D7%96%D7%99%D7%94" title="גאודזיה – Hebrew" lang="he" hreflang="he" data-title="גאודזיה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Geodesi" title="Geodesi – Javanese" lang="jv" hreflang="jv" data-title="Geodesi" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%92%E1%83%94%E1%83%9D%E1%83%93%E1%83%94%E1%83%96%E1%83%98%E1%83%90" title="გეოდეზია – Georgian" lang="ka" hreflang="ka" data-title="გეოდეზია" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D1%8F" title="Геодезия – Kazakh" lang="kk" hreflang="kk" data-title="Геодезия" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Upimaji_dunia" title="Upimaji dunia – Swahili" lang="sw" hreflang="sw" data-title="Upimaji dunia" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D1%8F" title="Геодезия – Kyrgyz" lang="ky" hreflang="ky" data-title="Геодезия" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/%C4%A2eod%C4%93zija" title="Ģeodēzija – Latvian" lang="lv" hreflang="lv" data-title="Ģeodēzija" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Geodesie" title="Geodesie – Luxembourgish" lang="lb" hreflang="lb" data-title="Geodesie" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Geodezija" title="Geodezija – Lithuanian" lang="lt" hreflang="lt" data-title="Geodezija" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Geod%C3%A9zia" title="Geodézia – Hungarian" lang="hu" hreflang="hu" data-title="Geodézia" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D1%98%D0%B0" title="Геодезија – Macedonian" lang="mk" hreflang="mk" data-title="Геодезија" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AD%E0%A5%82%E0%A4%AA%E0%A5%83%E0%A4%B7%E0%A5%8D%E0%A4%A0%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A5%80%E0%A4%B6%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0" title="भूपृष्ठमितीशास्त्र – Marathi" lang="mr" hreflang="mr" data-title="भूपृष्ठमितीशास्त्र" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Geodesi" title="Geodesi – Malay" lang="ms" hreflang="ms" data-title="Geodesi" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Geodesi" title="Geodesi – Minangkabau" lang="min" hreflang="min" data-title="Geodesi" data-language-autonym="Minangkabau" data-language-local-name="Minangkabau" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/Du%C3%A2i-d%C3%AA_Ch%C3%A1ik-li%C3%B2ng-h%C5%8Fk" title="Duâi-dê Cháik-liòng-hŏk – Mindong" lang="cdo" hreflang="cdo" data-title="Duâi-dê Cháik-liòng-hŏk" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8" title="Геодези – Mongolian" lang="mn" hreflang="mn" data-title="Геодези" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Geodesie" title="Geodesie – Dutch" lang="nl" hreflang="nl" data-title="Geodesie" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%B8%AC%E5%9C%B0%E5%AD%A6" title="測地学 – Japanese" lang="ja" hreflang="ja" data-title="測地学" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Geodesi" title="Geodesi – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Geodesi" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Geodesi" title="Geodesi – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Geodesi" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D0%B9" title="Геодезий – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Геодезий" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Geodeziya" title="Geodeziya – Uzbek" lang="uz" hreflang="uz" data-title="Geodeziya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%DA%81%D9%85%DA%A9%D8%B3%D9%86%D8%AC%D9%8A" title="ځمکسنجي – Pashto" lang="ps" hreflang="ps" data-title="ځمکسنجي" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Geodezja" title="Geodezja – Polish" lang="pl" hreflang="pl" data-title="Geodezja" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Geod%C3%A9sia" title="Geodésia – Portuguese" lang="pt" hreflang="pt" data-title="Geodésia" 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/Geodezie" title="Geodezie – Romanian" lang="ro" hreflang="ro" data-title="Geodezie" 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%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D1%8F" title="Геодезия – Russian" lang="ru" hreflang="ru" data-title="Геодезия" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sc mw-list-item"><a href="https://sc.wikipedia.org/wiki/Geodesia" title="Geodesia – Sardinian" lang="sc" hreflang="sc" data-title="Geodesia" data-language-autonym="Sardu" data-language-local-name="Sardinian" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Gjeodezia" title="Gjeodezia – Albanian" lang="sq" hreflang="sq" data-title="Gjeodezia" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Geodesy" title="Geodesy – Simple English" lang="en-simple" hreflang="en-simple" data-title="Geodesy" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%AC%D9%8A%D9%88%DA%8A%D9%8A%D8%B3%D9%8A" title="جيوڊيسي – Sindhi" lang="sd" hreflang="sd" data-title="جيوڊيسي" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Geod%C3%A9zia" title="Geodézia – Slovak" lang="sk" hreflang="sk" data-title="Geodézia" 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/Geodezija" title="Geodezija – Slovenian" lang="sl" hreflang="sl" data-title="Geodezija" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AC%DB%8C%DB%86%D8%AF%DB%8C%D8%B2%DB%8C%D8%A7" title="جیۆدیزیا – Central Kurdish" lang="ckb" hreflang="ckb" data-title="جیۆدیزیا" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D1%98%D0%B0" title="Геодезија – Serbian" lang="sr" hreflang="sr" data-title="Геодезија" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Geodezija" title="Geodezija – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Geodezija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Geodesia" title="Geodesia – Finnish" lang="fi" hreflang="fi" data-title="Geodesia" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Geodesi" title="Geodesi – Swedish" lang="sv" hreflang="sv" data-title="Geodesi" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Heodesiya" title="Heodesiya – Tagalog" lang="tl" hreflang="tl" data-title="Heodesiya" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D1%8F" title="Геодезия – Tatar" lang="tt" hreflang="tt" data-title="Геодезия" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A0%E0%B8%B9%E0%B8%A1%E0%B8%B4%E0%B8%A1%E0%B8%B2%E0%B8%95%E0%B8%A3%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="ภูมิมาตรศาสตร์ – Thai" lang="th" hreflang="th" data-title="ภูมิมาตรศาสตร์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%97%D0%B0%D0%BC%D0%B8%D0%BD%D1%81%D0%B0%D0%BD%D2%B7%D3%A3" title="Заминсанҷӣ – Tajik" lang="tg" hreflang="tg" data-title="Заминсанҷӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Jeodezi" title="Jeodezi – Turkish" lang="tr" hreflang="tr" data-title="Jeodezi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tyv mw-list-item"><a href="https://tyv.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D0%B8%D1%8F" title="Геодезия – Tuvinian" lang="tyv" hreflang="tyv" data-title="Геодезия" data-language-autonym="Тыва дыл" data-language-local-name="Tuvinian" class="interlanguage-link-target"><span>Тыва дыл</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%B4%D0%B5%D0%B7%D1%96%D1%8F" title="Геодезія – Ukrainian" lang="uk" hreflang="uk" data-title="Геодезія" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%B3%D8%A7%D8%AD%DB%8C%D8%A7%D8%AA" title="مساحیات – Urdu" lang="ur" hreflang="ur" data-title="مساحیات" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Zeodezia" title="Zeodezia – Venetian" lang="vec" hreflang="vec" data-title="Zeodezia" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Tr%E1%BA%AFc_%C4%91%E1%BB%8Ba" title="Trắc địa – Vietnamese" lang="vi" hreflang="vi" data-title="Trắc địa" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Heodesiya" title="Heodesiya – Waray" lang="war" hreflang="war" data-title="Heodesiya" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%A4%A7%E5%9C%B0%E6%B5%8B%E9%87%8F%E5%AD%A6" title="大地测量学 – Wu" lang="wuu" hreflang="wuu" data-title="大地测量学" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%B8%AC%E5%9C%B0%E5%AD%B8" title="測地學 – Cantonese" lang="yue" hreflang="yue" data-title="測地學" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Geuodez%C4%97j%C4%97" title="Geuodezėjė – Samogitian" lang="sgs" hreflang="sgs" data-title="Geuodezėjė" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A4%A7%E5%9C%B0%E6%B5%8B%E9%87%8F%E5%AD%A6" title="大地测量学 – Chinese" lang="zh" hreflang="zh" data-title="大地测量学" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet 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Statements consisting only of original research should be removed.</span> <span class="date-container"><i>(<span class="date">October 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Geodetic_survey_instruments_07.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Geodetic_survey_instruments_07.jpg/220px-Geodetic_survey_instruments_07.jpg" decoding="async" width="220" height="165" class="mw-file-element" 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.sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><th class="sidebar-title" style="padding-bottom:0.4em;"><a class="mw-selflink selflink">Geodesy</a></th></tr><tr><td class="sidebar-image"><span typeof="mw:File"><a href="/wiki/File:Globe_Atlantic.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Globe_Atlantic.svg/120px-Globe_Atlantic.svg.png" decoding="async" width="120" height="121" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Globe_Atlantic.svg/180px-Globe_Atlantic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Globe_Atlantic.svg/240px-Globe_Atlantic.svg.png 2x" data-file-width="717" data-file-height="721" /></a></span></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)">Fundamentals</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a class="mw-selflink selflink">Geodesy</a></li> <li><a href="/wiki/Geodynamics" title="Geodynamics">Geodynamics</a></li> <li><a href="/wiki/Geomatics" title="Geomatics">Geomatics</a></li> <li><a href="/wiki/History_of_geodesy" title="History of geodesy">History</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)">Concepts</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Geographical_distance" title="Geographical distance">Geographical distance</a></li> <li><a href="/wiki/Geoid" title="Geoid">Geoid</a></li> <li><a href="/wiki/Figure_of_the_Earth" title="Figure of the Earth">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><b>Geodesy</b> or <b>geodetics</b><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> is the <a href="/wiki/Science" title="Science">science</a> of measuring and representing the <a href="/wiki/Figure_of_the_Earth" title="Figure of the Earth">geometry</a>, <a href="/wiki/Gravity_of_Earth" title="Gravity of Earth">gravity</a>, and <a href="/wiki/Earth%27s_rotation" title="Earth's rotation">spatial orientation</a> of the <a href="/wiki/Earth" title="Earth">Earth</a> in <a href="/wiki/Relative_change" title="Relative change">temporally varying</a> <a href="/wiki/Three-dimensional_space" title="Three-dimensional space">3D</a>. It is called <a href="/wiki/Planetary_geodesy" class="mw-redirect" title="Planetary geodesy">planetary geodesy</a> when studying other <a href="/wiki/Astronomical_body" class="mw-redirect" title="Astronomical body">astronomical bodies</a>, such as <a href="/wiki/Planet" title="Planet">planets</a> or <a href="/wiki/Natural_satellite" title="Natural satellite">circumplanetary systems</a>.<sup id="cite_ref-VK_2-0" class="reference"><a href="#cite_note-VK-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Geodesy is an <a href="/wiki/Earth_science" title="Earth science">earth science</a> and many consider the study of Earth's shape and gravity to be central to that science.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><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> It is also a discipline of <a href="/wiki/Applied_mathematics" title="Applied mathematics">applied mathematics</a>.<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><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Geodynamics" title="Geodynamics">Geodynamical</a> phenomena, including <a href="/wiki/Crust_(geology)" title="Crust (geology)">crustal</a> motion, <a href="/wiki/Tide" title="Tide">tides</a>, and <a href="/wiki/Polar_motion" title="Polar motion">polar motion</a>, can be studied by designing global and national <a href="/wiki/Geodetic_control_network" title="Geodetic control network">control networks</a>, applying <a href="/wiki/Space_geodesy" title="Space geodesy">space geodesy</a> and terrestrial geodetic techniques, and relying on <a href="/wiki/Geodetic_datum" title="Geodetic datum">datums</a> and <a href="/wiki/Coordinate_system" title="Coordinate system">coordinate systems</a>. Geodetic job titles include <b>geodesist</b> and <b>geodetic surveyor</b>.<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> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=1" title="Edit section: History"><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/History_of_geodesy" title="History of geodesy">History of geodesy</a></div> <p>Geodesy began in pre-scientific <a href="/wiki/Classical_antiquity" title="Classical antiquity">antiquity</a>, so the very word geodesy comes from the <a href="/wiki/Ancient_Greek" title="Ancient Greek">Ancient Greek</a> word <span title="Ancient Greek (to 1453)-language text"><span lang="grc">γεωδαισία</span></span> or <i>geodaisia</i> (literally, "division of Earth").<sup id="cite_ref-routledge_8-0" class="reference"><a href="#cite_note-routledge-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Early ideas about the figure of the Earth held the Earth to be <a href="/wiki/Flat_Earth" title="Flat Earth">flat</a> and the heavens a <a href="/wiki/Firmament" title="Firmament">physical dome</a> spanning over it.<sup id="cite_ref-Webb_9-0" class="reference"><a href="#cite_note-Webb-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Two early arguments for a spherical Earth were that lunar eclipses appear to an observer as circular shadows and that <a href="/wiki/Polaris" title="Polaris">Polaris</a> appears lower and lower in the sky to a traveler headed South.<sup id="cite_ref-Posa_10-0" class="reference"><a href="#cite_note-Posa-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=2" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/English_language" title="English language">English</a>, geodesy refers to the <a href="/wiki/Science" title="Science">science</a> of measuring and representing <a href="/wiki/Geospatial_information" class="mw-redirect" title="Geospatial information">geospatial information</a>, while <a href="/wiki/Geomatics" title="Geomatics">geomatics</a> encompasses practical applications of geodesy on local and regional scales, including <a href="/wiki/Surveying" title="Surveying">surveying</a>. </p><p>In <a href="/wiki/German_language" title="German language">German</a>, geodesy can refer to either <i>higher geodesy</i> (<span title="German-language text"><i lang="de">höhere Geodäsie</i></span> or <span title="German-language text"><i lang="de">Erdmessung</i></span>, literally "geomensuration") — concerned with measuring Earth on the global scale, or <i>engineering geodesy</i> (<span title="German-language text"><i lang="de">Ingenieurgeodäsie</i></span>) that includes surveying — measuring parts or regions of Earth. </p><p>For the longest time, geodesy was the science of measuring and understanding Earth's geometric shape, orientation in space, and gravitational field; however, geodetic science and operations are applied to other <a href="/wiki/Astronomical_object" title="Astronomical object">astronomical bodies</a> in our <a href="/wiki/Solar_System" title="Solar System">Solar System</a> also.