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lang="da" hreflang="da" data-title="GRS 80" 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%A4tisches_Referenzsystem_1980" title="Geodätisches Referenzsystem 1980 – German" lang="de" hreflang="de" data-title="Geodätisches Referenzsystem 1980" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B3%D8%A7%D9%85%D8%A7%D9%86%D9%87_%D9%85%D8%B1%D8%AC%D8%B9_%DA%98%D8%A6%D9%88%D8%AF%D8%AA%DB%8C%DA%A9_%DB%B1%DB%B9%DB%B8%DB%B0" title="سامانه مرجع ژئودتیک ۱۹۸۰ – Persian" lang="fa" hreflang="fa" data-title="سامانه مرجع ژئودتیک ۱۹۸۰" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/GRS-80" title="GRS-80 – Icelandic" lang="is" hreflang="is" data-title="GRS-80" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/GRS80" title="GRS80 – Dutch" lang="nl" hreflang="nl" data-title="GRS80" 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/GRS80" title="GRS80 – Japanese" lang="ja" hreflang="ja" data-title="GRS80" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/System_odniesienia_GRS_80" title="System odniesienia GRS 80 – Polish" lang="pl" hreflang="pl" data-title="System odniesienia GRS 80" 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/GRS_80" title="GRS 80 – Portuguese" lang="pt" hreflang="pt" data-title="GRS 80" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/GRS80" title="GRS80 – Russian" lang="ru" hreflang="ru" data-title="GRS80" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a 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.sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .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 href="/wiki/Geodesy" title="Geodesy">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 href="/wiki/Geodesy" title="Geodesy">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>The <b>Geodetic Reference System 1980</b> (<b>GRS80</b>) consists of a global <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">reference ellipsoid</a> and a <a href="/wiki/Normal_gravity" class="mw-redirect" title="Normal gravity">normal gravity</a> model.<sup id="cite_ref-Moritz1980_1-0" class="reference"><a href="#cite_note-Moritz1980-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Moritz1992_2-0" class="reference"><a href="#cite_note-Moritz1992-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Moritz2000_3-0" class="reference"><a href="#cite_note-Moritz2000-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The GRS80 gravity model has been followed by the newer more accurate <a href="/wiki/Earth_Gravitational_Model" title="Earth Gravitational Model">Earth Gravitational Models</a>, but the <b>GRS80 reference ellipsoid</b> is still the most accurate in use for <a href="/wiki/Coordinate_reference_system" class="mw-redirect" title="Coordinate reference system">coordinate reference systems</a>, e.g. for the international <a href="/wiki/International_Terrestrial_Reference_System_and_Frame" title="International Terrestrial Reference System and Frame">ITRS</a>, the European <a href="/wiki/European_Terrestrial_Reference_System_1989" title="European Terrestrial Reference System 1989">ETRS89</a> and (with a 0,1 mm rounding error) for <a href="/wiki/World_Geodetic_System" title="World Geodetic System">WGS 84</a> used for the American <a href="/wiki/Satellite_navigation" title="Satellite navigation">Global Navigation Satellite System</a> (<a href="/wiki/Global_Positioning_System" title="Global Positioning System">GPS</a>). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Background">Background</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodetic_Reference_System_1980&action=edit&section=1" title="Edit section: Background"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Geodesy" title="Geodesy">Geodesy</a> is the scientific discipline that deals with the measurement and representation of the <a href="/wiki/Earth" title="Earth">earth</a>, its <a href="/wiki/Gravitation" class="mw-redirect" title="Gravitation">gravitational</a> field and geodynamic phenomena (<a href="/wiki/Polar_motion" title="Polar motion">polar motion</a>, earth <a href="/wiki/Tide" title="Tide">tides</a>, and crustal motion) in three-dimensional, time-varying space. </p><p>The <a href="/wiki/Geoid" title="Geoid">geoid</a> is essentially the figure of the Earth abstracted from its topographic features. It is an idealized equilibrium surface of sea water, the mean sea level surface in the absence of currents, air pressure variations etc. and continued under the continental masses. The geoid, unlike the