<sup id="cite_ref-VK_2-1" class="reference"><a href="#cite_note-VK-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>To a large extent, Earth's shape is the result of <a href="/wiki/Earth%27s_rotation" title="Earth's rotation">rotation</a>, which causes its <a href="/wiki/Equatorial_bulge" title="Equatorial bulge">equatorial bulge</a>, and the competition of geological processes such as the <a href="/wiki/Continental_collision" title="Continental collision">collision of plates</a>, as well as of <a href="/wiki/Volcano" title="Volcano">volcanism</a>, resisted by Earth's gravitational field. This applies to the solid surface, the liquid surface (<a href="/wiki/Dynamic_sea_surface_topography" class="mw-redirect" title="Dynamic sea surface topography">dynamic sea surface topography</a>), and <a href="/wiki/Earth%27s_atmosphere" class="mw-redirect" title="Earth's atmosphere">Earth's atmosphere</a>. For this reason, the study of Earth's gravitational field is called <a href="/wiki/Physical_geodesy" title="Physical geodesy">physical geodesy</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Geoid_and_reference_ellipsoid">Geoid and reference ellipsoid</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=3" title="Edit section: Geoid and reference ellipsoid"><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 articles: <a href="/wiki/Geoid" title="Geoid">Geoid</a> and <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">Reference ellipsoid</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444" /><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Geodesy" title="Special:EditPage/Geodesy">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">February 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Geoid_undulation_10k_scale.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Geoid_undulation_10k_scale.jpg/220px-Geoid_undulation_10k_scale.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Geoid_undulation_10k_scale.jpg/330px-Geoid_undulation_10k_scale.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Geoid_undulation_10k_scale.jpg/440px-Geoid_undulation_10k_scale.jpg 2x" data-file-width="1200" data-file-height="1200" /></a><figcaption><a href="/wiki/Geoid" title="Geoid">Geoid</a>, an approximation for the shape of the <a href="/wiki/Earth" title="Earth">Earth</a>; shown here with <a href="/wiki/Vertical_exaggeration" title="Vertical exaggeration">vertical exaggeration</a> (10000 vertical scaling factor).</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Surface_of_latitude_ellipsoid_cone.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Surface_of_latitude_ellipsoid_cone.gif/220px-Surface_of_latitude_ellipsoid_cone.gif" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Surface_of_latitude_ellipsoid_cone.gif/330px-Surface_of_latitude_ellipsoid_cone.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/26/Surface_of_latitude_ellipsoid_cone.gif/440px-Surface_of_latitude_ellipsoid_cone.gif 2x" data-file-width="512" data-file-height="512" /></a><figcaption><a href="/wiki/Ellipsoid" title="Ellipsoid">Ellipsoid</a> - a mathematical representation of the <a href="/wiki/Earth" title="Earth">Earth</a>. When mapping in geodetic coordinates, a latitude circle forms a truncated cone.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:WGS84_mean_Earth_radius.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/WGS84_mean_Earth_radius.svg/220px-WGS84_mean_Earth_radius.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/WGS84_mean_Earth_radius.svg/330px-WGS84_mean_Earth_radius.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/WGS84_mean_Earth_radius.svg/440px-WGS84_mean_Earth_radius.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>Equatorial (<span class="texhtml mvar" style="font-style:italic;">a</span>), polar (<span class="texhtml mvar" style="font-style:italic;">b</span>) and mean Earth radii as defined in the 1984 <a href="/wiki/World_Geodetic_System" title="World Geodetic System">World Geodetic System</a></figcaption></figure> <p>The <a href="/wiki/Geoid" title="Geoid">geoid</a> essentially is the figure of Earth abstracted from its <a href="/wiki/Topography" title="Topography">topographical</a> features. It is an idealized equilibrium surface of <a href="/wiki/Seawater" title="Seawater">seawater</a>, the <a href="/wiki/Mean_sea_level" class="mw-redirect" title="Mean sea level">mean sea level</a> surface in the absence of <a href="/wiki/Ocean_current" title="Ocean current">currents</a> and <a href="/wiki/Atmospheric_pressure" title="Atmospheric pressure">air pressure</a> variations, and continued under the continental masses. Unlike a <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">reference ellipsoid</a>, the geoid is irregular and too complicated to serve as the computational <a href="/wiki/Surface_(mathematics)" title="Surface (mathematics)">surface</a> for solving geometrical problems like point positioning. The geometrical separation between the geoid and a reference ellipsoid is called <i>geoidal <a href="https://en.wiktionary.org/wiki/undulate" class="extiw" title="wiktionary:undulate">undulation</a></i>, and it varies globally between ±110 m based on the GRS 80 ellipsoid. </p><p>A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) <i>a</i> and flattening <i>f</i>. The quantity <i>f</i> = <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num"><i>a</i> − <i>b</i></span><span class="sr-only">/</span><span class="den"><i>a</i></span></span>⁠</span>, where <i>b</i> is the semi-minor axis (polar radius), is purely geometrical. The mechanical <a href="/wiki/Flattening" title="Flattening">ellipticity</a> of Earth (dynamical flattening, symbol <i>J</i><sub>2</sub>) can be determined to high precision by observation of satellite <a href="/wiki/Orbital_perturbation_analysis" class="mw-redirect" title="Orbital perturbation analysis">orbit perturbations</a>. Its relationship with geometrical flattening is indirect and depends on the internal density distribution or, in simplest terms, the degree of central concentration of mass. </p><p>The 1980 Geodetic Reference System (<a href="/wiki/GRS80" class="mw-redirect" title="GRS80">GRS 80</a>), adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics (<a href="/wiki/IUGG" class="mw-redirect" title="IUGG">IUGG</a>), posited a 6,378,137 m semi-major axis and a 1:298.257 flattening. GRS 80 essentially constitutes the basis for geodetic positioning by the <a href="/wiki/Global_Positioning_System" title="Global Positioning System">Global Positioning System</a> (GPS) and is thus also in widespread use outside the geodetic community. Numerous systems used for mapping and charting are becoming obsolete as countries increasingly move to global, geocentric reference systems utilizing the GRS 80 reference ellipsoid. </p><p>The geoid is a "realizable" surface, meaning it can be consistently located on Earth by suitable simple measurements from physical objects like a <a href="/wiki/Tide_gauge" title="Tide gauge">tide gauge</a>. The geoid can, therefore, be considered a physical ("real") surface. The reference ellipsoid, however, has many possible instantiations and is not readily realizable, so it is an abstract surface. The third primary surface of geodetic interest — the <a href="/wiki/Terrain" title="Terrain">topographic surface</a> of Earth — is also realizable. </p> <div class="mw-heading mw-heading2"><h2 id="Coordinate_systems_in_space">Coordinate systems in space</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=4" title="Edit section: Coordinate systems in space"><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/Geodetic_system" class="mw-redirect" title="Geodetic system">Geodetic system</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/World_Geodetic_System" title="World Geodetic System">World Geodetic System</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444" /><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Geodesy" title="Special:EditPage/Geodesy">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">February 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Datum_Shift_Between_NAD27_and_NAD83.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Datum_Shift_Between_NAD27_and_NAD83.png/250px-Datum_Shift_Between_NAD27_and_NAD83.png" decoding="async" width="220" height="115" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/41/Datum_Shift_Between_NAD27_and_NAD83.png/330px-Datum_Shift_Between_NAD27_and_NAD83.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/41/Datum_Shift_Between_NAD27_and_NAD83.png/500px-Datum_Shift_Between_NAD27_and_NAD83.png 2x" data-file-width="1115" data-file-height="581" /></a><figcaption>Datum shift between <a href="/wiki/NAD27" class="mw-redirect" title="NAD27">NAD27</a> and <a href="/wiki/NAD83" class="mw-redirect" title="NAD83">NAD83</a>, in metres</figcaption></figure> <p>The locations of points in 3D space most conveniently are described by three <a href="/wiki/Cartesian_coordinate_system" title="Cartesian coordinate system">cartesian</a> or rectangular coordinates, <i>X</i>, <i>Y</i>, and <i>Z</i>. Since the advent of satellite positioning, such coordinate systems are typically <a href="/wiki/Geocentric" class="mw-redirect" title="Geocentric">geocentric</a>, with the Z-axis aligned to Earth's (conventional or instantaneous) rotation axis. </p><p>Before the era of <a href="/wiki/Satellite_geodesy" title="Satellite geodesy">satellite geodesy</a>, the coordinate systems associated with a geodetic <a href="/wiki/Datum_(geodesy)" class="mw-redirect" title="Datum (geodesy)">datum</a> attempted to be <a href="/wiki/Geocentric" class="mw-redirect" title="Geocentric">geocentric</a>, but with the origin differing from the geocenter by hundreds of meters due to regional deviations in the direction of the <a href="/wiki/Plumbline" class="mw-redirect" title="Plumbline">plumbline</a> (vertical). These regional geodetic datums, such as <a href="/wiki/ED50" title="ED50">ED 50</a> (European Datum 1950) or <a href="/wiki/North_American_Datum#North_American_Datum_of_1927" title="North American Datum">NAD 27</a> (North American Datum 1927), have ellipsoids associated with them that are regional "best fits" to the <a href="/wiki/Geoid" title="Geoid">geoids</a> within their areas of validity, minimizing the deflections of the vertical over these areas. </p><p>It is only because <a href="/wiki/Global_Positioning_System" title="Global Positioning System">GPS</a> satellites orbit about the geocenter that this point becomes naturally the origin of a coordinate system defined by satellite geodetic means, as the satellite positions in space themselves get computed within such a system. </p><p>Geocentric coordinate systems used in geodesy can be divided naturally into two classes: </p> <ol><li>The <a href="/wiki/Inertial" class="mw-redirect" title="Inertial">inertial</a> reference systems, where the coordinate axes retain their orientation relative to the <a href="/wiki/Fixed_star" class="mw-redirect" title="Fixed star">fixed stars</a> or, equivalently, to the rotation axes of ideal <a href="/wiki/Gyroscopes" class="mw-redirect" title="Gyroscopes">gyroscopes</a>. The <i>X</i>-axis points to the <a href="/wiki/Equinox_(celestial_coordinates)" title="Equinox (celestial coordinates)">vernal equinox</a>.</li> <li>The co-rotating reference systems (also <a href="/wiki/ECEF" class="mw-redirect" title="ECEF">ECEF</a> or "Earth Centred, Earth Fixed"), in which the axes are "attached" to the solid body of Earth. The <i>X</i>-axis lies within the <a href="/wiki/Greenwich_meridian" class="mw-redirect" title="Greenwich meridian">Greenwich</a> observatory's <a href="/wiki/Meridian_(geography)" title="Meridian (geography)">meridian</a> plane.</li></ol> <p>The coordinate transformation between these two systems to good approximation is described by (apparent) <a href="/wiki/Sidereal_time" title="Sidereal time">sidereal time</a>, which accounts for variations in Earth's axial rotation (<a href="/wiki/Day" title="Day">length-of-day</a> variations). A more accurate description also accounts for <a href="/wiki/Polar_motion" title="Polar motion">polar motion</a> as a phenomenon closely monitored by geodesists. </p> <div class="mw-heading mw-heading3"><h3 id="Coordinate_systems_in_the_plane">Coordinate systems in the plane</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=5" title="Edit section: Coordinate systems in the plane"><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/Horizontal_position" class="mw-redirect" title="Horizontal position">Horizontal position</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Elliptical_coordinates_grid.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Elliptical_coordinates_grid.svg/225px-Elliptical_coordinates_grid.svg.png" decoding="async" width="225" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Elliptical_coordinates_grid.svg/338px-Elliptical_coordinates_grid.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Elliptical_coordinates_grid.svg/450px-Elliptical_coordinates_grid.svg.png 2x" data-file-width="800" data-file-height="600" /></a><figcaption>2D grid for elliptical coordinates</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Litography_archive_of_the_Bayerisches_Vermessungsamt.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Litography_archive_of_the_Bayerisches_Vermessungsamt.jpg/225px-Litography_archive_of_the_Bayerisches_Vermessungsamt.jpg" decoding="async" width="225" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Litography_archive_of_the_Bayerisches_Vermessungsamt.jpg/338px-Litography_archive_of_the_Bayerisches_Vermessungsamt.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/Litography_archive_of_the_Bayerisches_Vermessungsamt.jpg/450px-Litography_archive_of_the_Bayerisches_Vermessungsamt.jpg 2x" data-file-width="1600" data-file-height="1200" /></a><figcaption>A <a href="/wiki/Munich" title="Munich">Munich</a> archive with <a href="/wiki/Lithography" title="Lithography">lithography</a> plates of maps of <a href="/wiki/Bavaria" title="Bavaria">Bavaria</a></figcaption></figure> <p>In geodetic applications like <a href="/wiki/Surveying" title="Surveying">surveying</a> and <a href="/wiki/Map" title="Map">mapping</a>, two general types of coordinate systems in the plane are in use: </p> <ol><li><b>Plano-polar</b>, with points in the plane defined by their distance, <i>s</i>, from a specified point along a ray having a direction <i>α</i> from a baseline or axis.</li> <li><b>Rectangular</b>, with points defined by distances from two mutually perpendicular axes, <i>x</i> and <i>y</i>. Contrary to the mathematical convention, in geodetic practice, the <i>x</i>-axis points <a href="/wiki/Northing" class="mw-redirect" title="Northing">North</a> and the <i>y</i>-axis <a href="/wiki/Easting" class="mw-redirect" title="Easting">East</a>.</li></ol> <p>One can intuitively use rectangular coordinates in the plane for one's current location, in which case the <i>x</i>-axis will point to the local north. More formally, such coordinates can be obtained from 3D coordinates using the artifice of a <a href="/wiki/Map_projection" title="Map projection">map projection</a>. It is impossible to map the curved surface of Earth onto a flat map surface without deformation. The compromise most often chosen — called a <a href="/wiki/Conformal_projection" class="mw-redirect" title="Conformal projection">conformal projection</a> — preserves angles and length ratios so that small circles get mapped as small circles and small squares as squares. </p><p>An example of such a projection is UTM (<a href="/wiki/Universal_Transverse_Mercator" class="mw-redirect" title="Universal Transverse Mercator">Universal Transverse Mercator</a>). Within the map plane, we have rectangular coordinates <i>x</i> and <i>y</i>. In this case, the north direction used for reference is the <i>map</i> north, not the <i>local</i> north. The difference between the two is called <a href="/wiki/Transverse_Mercator_projection#Convergence" title="Transverse Mercator projection">meridian convergence</a>. </p><p>It is easy enough to "translate" between polar and rectangular coordinates in the plane: let, as above, direction and distance be <i>α</i> and <i>s</i> respectively; then we have: </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 {\begin{aligned}x&=s\cos \alpha \\y&=s\sin \alpha \end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>x</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>s</mi> <mi>cos</mi> <mo>⁡</mo> <mi>α</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>s</mi> <mi>sin</mi> <mo>⁡</mo> <mi>α</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}x&=s\cos \alpha \\y&=s\sin \alpha \end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/452b70962d2af7e2cce527f5ba5c27d8194c57d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.643ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}x&=s\cos \alpha \\y&=s\sin \alpha \end{aligned}}}" /></span></dd></dl> <p>The reverse transformation is given by: </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 {\begin{aligned}s&={\sqrt {x^{2}+y^{2}}}\\\alpha &=\arctan {\frac {y}{x}}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>s</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>α</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>arctan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>y</mi> <mi>x</mi> </mfrac> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}s&={\sqrt {x^{2}+y^{2}}}\\\alpha &=\arctan {\frac {y}{x}}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4f8e80cfcaef1ce1dfc52d2363d2de16a0a34a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:15.1ex; height:9.843ex;" alt="{\displaystyle {\begin{aligned}s&={\sqrt {x^{2}+y^{2}}}\\\alpha &=\arctan {\frac {y}{x}}.\end{aligned}}}" /></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Heights">Heights</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=6" title="Edit section: Heights"><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">Further information: <a href="/wiki/Vertical_position" title="Vertical position">Vertical position</a> and <a href="/wiki/Vertical_datum" title="Vertical datum">Vertical datum</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:An-illustration-of-height-measurement-using-satellite-altimetry.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/An-illustration-of-height-measurement-using-satellite-altimetry.jpg/330px-An-illustration-of-height-measurement-using-satellite-altimetry.jpg" decoding="async" width="285" height="322" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/An-illustration-of-height-measurement-using-satellite-altimetry.jpg/428px-An-illustration-of-height-measurement-using-satellite-altimetry.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/c/cb/An-illustration-of-height-measurement-using-satellite-altimetry.jpg 2x" data-file-width="478" data-file-height="540" /></a><figcaption>Height measurement using satellite altimetry</figcaption></figure> <p>In geodesy, point or terrain <i><a href="/wiki/Height" title="Height">heights</a></i> are "<a href="/wiki/Above_sea_level" class="mw-redirect" title="Above sea level">above sea level</a>" as an irregular, physically defined surface. Height systems in use are: </p> <ol><li><a href="/wiki/Orthometric_height" title="Orthometric height">Orthometric heights</a></li> <li><a href="/wiki/Dynamic_height" title="Dynamic height">Dynamic heights</a></li> <li><a href="/wiki/Geopotential_height" title="Geopotential height">Geopotential heights</a></li> <li><a href="/wiki/Normal_height" title="Normal height">Normal heights</a></li></ol> <p>Each system has its advantages and disadvantages. Both orthometric and normal heights are expressed in <a href="/wiki/Metre" title="Metre">metres</a> above sea level, whereas geopotential numbers are measures of potential energy (unit: m<sup>2</sup> s<sup>−2</sup>) and not metric. The reference surface is the <a href="/wiki/Geoid" title="Geoid">geoid</a>, an <a href="/wiki/Equigeopotential" class="mw-redirect" title="Equigeopotential">equigeopotential</a> surface approximating the mean sea level as described above. For normal heights, the reference surface is the so-called <i><a href="/wiki/Quasi-geoid" class="mw-redirect" title="Quasi-geoid">quasi-geoid</a></i>, which has a few-metre separation from the geoid due to the density assumption in its continuation under the continental masses.<sup id="cite_ref-ForoughiTenzer2017_11-0" class="reference"><a href="#cite_note-ForoughiTenzer2017-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>One can relate these heights through the <a href="/wiki/Geoid_undulation" class="mw-redirect" title="Geoid undulation">geoid undulation</a> concept to <i><a href="/wiki/Ellipsoidal_height" class="mw-redirect" title="Ellipsoidal height">ellipsoidal heights</a></i> (also known as <i>geodetic heights</i>), representing the height of a point above the <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">reference ellipsoid</a>. <a href="/wiki/Satellite_positioning_receiver" class="mw-redirect" title="Satellite positioning receiver">Satellite positioning receivers</a> typically provide ellipsoidal heights unless fitted with special conversion software based on a model of the geoid. </p> <div class="mw-heading mw-heading2"><h2 id="Geodetic_datums">Geodetic datums</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=7" title="Edit section: Geodetic datums"><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/Geodetic_datum" title="Geodetic datum">Geodetic datum</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/Datum_transformation" class="mw-redirect" title="Datum transformation">Datum transformation</a></div> <p>Because coordinates and heights of geodetic points always get obtained within a system that itself was constructed based on real-world observations, geodesists introduced the concept of a "geodetic datum" (plural <i>datums</i>): a physical (real-world) realization of a coordinate system used for describing point locations. This realization follows from <i>choosing</i> (therefore conventional) coordinate values for one or more datum points. In the case of height data, it suffices to choose <i>one</i> datum point — the reference benchmark, typically a tide gauge at the shore. Thus we have vertical datums, such as the NAVD 88 (North American Vertical Datum 1988), NAP (<a href="/wiki/Normaal_Amsterdams_Peil" class="mw-redirect" title="Normaal Amsterdams Peil">Normaal Amsterdams Peil</a>), the Kronstadt datum, the Trieste datum, and numerous others. </p><p>In both mathematics and geodesy, a coordinate system is a "coordinate system" per <a href="/wiki/International_Organization_for_Standardization" title="International Organization for Standardization">ISO</a> terminology, whereas the <a href="/wiki/International_Earth_Rotation_and_Reference_Systems_Service" title="International Earth Rotation and Reference Systems Service">International Earth Rotation and Reference Systems Service</a> (IERS) uses the term "reference system" for the same. When coordinates are realized by choosing datum points and fixing a geodetic datum, ISO speaks of a "coordinate reference system", whereas IERS uses a "reference frame" for the same. The ISO term for a datum transformation again is a "coordinate transformation".<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> </p> <div class="mw-heading mw-heading2"><h2 id="Positioning">Positioning</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=8" title="Edit section: Positioning"><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">See also: <a href="/wiki/Geodetic_network#Measurement_techniques" class="mw-redirect" title="Geodetic network">Geodetic network § Measurement techniques</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444" /><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Geodesy" title="Special:EditPage/Geodesy">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">February 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:GPS_satellite_approaching_23_years_on_orbit_(1060259).jpeg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/GPS_satellite_approaching_23_years_on_orbit_%281060259%29.jpeg/250px-GPS_satellite_approaching_23_years_on_orbit_%281060259%29.jpeg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/GPS_satellite_approaching_23_years_on_orbit_%281060259%29.jpeg/330px-GPS_satellite_approaching_23_years_on_orbit_%281060259%29.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f4/GPS_satellite_approaching_23_years_on_orbit_%281060259%29.jpeg/500px-GPS_satellite_approaching_23_years_on_orbit_%281060259%29.jpeg 2x" data-file-width="680" data-file-height="680" /></a><figcaption><a href="/wiki/GPS" class="mw-redirect" title="GPS">GPS</a> Block IIA satellite orbits over the <a href="/wiki/Earth" title="Earth">Earth</a>.</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Geodetic_Control_Mark.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Geodetic_Control_Mark.jpg/220px-Geodetic_Control_Mark.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Geodetic_Control_Mark.jpg/330px-Geodetic_Control_Mark.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Geodetic_Control_Mark.jpg/440px-Geodetic_Control_Mark.jpg 2x" data-file-width="1600" data-file-height="1200" /></a><figcaption>Geodetic control mark</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Apollo_IMU_at_Draper_Hack_the_Moon_exhibit.agr.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Apollo_IMU_at_Draper_Hack_the_Moon_exhibit.agr.jpg/250px-Apollo_IMU_at_Draper_Hack_the_Moon_exhibit.agr.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Apollo_IMU_at_Draper_Hack_the_Moon_exhibit.agr.jpg/330px-Apollo_IMU_at_Draper_Hack_the_Moon_exhibit.agr.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Apollo_IMU_at_Draper_Hack_the_Moon_exhibit.agr.jpg/500px-Apollo_IMU_at_Draper_Hack_the_Moon_exhibit.agr.jpg 2x" data-file-width="4032" data-file-height="3024" /></a><figcaption><a href="/wiki/Inertial_navigation" class="mw-redirect" title="Inertial navigation">Navigation</a> device, <a href="/wiki/Apollo_program" title="Apollo program">Apollo program</a></figcaption></figure> <p>General <a href="/wiki/Geopositioning" title="Geopositioning">geopositioning</a>, or simply positioning, is the determination of the location of points on Earth, by myriad techniques. <b>Geodetic positioning</b> employs geodetic methods to determine a set of precise geodetic coordinates of a point on land, at sea, or in space. It may be done within a coordinate system (<b>point positioning</b> or <b>absolute positioning</b>) or relative to another point (<b>relative positioning</b>). One computes the position of a point in space from measurements linking terrestrial or extraterrestrial points of known location ("known points") with terrestrial ones of unknown location ("unknown points"). The computation may involve transformations between or among astronomical and terrestrial coordinate systems. Known points used in point positioning can be <a href="/wiki/Global_Navigation_Satellite_Systems" class="mw-redirect" title="Global Navigation Satellite Systems">GNSS</a> <a href="/wiki/Continuously_operating_reference_station" class="mw-redirect" title="Continuously operating reference station">continuously operating reference stations</a> or <a href="/wiki/Triangulation_(surveying)" title="Triangulation (surveying)">triangulation points</a> of a higher-order network. </p><p>Traditionally, geodesists built a hierarchy of networks to allow point positioning within a country. The highest in this hierarchy were triangulation networks, densified into the networks of <a href="/wiki/Traverse_(surveying)" title="Traverse (surveying)">traverses</a> (<a href="/wiki/Polygons" class="mw-redirect" title="Polygons">polygons</a>) into which local mapping and surveying measurements, usually collected using a measuring tape, a <a href="/wiki/Corner_reflector" title="Corner reflector">corner prism</a>, and the red-and-white poles, are tied. </p><p>Commonly used nowadays is GPS, except for specialized measurements (e.g., in underground or high-precision engineering). The higher-order networks are measured with <a href="/wiki/Global_Positioning_System" title="Global Positioning System">static GPS</a>, using <a href="/wiki/Differential_GPS" title="Differential GPS">differential measurement</a> to determine vectors between terrestrial points. These vectors then get adjusted in a traditional network fashion. A global polyhedron of permanently operating GPS stations under the auspices of the <a href="/wiki/IERS" class="mw-redirect" title="IERS">IERS</a> is the basis for defining a single global, geocentric reference frame that serves as the "zero-order" (global) reference to which national measurements are attached. </p><p><a href="/wiki/Real-time_kinematic_positioning" title="Real-time kinematic positioning">Real-time kinematic positioning</a> (RTK GPS) is employed frequently in <a href="/wiki/Surveying" title="Surveying">survey</a> mapping. In that measurement technique, unknown points can get quickly tied into nearby terrestrial known points. </p><p>One purpose of point positioning is the provision of known points for mapping measurements, also known as (horizontal and vertical) control. There can be thousands of those geodetically determined points in a country, usually documented by national mapping agencies. Surveyors involved in real estate and insurance will use these to tie their local measurements. </p> <div class="mw-heading mw-heading2"><h2 id="Geodetic_problems">Geodetic problems <span class="anchor" id="Problems"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=9" title="Edit section: Geodetic problems"><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">Further information: <a href="/wiki/Geodesics_on_an_ellipsoid#Solution_of_the_direct_and_inverse_problems" title="Geodesics on an ellipsoid">Geodesics on an ellipsoid § Solution of the direct and inverse problems</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Bearing_(navigation)#Arcs" title="Bearing (navigation)">Bearing (navigation) § Arcs</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444" /><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Geodesy" title="Special:EditPage/Geodesy">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">February 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>In geometrical geodesy, there are two main problems: </p> <ul><li><b>First geodetic problem</b> (also known as <i>direct</i> or <i>forward geodetic problem</i>): given the coordinates of a point and the directional (<a href="/wiki/Azimuth" title="Azimuth">azimuth</a>) and <a href="/wiki/Distance" title="Distance">distance</a> to a second point, determine the coordinates of that second point.