ellipsoid, is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning. The geometrical separation between it and the reference ellipsoid is called the geoidal <a href="https://en.wiktionary.org/wiki/undulation" class="extiw" title="wiktionary:undulation">undulation</a>, or more usually the geoid-ellipsoid separation, <i>N</i>. It varies globally between <span class="nowrap"><span data-sort-value="7002110000000000000♠"></span>±110 m</span>. </p><p>A <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">reference ellipsoid</a>, 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> = (<i>a</i>−<i>b</i>)/<i>a</i>, where <i>b</i> is the semi-minor axis (polar radius), is a purely geometrical one. The mechanical ellipticity of the earth (dynamical flattening, symbol <i>J</i><sub>2</sub>) is determined to high precision by observation of satellite orbit perturbations. Its relationship with the geometric flattening is indirect. The relationship depends on the internal density distribution. </p><p>The 1980 Geodetic Reference System (GRS 80) posited a <span class="nowrap"><span data-sort-value="7006637813700000000♠"></span>6<span style="margin-left:.25em;">378</span><span style="margin-left:.25em;">137</span> m</span> semi-major axis and a <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.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="frac"><span class="num">1</span>⁄<span class="den">298.257222101</span></span> flattening. This system was 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>) in Canberra, Australia, 1979. </p><p>The GRS 80 reference system was originally used by the <a href="/wiki/WGS_84" class="mw-redirect" title="WGS 84">World Geodetic System 1984</a> (WGS 84). The reference ellipsoid of WGS 84 now differs slightly due to later refinements.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (May 2024)">citation needed</span></a></i>]</sup> </p><p>The numerous other systems which have been used by diverse countries for their maps and charts are gradually dropping out of use as more and more countries move to global, geocentric reference systems using the GRS80 reference ellipsoid. </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=Geodetic_Reference_System_1980&action=edit&section=2" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The reference ellipsoid is usually defined by its <a href="/wiki/Semi-major_axis" class="mw-redirect" title="Semi-major axis">semi-major axis</a> (equatorial radius) <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> and either its <a href="/wiki/Semi-minor_axis" class="mw-redirect" title="Semi-minor axis">semi-minor axis</a> (polar radius) <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span>, <a href="/wiki/Aspect_ratio" title="Aspect ratio">aspect ratio</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (b/a)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>a</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (b/a)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2983db16441b48aa0b728f1cab7514acf6fec8d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.199ex; height:2.843ex;" alt="{\displaystyle (b/a)}"></span> or <a href="/wiki/Flattening" title="Flattening">flattening</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span>, but GRS80 is an exception: <i>four</i> independent constants are required for a complete definition. GRS80 chooses as these <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle GM}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle GM}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2d9b5427dc6e6f3c11f13d88a5b637b4bc24585" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.269ex; height:2.176ex;" alt="{\displaystyle GM}"></span>, <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 J_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f9986a8fbfd51097a5ff5e82d3252c9572b5835" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.344ex; height:2.509ex;" alt="{\displaystyle J_{2}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span>, making the geometrical constant <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> a derived quantity. </p> <dl><dt>Defining <a href="/wiki/Geometrical" class="mw-redirect" title="Geometrical">geometrical</a> <a href="/wiki/Constant_(mathematics)" title="Constant (mathematics)">constants</a></dt> <dd>Semi-major axis = Equatorial Radius = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=6\,378\,137\,\mathrm {m} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mn>6</mn> <mspace width="thinmathspace" /> <mn>378</mn> <mspace