</li> <li><b>Second geodetic problem</b> (also known as <i>inverse</i> or <i>reverse geodetic problem</i>): given the coordinates of two points, determine the azimuth and length of the (straight, curved, or <a href="/wiki/Geodesic" title="Geodesic">geodesic</a>) line connecting those points.</li></ul> <p>The solutions to both problems in plane geometry reduce to simple <a href="/wiki/Trigonometry" title="Trigonometry">trigonometry</a> and are valid for small areas on Earth's surface; on a sphere, solutions become significantly more complex as, for example, in the inverse problem, the azimuths differ going between the two end points along the arc of the connecting <a href="/wiki/Great_circle" title="Great circle">great circle</a>. </p><p>The general solution is called the <a href="/wiki/Geodesic" title="Geodesic">geodesic</a> for the surface considered, and the <a href="/wiki/Differential_equation" title="Differential equation">differential equations</a> for the <a href="/wiki/Geodesic" title="Geodesic">geodesic</a> are solvable numerically. On the ellipsoid of revolution, geodesics are expressible in terms of elliptic integrals, which are usually evaluated in terms of a series expansion — see, for example, <a href="/wiki/Vincenty%27s_formulae" title="Vincenty's formulae">Vincenty's formulae</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Observational_concepts">Observational concepts</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=10" title="Edit section: Observational concepts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:AxialTiltObliquity.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/AxialTiltObliquity.png/330px-AxialTiltObliquity.png" decoding="async" width="285" height="221" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/AxialTiltObliquity.png/500px-AxialTiltObliquity.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/61/AxialTiltObliquity.png/570px-AxialTiltObliquity.png 2x" data-file-width="760" data-file-height="590" /></a><figcaption>Axial tilt (or <a href="/wiki/Obliquity" class="mw-redirect" title="Obliquity">Obliquity</a>), rotation axis, plane of <a href="/wiki/Orbit" title="Orbit">orbit</a>, <a href="/wiki/Celestial_equator" title="Celestial equator">celestial equator</a> and <a href="/wiki/Ecliptic" title="Ecliptic">ecliptic</a>. <a href="/wiki/Earth" title="Earth">Earth</a> is shown as viewed from the <a href="/wiki/Sun" title="Sun">Sun</a>; the orbit direction is counter-clockwise (to the left).</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Global_Gravity_Anomaly_Animation_over_OCEANS.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Global_Gravity_Anomaly_Animation_over_OCEANS.gif/330px-Global_Gravity_Anomaly_Animation_over_OCEANS.gif" decoding="async" width="285" height="148" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Global_Gravity_Anomaly_Animation_over_OCEANS.gif/500px-Global_Gravity_Anomaly_Animation_over_OCEANS.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/b/b4/Global_Gravity_Anomaly_Animation_over_OCEANS.gif 2x" data-file-width="500" data-file-height="260" /></a><figcaption>Global <a href="/wiki/Gravity_anomaly" title="Gravity anomaly">gravity anomaly</a> animation over oceans from the NASA's GRACE (Gravity Recovery and Climate Experiment)</figcaption></figure> <p>As defined in geodesy (and also <a href="/wiki/Astronomy" title="Astronomy">astronomy</a>), some basic observational concepts like angles and coordinates include (most commonly from the viewpoint of a local observer): </p> <ul><li><b><a href="/wiki/Plumbline" class="mw-redirect" title="Plumbline">Plumbline</a></b> or <b>vertical</b>: (the line along) the direction of local gravity.</li> <li><b><a href="/wiki/Zenith" title="Zenith">Zenith</a></b>: the (direction to the) intersection of the upwards-extending gravity vector at a point and the <a href="/wiki/Celestial_sphere" title="Celestial sphere">celestial sphere</a>.</li> <li><b><a href="/wiki/Nadir" title="Nadir">Nadir</a></b>: the (direction to the) antipodal point where the downward-extending gravity vector intersects the (obscured) celestial sphere.</li> <li><b>Celestial horizon</b>: a plane perpendicular to the gravity vector at a point.</li> <li><b><a href="/wiki/Azimuth" title="Azimuth">Azimuth</a></b>: the direction angle within the plane of the horizon, typically counted clockwise from the north (in geodesy and astronomy) or the south (in France).</li> <li><b><a href="/wiki/Elevation" title="Elevation">Elevation</a></b>: the angular height of an object above the horizon; alternatively: <a href="/wiki/Zenith_distance" class="mw-redirect" title="Zenith distance">zenith distance</a> equal to 90 degrees minus elevation.</li> <li><b>Local topocentric coordinates</b>: azimuth (direction angle within the plane of the horizon), elevation angle (or zenith angle), distance.</li> <li><b>North <a href="/wiki/Celestial_pole" title="Celestial pole">celestial pole</a></b>: the extension of Earth's (<a href="/wiki/Precession" title="Precession">precessing</a> and <a href="/wiki/Nutation" title="Nutation">nutating</a>) instantaneous spin axis extended northward to intersect the celestial sphere. (Similarly for the south celestial pole.)</li> <li><b>Celestial equator</b>: the (instantaneous) intersection of Earth's equatorial plane with the celestial sphere.</li> <li><b><a href="/wiki/Meridian_(geography)" title="Meridian (geography)">Meridian</a> plane</b>: any plane perpendicular to the celestial equator and containing the celestial poles.</li> <li><b>Local meridian</b>: the plane which contains the direction to the zenith and the celestial pole.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Measurements">Measurements</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=11" title="Edit section: Measurements"><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">Further information: <a href="/wiki/Satellite_geodesy" title="Satellite geodesy">Satellite geodesy</a>, <a href="/wiki/Geodetic_astronomy" title="Geodetic astronomy">Geodetic astronomy</a>, <a href="/wiki/Surveying" title="Surveying">Surveying</a>, <a href="/wiki/Gravimetry" title="Gravimetry">Gravimetry</a>, and <a href="/wiki/Levelling" title="Levelling">Levelling</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444" /><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Geodesy" title="Special:EditPage/Geodesy">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">February 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:GRAIL%27s_gravity_map_of_the_moon.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/GRAIL%27s_gravity_map_of_the_moon.jpg/285px-GRAIL%27s_gravity_map_of_the_moon.jpg" decoding="async" width="285" height="214" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/GRAIL%27s_gravity_map_of_the_moon.jpg/428px-GRAIL%27s_gravity_map_of_the_moon.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/GRAIL%27s_gravity_map_of_the_moon.jpg/570px-GRAIL%27s_gravity_map_of_the_moon.jpg 2x" data-file-width="1440" data-file-height="1080" /></a><figcaption>Variations in the gravity field of the <a href="/wiki/Moon" title="Moon">Moon</a>, from <a href="/wiki/NASA" title="NASA">NASA</a></figcaption></figure><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Gravity_measurement_devices,_pendulum_(left)_and_absolute_(right)_-_National_Museum_of_Nature_and_Science,_Tokyo_-_DSC07808.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Gravity_measurement_devices%2C_pendulum_%28left%29_and_absolute_%28right%29_-_National_Museum_of_Nature_and_Science%2C_Tokyo_-_DSC07808.JPG/330px-Gravity_measurement_devices%2C_pendulum_%28left%29_and_absolute_%28right%29_-_National_Museum_of_Nature_and_Science%2C_Tokyo_-_DSC07808.JPG" decoding="async" width="285" height="190" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Gravity_measurement_devices%2C_pendulum_%28left%29_and_absolute_%28right%29_-_National_Museum_of_Nature_and_Science%2C_Tokyo_-_DSC07808.JPG/500px-Gravity_measurement_devices%2C_pendulum_%28left%29_and_absolute_%28right%29_-_National_Museum_of_Nature_and_Science%2C_Tokyo_-_DSC07808.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d3/Gravity_measurement_devices%2C_pendulum_%28left%29_and_absolute_%28right%29_-_National_Museum_of_Nature_and_Science%2C_Tokyo_-_DSC07808.JPG/960px-Gravity_measurement_devices%2C_pendulum_%28left%29_and_absolute_%28right%29_-_National_Museum_of_Nature_and_Science%2C_Tokyo_-_DSC07808.JPG 2x" data-file-width="5472" data-file-height="3648" /></a><figcaption>Gravity measurement devices, pendulum (left) and absolute gravimeter (right)</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Autograv_CG5_P1150838.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Autograv_CG5_P1150838.JPG/120px-Autograv_CG5_P1150838.JPG" decoding="async" width="85" height="113" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Autograv_CG5_P1150838.JPG/250px-Autograv_CG5_P1150838.JPG 1.5x" data-file-width="1536" data-file-height="2048" /></a><figcaption>A relative gravimeter</figcaption></figure> <p>The reference surface (level) used to determine height differences and height reference systems is known as <a href="/wiki/Mean_sea_level" class="mw-redirect" title="Mean sea level">mean sea level</a>. The traditional <a href="/wiki/Spirit_level" title="Spirit level">spirit level</a> directly produces such (for practical purposes most useful) heights above <a href="/wiki/Sea_level" title="Sea level">sea level</a>; the more economical use of GPS instruments for height determination requires precise knowledge of the figure of the <a href="/wiki/Geoid" title="Geoid">geoid</a>, as GPS only gives heights above the <a href="/wiki/GRS80" class="mw-redirect" title="GRS80">GRS80</a> reference ellipsoid. As geoid determination improves, one may expect that the use of GPS in height determination shall increase, too. </p><p>The <a href="/wiki/Theodolite" title="Theodolite">theodolite</a> is an instrument used to measure horizontal and vertical (relative to the local vertical) angles to target points. In addition, the <a href="/wiki/Tachymeter_(survey)" class="mw-redirect" title="Tachymeter (survey)">tachymeter</a> determines, electronically or <a href="/wiki/Electro-optics" title="Electro-optics">electro-optically</a>, the distance to a target and is highly automated or even robotic in operations. Widely used for the same purpose is the method of free station position. </p><p>Commonly for local detail surveys, tachymeters are employed, although the old-fashioned rectangular technique using an angle prism and steel tape is still an inexpensive alternative. As mentioned, also there are quick and relatively accurate real-time kinematic (RTK) GPS techniques. Data collected are tagged and recorded digitally for entry into <a href="/wiki/Geographic_information_system" title="Geographic information system">Geographic Information System</a> (GIS) databases. </p><p>Geodetic GNSS (most commonly <a href="/wiki/Global_Positioning_System" title="Global Positioning System">GPS</a>) receivers directly produce 3D coordinates in a <a href="/wiki/Geocentric" class="mw-redirect" title="Geocentric">geocentric</a> coordinate frame. One such frame is <a href="/wiki/WGS84" class="mw-redirect" title="WGS84">WGS84</a>, as well as frames by the International Earth Rotation and Reference Systems Service (<a href="/wiki/IERS" class="mw-redirect" title="IERS">IERS</a>). GNSS receivers have almost completely replaced terrestrial instruments for large-scale base network surveys. </p><p>To monitor the Earth's rotation irregularities and plate tectonic motions and for planet-wide geodetic surveys, methods of <a href="/wiki/Very-long-baseline_interferometry" title="Very-long-baseline interferometry">very-long-baseline interferometry</a> (VLBI) measuring distances to <a href="/wiki/Quasar" title="Quasar">quasars</a>, <a href="/wiki/Lunar_laser_ranging" class="mw-redirect" title="Lunar laser ranging">lunar laser ranging</a> (LLR) measuring distances to prisms on the Moon, and <a href="/wiki/Satellite_laser_ranging" title="Satellite laser ranging">satellite laser ranging</a> (SLR) measuring distances to prisms on <a href="/wiki/Artificial_satellites" class="mw-redirect" title="Artificial satellites">artificial satellites</a>, are employed. </p><p><a href="/wiki/Gravity" title="Gravity">Gravity</a> is measured using <a href="/wiki/Gravimeters" class="mw-redirect" title="Gravimeters">gravimeters</a>, of which there are two kinds. First are <i><a href="/wiki/Absolute_gravimeter" class="mw-redirect" title="Absolute gravimeter">absolute gravimeter</a></i>s, based on measuring the acceleration of <a href="/wiki/Free_fall" title="Free fall">free fall</a> (e.g., of a reflecting prism in a <a href="/wiki/Vacuum_tube" title="Vacuum tube">vacuum tube</a>). They are used to establish vertical geospatial control or in the field. Second, <i><a href="/wiki/Relative_gravimeter" class="mw-redirect" title="Relative gravimeter">relative gravimeter</a></i>s are spring-based and more common. They are used in gravity surveys over large areas — to establish the figure of the geoid over these areas. The most accurate relative gravimeters are called <i><a href="/wiki/Superconducting_gravimeter" class="mw-redirect" title="Superconducting gravimeter">superconducting gravimeter</a></i>s, which are sensitive to one-thousandth of one-billionth of Earth-surface gravity. Twenty-some superconducting gravimeters are used worldwide in studying Earth's <a href="/wiki/Tide" title="Tide">tides</a>, <a href="/wiki/Rotation" title="Rotation">rotation</a>, interior, <a href="/wiki/Ocean" title="Ocean">oceanic</a> and atmospheric loading, as well as in verifying the <a href="/wiki/Newtonian_constant_of_gravitation" class="mw-redirect" title="Newtonian constant of gravitation">Newtonian constant of gravitation</a>. </p><p>In the future, gravity and altitude might become measurable using the special-relativistic concept of <a href="/wiki/Time_dilation" title="Time dilation">time dilation</a> as gauged by <a href="/wiki/Atomic_clock#Research" title="Atomic clock">optical clocks</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Units_and_measures_on_the_ellipsoid">Units and measures on the ellipsoid</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=12" title="Edit section: Units and measures on the ellipsoid"><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">Further information: <a href="/wiki/Geodetic_coordinates" title="Geodetic coordinates">Geodetic coordinates</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444" /><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Geodesy" title="Special:EditPage/Geodesy">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">February 2024</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Latitude_and_longitude_graticule_on_an_ellipsoid.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Latitude_and_longitude_graticule_on_an_ellipsoid.svg/225px-Latitude_and_longitude_graticule_on_an_ellipsoid.svg.png" decoding="async" width="225" height="205" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Latitude_and_longitude_graticule_on_an_ellipsoid.svg/338px-Latitude_and_longitude_graticule_on_an_ellipsoid.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Latitude_and_longitude_graticule_on_an_ellipsoid.svg/450px-Latitude_and_longitude_graticule_on_an_ellipsoid.svg.png 2x" data-file-width="825" data-file-height="750" /></a><figcaption>The definition of latitude (φ) and longitude (λ) on an ellipsoid of revolution (or spheroid). The graticule spacing is 10 degrees. The latitude is defined as the angle between the normal to the ellipsoid and the equatorial plane.</figcaption></figure> <p>Geographical <a href="/wiki/Latitude" title="Latitude">latitude</a> and <a href="/wiki/Longitude" title="Longitude">longitude</a> are stated in the units degree, minute of arc, and second of arc. They are <i>angles</i>, not metric measures, and describe the <i>direction</i> of the local normal to the <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">reference ellipsoid</a> of revolution. This direction is <i>approximately</i> the same as the direction of the plumbline, i.e., local gravity, which is also the normal to the geoid surface. For this reason, astronomical position determination – measuring the direction of the plumbline by astronomical means – works reasonably well when one also uses an ellipsoidal model of the figure of the Earth. </p><p>One geographical mile, defined as one minute of arc on the equator, equals 1,855.32571922 m. One <a href="/wiki/Nautical_mile" title="Nautical mile">nautical mile</a> is one minute of astronomical latitude. The radius of curvature of the ellipsoid varies with latitude, being the longest at the pole and the shortest at the equator same as with the nautical mile. </p><p>A <a href="/wiki/Metre" title="Metre">metre</a> was originally defined as the 10-millionth part of the length from the equator to the North Pole along the meridian through Paris (the target was not quite reached in actual implementation, as it is off by 200 <a href="/wiki/Parts-per_notation#ppm" title="Parts-per notation">ppm</a> in the current definitions). This situation means that one kilometre roughly equals (1/40,000) * 360 * 60 meridional minutes of arc, or 0.54 nautical miles. (This is not exactly so as the two units had been defined on different bases, so the international nautical mile is 1,852 m exactly, which corresponds to rounding the quotient from 1,000/0.54 m to four digits). </p> <div class="mw-heading mw-heading2"><h2 id="Temporal_changes">Temporal changes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=13" title="Edit section: Temporal changes"><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">See also: <a href="/wiki/Geoid#Temporal_change" title="Geoid">Geoid § Temporal change</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Global_plate_motion.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Global_plate_motion.jpg/280px-Global_plate_motion.jpg" decoding="async" width="280" height="212" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Global_plate_motion.jpg/420px-Global_plate_motion.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Global_plate_motion.jpg/560px-Global_plate_motion.jpg 2x" data-file-width="700" data-file-height="530" /></a><figcaption>Global plate tectonic movement using GPS</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:How_VLBI_Works.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/How_VLBI_Works.gif/280px-How_VLBI_Works.gif" decoding="async" width="280" height="262" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/How_VLBI_Works.gif/420px-How_VLBI_Works.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/3/36/How_VLBI_Works.gif 2x" data-file-width="530" data-file-height="496" /></a><figcaption>How <a href="/wiki/Very-long-baseline_interferometry" title="Very-long-baseline interferometry">very-long-baseline interferometry</a> (VLBI) works</figcaption></figure> <p>Various techniques are used in geodesy to study temporally changing surfaces, bodies of mass, physical fields, and dynamical systems. Points on Earth's surface change their location due to a variety of mechanisms: </p> <ul><li>Continental plate motion, <a href="/wiki/Plate_tectonics" title="Plate tectonics">plate tectonics</a><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></li> <li>The episodic motion of tectonic origin, especially close to <a href="/wiki/Fault_line" class="mw-redirect" title="Fault line">fault lines</a></li> <li>Periodic effects due to tides and tidal loading<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></li> <li><a href="/wiki/Glaciation" class="mw-redirect" title="Glaciation">Postglacial</a> land uplift due to isostatic adjustment</li> <li>Mass variations due to hydrological changes, including the atmosphere, cryosphere, land hydrology, and oceans</li> <li>Sub-daily polar motion<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup></li> <li>Length-of-day variability<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup></li> <li>Earth's center-of-mass (geocenter) variations<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></li> <li>Anthropogenic movements such as reservoir construction or <a href="/wiki/Petroleum" title="Petroleum">petroleum</a> or water extraction</li></ul> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_0" poster="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv/280px--Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="280" height="158" data-durationhint="128" data-mwtitle="Stephen_Merkowitz_NASA's_Space_Geodesy_Project.ogv" data-mwprovider="wikimediacommons" resource="/wiki/File:Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9f/Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv/Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv.480p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9f/Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv/Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv.720p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/9/9f/Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv" type="video/ogg; codecs="theora, vorbis"" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9f/Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv/Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv.240p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9f/Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv/Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv.360p.vp9.webm" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9f/Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv/Stephen_Merkowitz_NASA%27s_Space_Geodesy_Project.ogv.360p.webm" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /></video></span><figcaption>A NASA project manager talks about his work for the <a href="/wiki/Space_geodesy" title="Space geodesy">Space Geodesy</a> Project, including an overview of its four fundamental techniques: GPS, <a href="/wiki/Very-long-baseline_interferometry" title="Very-long-baseline interferometry">VLBI</a>, <a href="/wiki/Lunar_laser_ranging" class="mw-redirect" title="Lunar laser ranging">LLR</a>/<a href="/wiki/Satellite_laser_ranging" title="Satellite laser ranging">SLR</a>, and <a href="/wiki/DORIS_(geodesy)" class="mw-redirect" title="DORIS (geodesy)">DORIS</a>.</figcaption></figure> <p><a href="/wiki/Geodynamics" title="Geodynamics">Geodynamics</a> is the discipline that studies deformations and motions of Earth's crust and its solidity as a whole. Often the study of Earth's irregular rotation is included in the above definition. Geodynamical studies require terrestrial reference frames<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> realized by the stations belonging to the Global Geodetic Observing System (GGOS<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>). </p><p>Techniques for studying geodynamic phenomena on global scales include: </p> <ul><li>Satellite positioning by <a href="/wiki/Global_Positioning_System" title="Global Positioning System">GPS</a>, <a href="/wiki/GLONASS" title="GLONASS">GLONASS</a>, <a href="/wiki/Galileo_(satellite_navigation)" title="Galileo (satellite navigation)">Galileo</a>, and <a href="/wiki/BeiDou" title="BeiDou">BeiDou</a></li> <li><a href="/wiki/Very-long-baseline_interferometry" title="Very-long-baseline interferometry">Very-long-baseline interferometry</a> (VLBI)</li> <li><a href="/wiki/Satellite_laser_ranging" title="Satellite laser ranging">Satellite laser ranging</a> (SLR)<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> and lunar <a href="/wiki/Laser_ranging" class="mw-redirect" title="Laser ranging">laser ranging</a> (LLR)</li> <li><a href="/wiki/DORIS_(satellite_system)" title="DORIS (satellite system)">DORIS</a></li> <li>Regionally and locally precise leveling</li> <li>Precise tachymeters</li> <li>Monitoring of gravity change using land, airborne, shipborne, and spaceborne <a href="/wiki/Gravimetry" title="Gravimetry">gravimetry</a></li> <li>Satellite <a href="/wiki/Altimetry" class="mw-redirect" title="Altimetry">altimetry</a> based on microwave and laser observations for studying the ocean surface, sea level rise, and ice cover monitoring</li> <li><a href="/wiki/Interferometric_synthetic_aperture_radar" class="mw-redirect" title="Interferometric synthetic aperture radar">Interferometric synthetic aperture radar</a> (InSAR) using satellite images.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Notable_geodesists">Notable geodesists</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodesy&action=edit&section=14" title="Edit section: Notable geodesists"><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/List_of_geodesists" title="List of geodesists">List of geodesists</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Surveying#Notable_surveyors" title="Surveying">Notable surveyors</a></div> <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=Geodesy&action=edit&section=15" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output 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rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Outline_of_metrology_and_measurement#Geodesy" title="Outline of metrology and measurement">Outline of metrology and measurement § Geodesy</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">Main category: <a href="/wiki/Category:Geodesy" title="Category:Geodesy">Geodesy</a></div> <ul><li><a href="/wiki/Earth_system_science" title="Earth system science">Earth system science</a> – Scientific study of the Earth's spheres and their natural integrated systems</li> <li><a href="/wiki/List_of_geodesists" title="List of geodesists">List of geodesists</a> – Notable geodesists</li> <li><a href="/wiki/Geomatics_engineering" class="mw-redirect" title="Geomatics engineering">Geomatics engineering</a> – Geographic data discipline<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li> <li><a href="/wiki/History_of_geophysics" title="History of geophysics">History of geophysics</a></li> <li><a href="/wiki/Geodynamics" title="Geodynamics">Geodynamics</a> – Study of dynamics of the Earth</li> <li><a href="/wiki/Planetary_science" title="Planetary science">Planetary science</a> – Science of planets and planetary systems</li></ul> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col"> <p><b>Fundamentals</b> </p> <ul><li><a href="/wiki/Geodesy_(book)" title="Geodesy (book)"><i>Geodesy</i> (book)</a></li> <li><i><a href="/wiki/Concepts_and_Techniques_in_Modern_Geography" title="Concepts and Techniques in Modern Geography">Concepts and Techniques in Modern Geography</a></i></li> <li><a href="/wiki/Geodesics_on_an_ellipsoid" title="Geodesics on an ellipsoid">Geodesics on an ellipsoid</a></li> <li><a href="/wiki/History_of_geodesy" title="History of geodesy">History of geodesy</a></li> <li><a href="/wiki/Physical_geodesy" title="Physical geodesy">Physical geodesy</a></li> <li><a href="/wiki/Earth%27s_circumference" title="Earth's circumference">Earth's circumference</a></li> <li><a href="/wiki/Physics" title="Physics">Physics</a></li> <li><a href="/wiki/Geosciences" class="mw-redirect" title="Geosciences">Geosciences</a></li></ul> <p><b>Governmental agencies</b> </p> <ul><li><a href="/wiki/National_mapping_agency" title="National mapping agency">National mapping agencies</a></li> <li><a href="/wiki/U.S._National_Geodetic_Survey" title="U.S. National Geodetic Survey">U.S. National Geodetic Survey</a></li> <li><a href="/wiki/National_Geospatial-Intelligence_Agency" title="National Geospatial-Intelligence Agency">National Geospatial-Intelligence Agency</a></li> <li><a href="/wiki/Ordnance_Survey" title="Ordnance Survey">Ordnance Survey</a></li> <li><a href="/wiki/United_States_Coast_and_Geodetic_Survey" title="United States Coast and Geodetic Survey">United States Coast and Geodetic Survey</a></li> <li><a href="/wiki/United_States_Geological_Survey" title="United States Geological Survey">United States Geological Survey</a></li></ul> <p><b>International organizations</b> </p> <ul><li><a href="/wiki/International_Union_of_Geodesy_and_Geophysics" title="International Union of Geodesy and Geophysics">International Union of Geodesy and Geophysics</a> (IUGG)</li> <li><a href="/wiki/International_Association_of_Geodesy" title="International Association of Geodesy">International Association of Geodesy</a> (IAG)</li> <li><a href="/wiki/International_Federation_of_Surveyors" title="International Federation of Surveyors">International Federation of Surveyors</a> (IFS)</li> <li><a href="/wiki/International_Geodetic_Student_Organisation" title="International Geodetic Student Organisation">International Geodetic Student Organisation</a> (IGSO)</li></ul> <p><b>Other</b> </p> <ul><li><a href="/w/index.php?title=Council_of_European_Geodetic_Surveyors&action=edit&redlink=1" class="new" title="Council of European Geodetic Surveyors (page does not exist)">Council of European Geodetic Surveyors</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://fr.wikipedia.org/wiki/Comit%C3%A9_de_liaison_des_g%C3%A9om%C3%A8tres_europ%C3%A9ens" class="extiw" title="fr:Comité de liaison des géomètres européens">fr</a>]</span></li> <li><a href="/wiki/EPSG_Geodetic_Parameter_Dataset" title="EPSG Geodetic Parameter Dataset">EPSG Geodetic Parameter Dataset</a></li> <li><a href="/wiki/Meridian_arc" title="Meridian arc">Meridian arc</a></li> <li><a href="/wiki/Surveying" title="Surveying">Surveying</a></li></ul> </div> <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=Geodesy&action=edit&section=16" 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 class="citation book cs1"><a rel="nofollow" class="external text" href="https://dictionary.cambridge.org/us/dictionary/english/geodetics">"geodetics"</a>. <i><a href="/wiki/Cambridge_English_Dictionary" class="mw-redirect" title="Cambridge English Dictionary">Cambridge English Dictionary</a></i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-06-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=geodetics&rft.btitle=Cambridge+English+Dictionary&rft_id=https%3A%2F%2Fdictionary.cambridge.org%2Fus%2Fdictionary%2Fenglish%2Fgeodetics&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" class="Z3988"></span></span> </li> <li id="cite_note-VK-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-VK_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-VK_2-1"><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="CITEREFVaníčekKrakiwsky1986" class="citation book cs1"><a href="/wiki/Petr_Van%C3%AD%C4%8Dek" title="Petr Vaníček">Vaníček, Petr</a>; Krakiwsky, Edward J., eds. (November 1, 1986). "Structure of Geodesy". <a rel="nofollow" class="external text" href="https://shop.elsevier.com/books/geodesy/vanicek/978-0-444-87775-8"><i>Geodesy: The Concepts</i></a> (Second ed.). <a href="/wiki/Elsevier" title="Elsevier">Elsevier</a>. pp. <span class="nowrap">45–</span>51. <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%2FB978-0-444-87775-8.50009-5">10.1016/B978-0-444-87775-8.50009-5</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-444-87775-8" title="Special:BookSources/978-0-444-87775-8"><bdi>978-0-444-87775-8</bdi></a>. <q>...