width="thinmathspace" /> <mn>137</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=6\,378\,137\,\mathrm {m} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8760a3fbffa309ed6e5d3c628abd68104499816a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:15.563ex; height:2.176ex;" alt="{\displaystyle a=6\,378\,137\,\mathrm {m} }"></span>;</dd></dl> <dl><dt>Defining <a href="/wiki/Nature" title="Nature">physical</a> <a href="/wiki/Constant_(mathematics)" title="Constant (mathematics)">constants</a></dt> <dd><a href="/wiki/Geocentric_gravitational_constant" class="mw-redirect" title="Geocentric gravitational constant">Geocentric gravitational constant</a> determined from the <a href="/wiki/Gravitational_constant" title="Gravitational constant">gravitational constant</a> and the <a href="/wiki/Earth_mass" title="Earth mass">earth mass</a> with atmosphere <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle GM=3986005\times 10^{8}\,\mathrm {m^{3}/s^{2}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mi>M</mi> <mo>=</mo> <mn>3986005</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi mathvariant="normal">m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <msup> <mi mathvariant="normal">s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle GM=3986005\times 10^{8}\,\mathrm {m^{3}/s^{2}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9322da6446dc48bb5c0b693e0ceb3ff6892bcf6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.234ex; height:3.176ex;" alt="{\displaystyle GM=3986005\times 10^{8}\,\mathrm {m^{3}/s^{2}} }"></span>;</dd> <dd>Dynamical form factor <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 J_{2}=108\,263\times 10^{-8}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>108</mn> <mspace width="thinmathspace" /> <mn>263</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>8</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J_{2}=108\,263\times 10^{-8}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d72ad089763758fac52d3b2fad355d5f43aaa194" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.303ex; height:3.009ex;" alt="{\displaystyle J_{2}=108\,263\times 10^{-8}}"></span>;</dd> <dd>Angular velocity of rotation <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 \omega =7\,292\,115\times 10^{-11}\,\mathrm {s^{-1}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>=</mo> <mn>7</mn> <mspace width="thinmathspace" /> <mn>292</mn> <mspace width="thinmathspace" /> <mn>115</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>11</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi mathvariant="normal">s</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega =7\,292\,115\times 10^{-11}\,\mathrm {s^{-1}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3046c48357e6626db9c8fc2dbb1df9c3902427e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:25.412ex; height:2.676ex;" alt="{\displaystyle \omega =7\,292\,115\times 10^{-11}\,\mathrm {s^{-1}} }"></span>;</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Derived_quantities">Derived quantities</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geodetic_Reference_System_1980&action=edit&section=3" title="Edit section: Derived quantities"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dt>Derived geometrical constants (all rounded)</dt> <dd>Flattening = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> = 0.003 352 810 681 183 637 418;</dd> <dd>Reciprocal of flattening = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1/f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9cd0e60c02ddf533da2abed825389fe5a94b7d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.603ex; height:2.843ex;" alt="{\displaystyle 1/f}"></span> = 298.257 222 100 882 711 243;</dd> <dd>Semi-minor axis = Polar Radius = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> = 6 356 752.314 140 347 m;</dd> <dd>Aspect ratio = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b/a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b/a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e0082708c4a962619f1b493a22dc776b5fbab62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.39ex; height:2.843ex;" alt="{\displaystyle b/a}"></span> = 0.996 647 189 318 816 363;</dd> <dd><a href="/wiki/Earth_radius#Mean_radius:_R1" title="Earth radius">Mean radius</a> as defined by the <a href="/wiki/International_Union_of_Geodesy_and_Geophysics" title="International Union of Geodesy and Geophysics">International Union of Geodesy and