<span class="nowrap"> </span>geodesy was thought to occupy the space delimited by the following definition ... "the science of measuring and portraying the earth's surface." ... the new definition of geodesy ... "the discipline that deals with the measurement and representation of the earth, including its gravity field, in a three-dimensional time varying space." ... a virtually identical definition ... the inclusion of other celestial bodies and their respective gravity fields.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Structure+of+Geodesy&rft.btitle=Geodesy%3A+The+Concepts&rft.pages=%3Cspan+class%3D%22nowrap%22%3E45-%3C%2Fspan%3E51&rft.edition=Second&rft.pub=Elsevier&rft.date=1986-11-01&rft_id=info%3Adoi%2F10.1016%2FB978-0-444-87775-8.50009-5&rft.isbn=978-0-444-87775-8&rft_id=https%3A%2F%2Fshop.elsevier.com%2Fbooks%2Fgeodesy%2Fvanicek%2F978-0-444-87775-8&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://www.iag-aig.org/doc/5cb5b3660b6c4.pdf"><i>What is Geodesy?</i></a> <span class="cs1-format">(PDF)</span>. <a href="/wiki/International_Association_of_Geodesy" title="International Association of Geodesy">International Association of Geodesy</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=What+is+Geodesy%3F&rft.pub=International+Association+of+Geodesy&rft_id=https%3A%2F%2Fwww.iag-aig.org%2Fdoc%2F5cb5b3660b6c4.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" 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="CITEREFUS_Department_of_Commerce" class="citation web cs1">US Department of Commerce, National Oceanic and Atmospheric Administration. <a rel="nofollow" class="external text" href="https://oceanservice.noaa.gov/facts/geodesy.html">"What is geodesy?"</a>. <i>oceanservice.noaa.gov</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-06-09</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=oceanservice.noaa.gov&rft.atitle=What+is+geodesy%3F&rft.aulast=US+Department+of+Commerce&rft.aufirst=National+Oceanic+and+Atmospheric+Administration&rft_id=https%3A%2F%2Foceanservice.noaa.gov%2Ffacts%2Fgeodesy.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://c4g.lsu.edu/index.php/geodesy">"Geodesy"</a>. <i>LSU Center for GeoInformatics</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-06-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=LSU+Center+for+GeoInformatics&rft.atitle=Geodesy&rft_id=https%3A%2F%2Fc4g.lsu.edu%2Findex.php%2Fgeodesy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://study.com/academy/lesson/geodesy-definition-branches.html">"Geodesy Definition, Characteristics & Branches"</a>. <i>Study.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-06-08</span></span>. <q>The definition of geodesy can be explained as the academic field of earth science that is involved with measuring and comprehending the Earth's orientation in space, the Earth's gravity field, and the Earth's shape geometrically. ... Geodesy is an applied mathematics discipline used to understand various aspects of the Earth.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Study.com&rft.atitle=Geodesy+Definition%2C+Characteristics+%26+Branches&rft_id=https%3A%2F%2Fstudy.com%2Facademy%2Flesson%2Fgeodesy-definition-branches.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.onetonline.org/link/summary/17-1022.01">"Geodetic Surveyors"</a>. <i>Occupational Information Network</i>. 2020-11-26<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-01-28</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Occupational+Information+Network&rft.atitle=Geodetic+Surveyors&rft.date=2020-11-26&rft_id=https%3A%2F%2Fwww.onetonline.org%2Flink%2Fsummary%2F17-1022.01&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" class="Z3988"></span></span> </li> <li id="cite_note-routledge-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-routledge_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFKentVujakovic2017" class="citation book cs1">Kent, Alexander; Vujakovic, Peter (4 October 2017). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=dowEEAAAQBAJ&dq=translate+ancient+greek+%CE%B3%CE%B5%CF%89%CE%B4%CE%B1%CE%B9%CF%83%CE%AF%CE%B1&pg=PA187"><i>The Routledge Handbook of Mapping and Cartography</i></a>. 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Retrieved <span class="nowrap">6 December</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Dome+of+Eden%3A+A+New+Solution+to+the+Problem+of+Creation+and+Evolution&rft.pages=214&rft.pub=Wipf+and+Stock+Publishers&rft.date=2010-01-01&rft.isbn=978-1-60608-741-1&rft.aulast=Webb&rft.aufirst=Stephen+H.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DwStMAwAAQBAJ%26dq%3Dflat%2Bearth%2Bdome%2Bheavens%26pg%3DPA214&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" class="Z3988"></span></span> </li> <li id="cite_note-Posa-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Posa_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPosamentierMareschThallerSpreitzer2021" class="citation book cs1">Posamentier, Alfred S.; Maresch, Guenter; Thaller, Bernd; Spreitzer, Christian; Geretschlager, Robert; Stuhlpfarrer, David; Dorner, Christian (24 November 2021). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=DGxYEAAAQBAJ&dq=spherical+earth+lunar+eclipse+polaris&pg=PA114"><i>Geometry In Our Three-dimensional World</i></a>. 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Tenzer, Robert (2017). <a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fgji%2Fggx221">"Comparison of different methods for estimating the geoid-to-quasi-geoid separation"</a>. <i>Geophysical Journal International</i>. <b>210</b> (2): <span class="nowrap">1001–</span>1020. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fgji%2Fggx221">10.1093/gji/ggx221</a></span>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/10397%2F75053">10397/75053</a></span>. <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/0956-540X">0956-540X</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Geophysical+Journal+International&rft.atitle=Comparison+of+different+methods+for+estimating+the+geoid-to-quasi-geoid+separation&rft.volume=210&rft.issue=2&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1001-%3C%2Fspan%3E1020&rft.date=2017&rft_id=info%3Ahdl%2F10397%2F75053&rft.issn=0956-540X&rft_id=info%3Adoi%2F10.1093%2Fgji%2Fggx221&rft.aulast=Foroughi&rft.aufirst=Ismael&rft.au=Tenzer%2C+Robert&rft_id=https%3A%2F%2Fdoi.org%2F10.1093%252Fgji%252Fggx221&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" class="Z3988"></span></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">(ISO 19111: Spatial referencing by coordinates).</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="CITEREFAltamimiMétivierRebischungRouby2017" class="citation journal cs1">Altamimi, Zuheir; Métivier, Laurent; Rebischung, Paul; Rouby, Hélène; Collilieux, Xavier (June 2017). <a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fgji%2Fggx136">"ITRF2014 plate motion model"</a>. <i>Geophysical Journal International</i>. <b>209</b> (3): <span class="nowrap">1906–</span>1912. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fgji%2Fggx136">10.1093/gji/ggx136</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Geophysical+Journal+International&rft.atitle=ITRF2014+plate+motion+model&rft.volume=209&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1906-%3C%2Fspan%3E1912&rft.date=2017-06&rft_id=info%3Adoi%2F10.1093%2Fgji%2Fggx136&rft.aulast=Altamimi&rft.aufirst=Zuheir&rft.au=M%C3%A9tivier%2C+Laurent&rft.au=Rebischung%2C+Paul&rft.au=Rouby%2C+H%C3%A9l%C3%A8ne&rft.au=Collilieux%2C+Xavier&rft_id=https%3A%2F%2Fdoi.org%2F10.1093%252Fgji%252Fggx136&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSośnicaThallerDachJäggi2013" class="citation journal cs1">Sośnica, Krzysztof; 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Sośnica, Krzysztof; Bury, Grzegorz (January 2021). <a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10291-020-01037-3">"Geocenter coordinates derived from multi-GNSS: a look into the role of solar radiation pressure modeling"</a>. <i>GPS Solutions</i>. <b>25</b> (1): 1. <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/2021GPSS...25....1Z">2021GPSS...25....1Z</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10291-020-01037-3">10.1007/s10291-020-01037-3</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=GPS+Solutions&rft.atitle=Geocenter+coordinates+derived+from+multi-GNSS%3A+a+look+into+the+role+of+solar+radiation+pressure+modeling&rft.volume=25&rft.issue=1&rft.pages=1&rft.date=2021-01&rft_id=info%3Adoi%2F10.1007%2Fs10291-020-01037-3&rft_id=info%3Abibcode%2F2021GPSS...25....1Z&rft.aulast=Zajdel&rft.aufirst=Rados%C5%82aw&rft.au=So%C5%9Bnica%2C+Krzysztof&rft.au=Bury%2C+Grzegorz&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%252Fs10291-020-01037-3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFZajdelSośnicaDrożdżewskiBury2019" class="citation journal cs1">Zajdel, R.; Sośnica, K.; Drożdżewski, M.; Bury, G.; Strugarek, D. (November 2019). <a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs00190-019-01307-0">"Impact of network constraining on the terrestrial reference frame realization based on SLR observations to LAGEOS"</a>. <i>Journal of Geodesy</i>. <b>93</b> (11): <span class="nowrap">2293–</span>2313. <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/2019JGeod..93.2293Z">2019JGeod..93.2293Z</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs00190-019-01307-0">10.1007/s00190-019-01307-0</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Geodesy&rft.atitle=Impact+of+network+constraining+on+the+terrestrial+reference+frame+realization+based+on+SLR+observations+to+LAGEOS&rft.volume=93&rft.issue=11&rft.pages=%3Cspan+class%3D%22nowrap%22%3E2293-%3C%2Fspan%3E2313&rft.date=2019-11&rft_id=info%3Adoi%2F10.1007%2Fs00190-019-01307-0&rft_id=info%3Abibcode%2F2019JGeod..93.2293Z&rft.aulast=Zajdel&rft.aufirst=R.&rft.au=So%C5%9Bnica%2C+K.&rft.au=Dro%C5%BCd%C5%BCewski%2C+M.&rft.au=Bury%2C+G.&rft.au=Strugarek%2C+D.&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%252Fs00190-019-01307-0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFSośnicaBosy2019" class="citation journal cs1">Sośnica, Krzysztof; Bosy, Jarosław (2019). <a rel="nofollow" class="external text" href="https://doi.org/10.24425%2Fgac.2019.126090">"Global Geodetic Observing System 2015–2018"</a>. <i>Geodesy and Cartography</i>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.24425%2Fgac.2019.126090">10.24425/gac.2019.126090</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Geodesy+and+Cartography&rft.atitle=Global+Geodetic+Observing+System+2015%E2%80%932018&rft.date=2019&rft_id=info%3Adoi%2F10.24425%2Fgac.2019.126090&rft.aulast=So%C5%9Bnica&rft.aufirst=Krzysztof&rft.au=Bosy%2C+Jaros%C5%82aw&rft_id=https%3A%2F%2Fdoi.org%2F10.24425%252Fgac.2019.126090&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFPearlmanArnoldDavisBarlier2019" class="citation journal cs1">Pearlman, M.; Arnold, D.; Davis, M.; Barlier, F.; Biancale, R.; Vasiliev, V.; Ciufolini, I.; Paolozzi, A.; Pavlis, E. C.; Sośnica, K.; Bloßfeld, M. (November 2019). "Laser geodetic satellites: a high-accuracy scientific tool". <i>Journal of Geodesy</i>. <b>93</b> (11): <span class="nowrap">2181–</span>2194. <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/2019JGeod..93.2181P">2019JGeod..93.2181P</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%2Fs00190-019-01228-y">10.1007/s00190-019-01228-y</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:127408940">127408940</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+Geodesy&rft.atitle=Laser+geodetic+satellites%3A+a+high-accuracy+scientific+tool&rft.volume=93&rft.issue=11&rft.pages=%3Cspan+class%3D%22nowrap%22%3E2181-%3C%2Fspan%3E2194&rft.date=2019-11&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A127408940%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2Fs00190-019-01228-y&rft_id=info%3Abibcode%2F2019JGeod..93.2181P&rft.aulast=Pearlman&rft.aufirst=M.&rft.au=Arnold%2C+D.&rft.au=Davis%2C+M.&rft.au=Barlier%2C+F.&rft.au=Biancale%2C+R.&rft.au=Vasiliev%2C+V.&rft.au=Ciufolini%2C+I.&rft.au=Paolozzi%2C+A.&rft.au=Pavlis%2C+E.+C.&rft.au=So%C5%9Bnica%2C+K.&rft.au=Blo%C3%9Ffeld%2C+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodesy" class="Z3988"></span></span> </li> </ol></div></div> <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=Geodesy&action=edit&section=17" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>F. R. Helmert, <a rel="nofollow" class="external text" href="http://geographiclib.sf.net/geodesic-papers/helmert80-en.html"><i>Mathematical and Physical Theories of Higher Geodesy</i>, Part 1</a>, ACIC (St. Louis, 1964). This is an English translation of <i>Die mathematischen und physikalischen Theorieen der höheren Geodäsie</i>, Vol 1 (Teubner, Leipzig, 1880).</li> <li>F. R. Helmert, <a rel="nofollow" class="external text" href="http://geographiclib.sf.net/geodesic-papers/helmert84-en.html"><i>Mathematical and Physical Theories of Higher Geodesy</i>, Part 2</a>, ACIC (St. Louis, 1964). This is an English translation of <i>Die mathematischen und physikalischen Theorieen der höheren Geodäsie</i>, Vol 2 (Teubner, Leipzig, 1884).</li> <li>B. Hofmann-Wellenhof and H. Moritz, <i>Physical Geodesy</i>, Springer-Verlag Wien, 2005. (This text is an updated edition of the 1967 classic by W.A. Heiskanen and H. Moritz).</li> <li>W. Kaula, <i>Theory of Satellite Geodesy : Applications of Satellites to Geodesy</i>, Dover Publications, 2000. (This text is a reprint of the 1966 classic).</li> <li>Vaníček P. and E.J. Krakiwsky, <i>Geodesy: the Concepts</i>, pp. 714, Elsevier, 1986.</li> <li>Torge, W (2001), <i>Geodesy</i> (3rd edition), published by de Gruyter, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/3-11-017072-8" title="Special:BookSources/3-11-017072-8">3-11-017072-8</a>.</li> <li>Thomas H. Meyer, Daniel R. Roman, and David B. Zilkoski. "What does <i>height</i> really mean?" (This is a series of four articles published in <i>Surveying and Land Information Science, SaLIS</i>.) <ul><li><a rel="nofollow" class="external text" href="http://digitalcommons.uconn.edu/thmeyer_articles/2">"Part I: Introduction"</a> <i>SaLIS</i> Vol. 64, No. 4, pages 223–233, December 2004.</li> <li><a rel="nofollow" class="external text" href="http://digitalcommons.uconn.edu/thmeyer_articles/3">"Part II: Physics and gravity"</a> <i>SaLIS</i> Vol. 65, No. 1, pages 5–15, March 2005.</li> <li><a rel="nofollow" class="external text" href="http://digitalcommons.uconn.edu/nrme_articles/2">"Part III: Height systems"</a> <i>SaLIS</i> Vol. 66, No. 2, pages 149–160, June 2006.</li> <li><a rel="nofollow" class="external text" href="http://digitalcommons.uconn.edu/nrme_articles/5">"Part IV: GPS heighting"</a> <i>SaLIS</i> Vol. 66, No. 3, pages 165–183, September 2006.</li></ul></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=Geodesy&action=edit&section=18" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409" /> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/60px-Commons-logo.svg.png 1.5x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; 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title="commons:Category:Earth sciences">Commons</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Geodesy480" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Geodesy_navbox" title="Template:Geodesy navbox"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a 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0.25em"> <ul><li><a href="/wiki/Cartography" title="Cartography">Cartography</a> <ul><li><a href="/wiki/Computer_cartography" title="Computer cartography">Computer cartography</a></li> <li><a href="/wiki/Web_mapping" title="Web mapping">Web mapping</a></li></ul></li> <li><a href="/wiki/Earth%27s_orbit" title="Earth's orbit">Earth's orbit</a></li> <li><a href="/wiki/Geodetic_astronomy" title="Geodetic astronomy">Geodetic astronomy</a></li> <li><a href="/wiki/Geomatics" title="Geomatics">Geomatics</a></li> <li><a href="/wiki/Gravity_of_Earth" title="Gravity of Earth">Gravity of Earth</a></li> <li><a href="/wiki/Navigation" title="Navigation">Navigation</a></li> <li><a href="/wiki/Photogrammetry" title="Photogrammetry">Photogrammetry</a></li> <li><a href="/wiki/Remote_Sensing" class="mw-redirect" title="Remote Sensing">Remote Sensing</a></li> <li><a href="/wiki/Geopositioning" title="Geopositioning">Geopositioning</a></li> <li><a href="/wiki/Virtual_globe" title="Virtual globe">Virtual globe</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Physical <br />phenomena</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chandler_wobble" title="Chandler wobble">Chandler wobble</a></li> <li><a href="/wiki/Coriolis_force" title="Coriolis force">Coriolis effect</a></li> <li><a href="/wiki/Earth%27s_energy_budget" title="Earth's energy budget">Earth's energy budget</a></li> <li><a href="/wiki/Earth%27s_gravity_field" class="mw-redirect" title="Earth's gravity field">Earth's gravity field</a></li> <li><a href="/wiki/Dynamo_theory" title="Dynamo theory">Geodynamo</a></li> <li><a href="/wiki/Gravity_of_Earth" title="Gravity of Earth">Gravity of Earth</a></li> <li><a href="/wiki/Plate_tectonics" title="Plate tectonics">Plate tectonics</a></li> <li><a href="/wiki/Axial_precession" title="Axial precession">Precession of the equinoxes</a></li> <li><a href="/wiki/Tide" title="Tide">Tide</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related disciplines</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Astronomy" title="Astronomy">Astronomy</a></li> <li><a href="/wiki/Geology" title="Geology">Geology</a></li> <li><a href="/wiki/Geophysics" title="Geophysics">Geophysics</a></li> <li><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a></li> <li><a href="/wiki/Physics" title="Physics">Physics</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><b><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Latitude_and_longitude_graticule_on_an_ellipsoid.svg/17px-Latitude_and_longitude_graticule_on_an_ellipsoid.svg.png" decoding="async" width="17" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Latitude_and_longitude_graticule_on_an_ellipsoid.svg/25px-Latitude_and_longitude_graticule_on_an_ellipsoid.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Latitude_and_longitude_graticule_on_an_ellipsoid.svg/33px-Latitude_and_longitude_graticule_on_an_ellipsoid.svg.png 2x" data-file-width="825" data-file-height="750" /></span></span> </span><a href="/wiki/Portal:Geodesy" title="Portal:Geodesy">Geodesy portal</a> </b></li> <li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a href="/wiki/Category:Geodesy" title="Category:Geodesy">Category</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Geodesy" class="extiw" title="commons:Category:Geodesy">Commons</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Geography_topics903" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Geography_topics" title="Template:Geography topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Geography_topics" title="Template talk:Geography topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Geography_topics" title="Special:EditPage/Template:Geography topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Geography_topics903" style="font-size:114%;margin:0 4em"><a href="/wiki/Geography" title="Geography">Geography</a> <a href="/wiki/Outline_of_geography" title="Outline of geography">topics</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li>Glossary</li> <li><a href="/wiki/History_of_geography" title="History of geography">History</a></li> <li><a href="/wiki/Philosophy_of_geography" title="Philosophy of geography">Philosophy</a></li> <li><a href="/wiki/Index_of_geography_articles" title="Index of geography articles">Index</a></li> <li><a href="/wiki/Outline_of_geography" title="Outline of geography">Outline</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Branches</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks hlist navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Human_geography" title="Human geography">Human</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Behavioral_geography" title="Behavioral geography">Behavioral</a></li> <li><a href="/wiki/Cognitive_geography" title="Cognitive geography">Cognitive</a></li> <li><a href="/wiki/Critical_geography" title="Critical geography">Critical</a></li> <li><a href="/wiki/Cultural_geography" title="Cultural geography">Cultural</a> <ul><li><a href="/wiki/Animal_geographies" class="mw-redirect" title="Animal geographies">Animal</a></li> <li><a href="/wiki/Children%27s_geographies" title="Children's geographies">Children's</a></li> <li><a href="/wiki/Economic_geography" title="Economic geography">Economic</a> <ul><li><a href="/wiki/Agricultural_geography" title="Agricultural geography">Agricultural</a></li> <li><a href="/wiki/Cyber_geography" title="Cyber geography">Cyber</a></li> <li><a href="/wiki/Development_geography" title="Development geography">Development</a></li> <li><a href="/wiki/Geography_of_finance" title="Geography of finance">Financial</a></li> <li><a href="/wiki/Historical_economic_geography" title="Historical economic geography">Histo-economic</a></li> <li><a href="/wiki/Labor_geography" title="Labor geography">Labor</a></li> <li><a href="/wiki/Geomarketing" title="Geomarketing">Marketing</a></li> <li><a href="/wiki/Retail_geography" title="Retail geography">Retail</a></li> <li><a href="/wiki/Theoretical_economic_geography" title="Theoretical economic geography">Theoretical economic</a></li> <li><a href="/wiki/Transport_geography" title="Transport geography">Transport</a></li></ul></li> <li><a href="/wiki/Language_geography" title="Language geography">Language</a> <ul><li><a href="/wiki/Geolinguistics" title="Geolinguistics">Linguistics</a></li> <li><a href="/wiki/Music_geography" title="Music geography">Music</a></li> <li><a href="/wiki/Vernacular_geography" title="Vernacular geography">Vernacular</a></li></ul></li> <li><a href="/wiki/Moral_geography" title="Moral geography">Moral</a></li> <li><a href="/wiki/Psychogeography" title="Psychogeography">Psychological</a> <ul><li><a href="/wiki/Emotional_geography" title="Emotional geography">Emotional</a></li> <li><a href="/wiki/Neogeography" title="Neogeography">Neo</a></li></ul></li> <li><a href="/wiki/Sexuality_and_space" title="Sexuality and space">Sexuality</a></li> <li><a href="/wiki/Religion_and_geography" title="Religion and geography">Religion</a></li></ul></li> <li><a href="/wiki/Geography_of_food" title="Geography of food">Food</a></li> <li><a href="/wiki/Health_geography" title="Health geography">Health</a></li> <li><a href="/wiki/Historical_geography" title="Historical geography">Historical</a> <ul><li><a href="/wiki/Palaeogeography" title="Palaeogeography">Palaeo</a></li></ul></li> <li><a href="/wiki/Imagined_geographies" title="Imagined geographies">Imagined</a></li> <li><a href="/wiki/Internet_geography" title="Internet geography">Internet</a></li> <li><a href="/wiki/Political_geography" title="Political geography">Political</a> <ul><li><a href="/wiki/Critical_geopolitics" title="Critical geopolitics">Critical geopolitics</a></li> <li><a href="/wiki/Electoral_geography" title="Electoral geography">Electoral</a></li> <li><a href="/wiki/Geopolitics" title="Geopolitics">Geopolitics</a> <ul><li><a href="/wiki/Strategic_geography" title="Strategic geography">Strategic</a></li></ul></li> <li><a href="/wiki/Military_geography" title="Military geography">Military</a></li></ul></li> <li><a href="/wiki/Population_geography" title="Population geography">Population</a> <ul><li><a href="/wiki/Settlement_geography" title="Settlement geography">Settlement</a> <ul><li><a href="/wiki/Regional_geography" title="Regional geography">Regional</a></li> <li><a href="/wiki/Urban_geography" title="Urban geography">Urban</a> <ul><li><a href="/wiki/Music_geography" title="Music geography">Music</a></li> <li><a href="/wiki/Transport_geography" title="Transport geography">Transport</a></li></ul></li></ul></li></ul></li> <li><a href="/wiki/Social_geography" title="Social geography">Social</a></li> <li><a href="/wiki/Tourism_geography" title="Tourism geography">Tourism</a></li> <li><a href="/wiki/Tropical_geography" title="Tropical geography">Tropical</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Physical_geography" title="Physical geography">Physical</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biogeography" title="Biogeography">Biogeography</a> <ul><li><a href="/wiki/Ecology" title="Ecology">Ecology</a></li> <li><a href="/wiki/Phytogeography" title="Phytogeography">Phytogeography</a></li> <li><a href="/wiki/Zoogeography" title="Zoogeography">Zoogeography</a></li></ul></li> <li><a href="/wiki/Coastal_geography" title="Coastal geography">Coastal geography</a> / <a href="/wiki/Oceanography" title="Oceanography">Oceanography</a></li> <li><a href="/wiki/Earth_science" title="Earth science">Earth science</a> <ul><li><a href="/wiki/Atmospheric_science" title="Atmospheric science">Atmospheric science</a> / <a href="/wiki/Meteorology" title="Meteorology">Meteorology</a></li> <li><a href="/wiki/Environmental_science" title="Environmental science">Environmental science</a></li> <li><a href="/wiki/Climatology" title="Climatology">Climatology</a> / <a href="/wiki/Paleoclimatology" title="Paleoclimatology">Paleoclimatology</a> / <a href="/wiki/Palaeogeography" title="Palaeogeography">Palaeogeography</a></li> <li><a href="/wiki/Geobiology" title="Geobiology">Geobiology</a></li> <li><a href="/wiki/Geophysics" title="Geophysics">Geophysics</a> / <a class="mw-selflink selflink">Geodesy</a></li></ul></li> <li><a href="/wiki/Earth_system_science" title="Earth system science">Earth system science</a></li> <li><a href="/wiki/Geomorphology" title="Geomorphology">Geomorphology</a> / <a href="/wiki/Geology" title="Geology">Geology</a></li> <li><a href="/wiki/Glaciology" title="Glaciology">Glaciology</a></li> <li><a href="/wiki/Hydrology" title="Hydrology">Hydrology</a> / <a href="/wiki/Limnology" title="Limnology">Limnology</a></li> <li><a href="/wiki/Soil_science" title="Soil science">Soil science</a> (<a href="/wiki/Pedology" title="Pedology">Pedology</a>/<a href="/wiki/Edaphology" title="Edaphology">Edaphology</a>)</li> <li><a href="/wiki/Quaternary_science" title="Quaternary science">Quaternary science</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Technical_geography" title="Technical geography">Technical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Geodesign" title="Geodesign">Geodesign</a></li> <li><a class="mw-selflink selflink">Geodesy</a></li> <li><a href="/wiki/Geoinformatics" title="Geoinformatics">Geoinformatics</a></li> <li><a href="/wiki/Geographic_information_science" title="Geographic information science">Geographic information science</a></li> <li><a href="/wiki/Geomatics" title="Geomatics">Geomatics</a></li> <li><a href="/wiki/Statistical_geography" title="Statistical geography">Statistical geography</a></li> <li><a href="/wiki/Spatial_analysis" title="Spatial analysis">Spatial analysis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Integrated_geography" title="Integrated geography">Integrated</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Environmental_social_science" title="Environmental social science">Environmental social science</a></li> <li><a href="/wiki/Environmental_studies" title="Environmental studies">Environmental studies</a></li> <li><a href="/wiki/Landscape_architecture" title="Landscape architecture">Landscape architecture</a></li> <li><a href="/wiki/Landscape_ecology" title="Landscape ecology">Landscape ecology</a></li> <li><a href="/wiki/Time_geography" title="Time geography">Time geography</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Outline_of_geography#Tasks_and_tools_of_geography" title="Outline of geography">Techniques<br /> and tools</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks hlist navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantitative_geography" title="Quantitative geography">Quantitative</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cartography" title="Cartography">Cartography</a> <ul><li><a href="/wiki/Computer_cartography" title="Computer cartography">Computer cartography</a></li> <li><a href="/wiki/Web_mapping" title="Web mapping">Web mapping</a></li></ul></li> <li><a href="/wiki/Geochronology" title="Geochronology">Geochronology</a></li> <li><a href="/wiki/Geographic_information_system" title="Geographic information system">Geographic information system</a> <ul><li><a href="/wiki/Distributed_GIS" title="Distributed GIS">Distributed GIS</a></li> <li><a href="/wiki/Internet_GIS" title="Internet GIS">Internet GIS</a></li> <li><a href="/wiki/Web_GIS" title="Web GIS">Web GIS</a></li></ul></li> <li><a href="/wiki/Geologic_modelling" title="Geologic modelling">Geologic modelling</a></li> <li><a href="/wiki/Geomathematics" title="Geomathematics">Geomathematics</a></li> <li><a href="/wiki/Geostatistics" title="Geostatistics">Geostatistics</a></li> <li><a href="/wiki/Geovisualization" title="Geovisualization">Geovisualization</a></li> <li><a href="/wiki/Global_Positioning_System" title="Global Positioning System">Global Positioning System</a></li> <li><a href="/wiki/Hydrography" title="Hydrography">Hydrography</a></li> <li><a href="/wiki/Map_algebra" title="Map algebra">Map algebra</a></li> <li><a href="/wiki/Participant_observation" title="Participant observation">Participant observation</a></li> <li><a href="/wiki/Photogrammetry" title="Photogrammetry">Photogrammetry</a></li> <li><a href="/wiki/Remote_sensing" title="Remote sensing">Remote sensing</a></li> <li><a href="/wiki/Statistical_survey" class="mw-redirect" title="Statistical survey">Statistical survey</a></li> <li><a href="/wiki/Surveying" title="Surveying">Surveying</a></li> <li><a href="/wiki/Land_change_modeling" title="Land change modeling">Land change modeling</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Qualitative_geography" title="Qualitative geography">Qualitative</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ethnography" title="Ethnography">Ethnography</a></li> <li><a href="/wiki/Geopoetics" title="Geopoetics">Geopoetics</a></li> <li><a href="/wiki/Interview_(research)" title="Interview (research)">Interview (research)</a></li> <li><a href="/wiki/Survey_(human_research)" title="Survey (human research)">Survey (human research)</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Institutions,<br />organizations,<br />and societies</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Category:Geography_organizations" title="Category:Geography organizations"> Geography organizations</a></li> <li><a href="/wiki/Category:Geographic_data_and_information_organizations" title="Category:Geographic data and information organizations">Geographic data and information organizations</a></li> <li><a href="/wiki/List_of_geographical_societies" title="List of geographical societies">Geographical societies</a></li> <li><a href="/wiki/List_of_geoscience_organizations" title="List of geoscience organizations">Geoscience societies</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Geography_education" title="Category:Geography education">Education</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Geo-literacy" title="Geo-literacy">Geo-literacy</a></li> <li><a href="/wiki/Geographers_on_Film" title="Geographers on Film">Geographers on Film</a></li> <li><a href="/wiki/International_Geography_Olympiad" title="International Geography Olympiad">International Geography Olympiad</a></li> <li><a href="/wiki/National_Council_for_Geographic_Education" title="National Council for Geographic Education">National Council for Geographic Education</a></li> <li><a href="/wiki/Spatial_citizenship" title="Spatial citizenship">Spatial citizenship</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Geographic_literature" title="Category:Geographic literature">Publication</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Category:Geography_books" title="Category:Geography books">Geography books</a></li> <li><a href="/wiki/Category:Geography_journals" title="Category:Geography journals">Geography journals</a></li> <li><a href="/wiki/Category:Geographic_magazines" title="Category:Geographic magazines">Geographic magazines</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a href="/wiki/Category:Geography" title="Category:Geography">Category</a></b></li> <li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Symbol_portal_class.svg" class="mw-file-description" title="Portal"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/20px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/e2/Symbol_portal_class.svg/40px-Symbol_portal_class.svg.png 1.5x" data-file-width="180" data-file-height="185" /></a></span> <b><a href="/wiki/Portal:Geography" title="Portal:Geography">Portal</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Geography" class="extiw" title="commons:Category:Geography">Commons</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="WikiProject"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/16px-People_icon.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/24px-People_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/32px-People_icon.svg.png 2x" data-file-width="100" data-file-height="100" /></span></span> <b><a href="/wiki/Wikipedia:WikiProject_Geography" title="Wikipedia:WikiProject Geography">WikiProject</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Geology518" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Geology" title="Template:Geology"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Geology" title="Template talk:Geology"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Geology" title="Special:EditPage/Template:Geology"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Geology518" style="font-size:114%;margin:0 4em"><a href="/wiki/Geology" title="Geology">Geology</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Overviews</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Outline_of_geology" title="Outline of geology">Outline of geology</a></li> <li><a href="/wiki/Glossary_of_geology" title="Glossary of geology">Glossary of geology</a></li> <li><a href="/wiki/History_of_geology" title="History of geology">History of geology</a></li> <li><a href="/wiki/Index_of_geology_articles" title="Index of geology articles">Index of geology articles</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/History_of_geology" title="History of geology">History of geology</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Geochronology" title="Geochronology">Geochronology</a></li> <li><a href="/wiki/Geological_history_of_Earth" title="Geological history of Earth">Geological history of Earth</a></li> <li><a href="/wiki/Timeline_of_geology" title="Timeline of geology">Timeline of geology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Composition and structure</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cosmochemistry" title="Cosmochemistry">Cosmochemistry</a></li> <li><a href="/wiki/Crystallography" title="Crystallography">Crystallography</a></li> <li><a href="/wiki/Geochemistry" title="Geochemistry">Geochemistry</a></li> <li><a href="/wiki/Mineralogy" title="Mineralogy">Mineralogy</a></li> <li><a href="/wiki/Petrology" title="Petrology">Petrology</a></li> <li><a href="/wiki/Sedimentology" title="Sedimentology">Sedimentology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Historical_geology" title="Historical geology">Historical geology</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Stratigraphy" title="Stratigraphy">Stratigraphy</a></li> <li><a href="/wiki/Paleontology" title="Paleontology">Paleontology</a></li> <li><a href="/wiki/Paleoclimatology" title="Paleoclimatology">Paleoclimatology</a></li> <li><a href="/wiki/Palaeogeography" title="Palaeogeography">Palaeogeography</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Dynamic Earth</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Structural_geology" title="Structural geology">Structural geology</a></li> <li><a href="/wiki/Geodynamics" title="Geodynamics">Geodynamics</a></li> <li><a href="/wiki/Plate_tectonics" title="Plate tectonics">Plate tectonics</a></li> <li><a href="/wiki/Geomorphology" title="Geomorphology">Geomorphology</a></li> <li><a href="/wiki/Volcanology" title="Volcanology">Volcanology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Water</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Glaciology" title="Glaciology">Glaciology</a></li> <li><a href="/wiki/Hydrogeology" title="Hydrogeology">Hydrogeology</a></li> <li><a href="/wiki/Marine_geology" title="Marine geology">Marine geology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Geodesy</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cartography" title="Cartography">Cartography</a></li> <li><a href="/wiki/Earth%27s_orbit" title="Earth's orbit">Earth's orbit</a></li> <li><a href="/wiki/Geodetic_astronomy" title="Geodetic astronomy">Geodetic astronomy</a></li> <li><a href="/wiki/Geomatics" title="Geomatics">Geomatics</a></li> <li><a href="/wiki/Gravity_of_Earth" title="Gravity of Earth">Gravity of Earth</a></li> <li><a href="/wiki/Planetary_science#Planetary_geodesy" title="Planetary science">Planetary geodesy</a></li> <li><a href="/wiki/Remote_sensing" title="Remote sensing">Remote sensing</a></li> <li><a href="/wiki/Geopositioning" title="Geopositioning">Geopositioning</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Geophysics" title="Geophysics">Geophysics</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Geomagnetism" class="mw-redirect" title="Geomagnetism">Geomagnetism</a></li> <li><a href="/wiki/Geophysical_survey" title="Geophysical survey">Geophysical survey</a></li> <li><a href="/wiki/Planetary_science#Planetary_Geophysics_and_Space_Physics" title="Planetary science">Planetary geophysics</a></li> <li><a href="/wiki/Seismology" title="Seismology">Seismology</a></li> <li><a href="/wiki/Tectonophysics" title="Tectonophysics">Tectonophysics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applications</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biogeology" title="Biogeology">Biogeology</a></li> <li><a href="/wiki/Economic_geology" title="Economic geology">Economic geology</a></li> <li><a href="/wiki/Engineering_geology" title="Engineering geology">Engineering geology</a></li> <li><a href="/wiki/Environmental_geology" title="Environmental geology">Environmental geology</a></li> <li><a href="/wiki/Planetary_geology" title="Planetary geology">Planetary geology</a></li> <li><a href="/wiki/Geobiology" title="Geobiology">Geobiology</a></li> <li><a href="/wiki/Geologic_modelling" title="Geologic modelling">Geologic modelling</a></li> <li><a href="/wiki/Forensic_geology" title="Forensic geology">Forensic geology</a></li> <li><a href="/wiki/Forensic_geophysics" title="Forensic geophysics">Forensic geophysics</a></li> <li><a href="/wiki/Meteoritics" title="Meteoritics">Meteoritics</a></li> <li><a href="/wiki/Mining_geology" title="Mining geology">Mining geology</a></li> <li><a href="/wiki/Mineral_physics" title="Mineral physics">Mineral physics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Occupations</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Geologist" title="Geologist">Geologist</a></li> <li><a href="/wiki/Petroleum_geologist" title="Petroleum geologist">Petroleum geologist</a></li> <li><a href="/wiki/Volcanologist" title="Volcanologist">Volcanologist</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="2"><div> <ul><li><b><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:WikiProject_Geology.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/WikiProject_Geology.svg/20px-WikiProject_Geology.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/WikiProject_Geology.svg/40px-WikiProject_Geology.svg.png 1.5x" data-file-width="327" data-file-height="328" /></a></span> </span><a href="/wiki/Portal:Geology" title="Portal:Geology">Geology portal</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a href="/wiki/Category:Geology" title="Category:Geology">Geology</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="WikiProject"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/16px-People_icon.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/24px-People_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/32px-People_icon.svg.png 2x" data-file-width="100" data-file-height="100" /></span></span> <b><a href="/wiki/Wikipedia:Geology" class="mw-redirect" title="Wikipedia:Geology">Geology</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Major_branches_of_physics48" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Branches_of_physics" title="Template:Branches of physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Branches_of_physics" title="Template talk:Branches of physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Branches_of_physics" title="Special:EditPage/Template:Branches of physics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Major_branches_of_physics48" style="font-size:114%;margin:0 4em">Major <a href="/wiki/Branches_of_physics" title="Branches of physics">branches of physics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Divisions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Basic_research" title="Basic research">Pure</a></li> <li><a href="/wiki/Applied_physics" title="Applied physics">Applied</a> <ul><li><a href="/wiki/Engineering_physics" title="Engineering physics">Engineering</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Approaches</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Experimental_physics" title="Experimental physics">Experimental</a></li> <li><a href="/wiki/Theoretical_physics" title="Theoretical physics">Theoretical</a> <ul><li><a href="/wiki/Computational_physics" title="Computational physics">Computational</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Classical_physics" title="Classical physics">Classical</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a> <ul><li><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newtonian</a></li> <li><a href="/wiki/Analytical_mechanics" title="Analytical mechanics">Analytical</a></li> <li><a href="/wiki/Celestial_mechanics" title="Celestial mechanics">Celestial</a></li> <li><a href="/wiki/Continuum_mechanics" title="Continuum mechanics">Continuum</a></li></ul></li> <li><a href="/wiki/Acoustics" title="Acoustics">Acoustics</a></li> <li><a href="/wiki/Classical_electromagnetism" title="Classical electromagnetism">Classical electromagnetism</a></li> <li><a href="/wiki/Classical_optics" class="mw-redirect" title="Classical optics">Classical optics</a> <ul><li><a href="/wiki/Geometrical_optics" title="Geometrical optics">Ray</a></li> <li><a href="/wiki/Physical_optics" title="Physical optics">Wave</a></li></ul></li> <li><a href="/wiki/Thermodynamics" title="Thermodynamics">Thermodynamics</a> <ul><li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical</a></li> <li><a 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