Geophysics</a> (IUGG): <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{1}=(2a+b)/3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{1}=(2a+b)/3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd0e7b4af4e91123d962b74e42ce1ac836ccc938" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.281ex; height:2.843ex;" alt="{\displaystyle R_{1}=(2a+b)/3}"></span> = 6 371 008.7714 m;</dd> <dd><a href="/wiki/Earth_radius#Authalic_radius" title="Earth radius">Authalic mean radius</a> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35f571121c264178676d1df8ab899f238a39bc2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:2.509ex;" alt="{\displaystyle R_{2}}"></span> = 6 371 007.1809 m;</dd> <dd>Radius of a sphere of the same volume = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{3}=(a^{2}b)^{1/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>b</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{3}=(a^{2}b)^{1/3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6867aa92ab728e101285a26cd66cf96a1e3f4df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.706ex; height:3.343ex;" alt="{\displaystyle R_{3}=(a^{2}b)^{1/3}}"></span> = 6 371 000.7900 m;</dd> <dd>Linear eccentricity = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c={\sqrt {a^{2}-b^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c={\sqrt {a^{2}-b^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78a9d2e194c630274028a18c59e4289981aad14d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.605ex; height:3.509ex;" alt="{\displaystyle c={\sqrt {a^{2}-b^{2}}}}"></span> = 521 854.0097 m;</dd> <dd><a href="/wiki/Eccentricity_(mathematics)" title="Eccentricity (mathematics)">Eccentricity</a> of elliptical section through poles = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e={\frac {\sqrt {a^{2}-b^{2}}}{a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> <mi>a</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e={\frac {\sqrt {a^{2}-b^{2}}}{a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e547110997537f86ccb70c751df83b3b0959979" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.518ex; height:6.176ex;" alt="{\displaystyle e={\frac {\sqrt {a^{2}-b^{2}}}{a}}}"></span> = 0.081 819 191 0428;</dd> <dd>Polar radius of curvature = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{2}/b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}/b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97fcf4793890bb6162d22bc30ce3e3efe05ef407" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.444ex; height:3.176ex;" alt="{\displaystyle a^{2}/b}"></span> = 6 399 593.6259 m;</dd> <dd>Equatorial radius of curvature for a meridian = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b^{2}/a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b^{2}/a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7d021205fa73cc0e482b5ea56e635efc7573670" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.444ex; height:3.176ex;" alt="{\displaystyle b^{2}/a}"></span> = 6 335 439.3271 m;</dd> <dd>Meridian quadrant = 10 001 965.7292 m;</dd></dl> <dl><dt>Derived physical constants (rounded)</dt> <dd>Period of rotation (<a href="/wiki/Sidereal_day" class="mw-redirect" title="Sidereal day">sidereal day</a>) = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\pi /\omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\pi /\omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d0bc1e95b72696502acf4d7c3116fb6d4918167" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.103ex; height:2.843ex;" alt="{\displaystyle 2\pi /\omega }"></span> = 86 164.100 637 s</dd></dl> <p>The formula giving the eccentricity of the GRS80 spheroid is:<sup id="cite_ref-Moritz1980_1-1" class="reference"><a href="#cite_note-Moritz1980-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{2}={\frac {a^{2}-b^{2}}{a^{2}}}=3J_{2}+{\frac {4}{15}}{\frac {\omega ^{2}a^{3}}{GM}}{\frac {e^{3}}{2q_{0}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mn>3</mn> <msub> <mi>J</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>15</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <mrow> <mi>G</mi> <mi>M</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow> <mn>2</mn> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{2}={\frac {a^{2}-b^{2}}{a^{2}}}=3J_{2}+{\frac {4}{15}}{\frac {\omega ^{2}a^{3}}{GM}}{\frac {e^{3}}{2q_{0}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec9228a5fe7dd71621db58474d33b2a19e6a6ea9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:36.212ex; height:6.176ex;" alt="{\displaystyle e^{2}={\frac {a^{2}-b^{2}}{a^{2}}}=3J_{2}+{\frac {4}{15}}{\frac {\omega ^{2}a^{3}}{GM}}{\frac {e^{3}}{2q_{0}}},}"></span></dd></dl> <p>where </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 2q_{0}=\left(1+{\frac {3}{e'^{2}}}\right)\arctan e'-{\frac {3}{e'}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <msup> <mi>e</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mi>arctan</mi> <mo>⁡</mo> <msup> <mi>e</mi> <mo>′</mo> </msup> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <msup> <mi>e</mi> <mo>′</mo> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2q_{0}=\left(1+{\frac {3}{e'^{2}}}\right)\arctan e'-{\frac {3}{e'}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f05d5750e444804439cdd09fed99ca138cd6112e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:31.656ex; height:6.176ex;" alt="{\displaystyle 2q_{0}=\left(1+{\frac {3}{e'^{2}}}\right)\arctan e'-{\frac {3}{e'}}}"></span></dd></dl> <p>and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e'={\frac {e}{\sqrt {1-e^{2}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>e</mi> <msqrt> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e'={\frac {e}{\sqrt {1-e^{2}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36444e3fa774e4603d205d20bdde6598db5ef3dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:14.167ex; height:6.009ex;" alt="{\displaystyle e'={\frac {e}{\sqrt {1-e^{2}}}}}"></span> (so <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 \arctan e'=\arcsin e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>arctan</mi> <mo>⁡</mo> <msup> <mi>e</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>arcsin</mi> <mo>⁡</mo> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \arctan e'=\arcsin e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74e3805a1887326870253c43c8d76d0111fbd02b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:19.153ex; height:2.509ex;" alt="{\displaystyle \arctan e'=\arcsin e}"></span>). The equation is solved iteratively to give </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 e^{2}=0.00669\,43800\,22903\,41574\,95749\,48586\,28930\,62124\,43890\,\ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0.00669</mn> <mspace width="thinmathspace" /> <mn>43800</mn> <mspace width="thinmathspace" /> <mn>22903</mn> <mspace width="thinmathspace" /> <mn>41574</mn> <mspace width="thinmathspace" /> <mn>95749</mn> <mspace width="thinmathspace" /> <mn>48586</mn> <mspace width="thinmathspace" /> <mn>28930</mn> <mspace width="thinmathspace" /> <mn>62124</mn> <mspace width="thinmathspace" /> <mn>43890</mn> <mspace width="thinmathspace" /> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{2}=0.00669\,43800\,22903\,41574\,95749\,48586\,28930\,62124\,43890\,\ldots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cc86fc0449d56ac572ea6abb378449ea4cc566b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:65.95ex; height:2.676ex;" alt="{\displaystyle e^{2}=0.00669\,43800\,22903\,41574\,95749\,48586\,28930\,62124\,43890\,\ldots }"></span></dd></dl> <p>which gives </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 f=1/298.25722\,21008\,82711\,24316\,28366\,\ldots .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>298.25722</mn> <mspace width="thinmathspace" /> <mn>21008</mn> <mspace width="thinmathspace" /> <mn>82711</mn> <mspace width="thinmathspace" /> <mn>24316</mn> <mspace width="thinmathspace" /> <mn>28366</mn> <mspace width="thinmathspace" /> <mo>…</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f=1/298.25722\,21008\,82711\,24316\,28366\,\ldots .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea09319343f9ed2c6a6619b426ba47a86bebc01d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:45.977ex; height:2.843ex;" alt="{\displaystyle f=1/298.25722\,21008\,82711\,24316\,28366\,\ldots .}"></span></dd></dl> <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=Geodetic_Reference_System_1980&action=edit&section=4" 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"><ol class="references"> <li id="cite_note-Moritz1980-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Moritz1980_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Moritz1980_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFMoritz1980" class="citation journal cs1"><a href="/wiki/Helmut_Moritz" title="Helmut Moritz">Moritz, Helmut</a> (September 1980). <a rel="nofollow" class="external text" href="http://geoweb.mit.edu/~tah/12.221_2005/grs80_corr.pdf">"Geodetic Reference System 1980"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Bulletin_G%C3%A9od%C3%A9sique" class="mw-redirect" title="Bulletin Géodésique">Bulletin Géodésique</a></i>. <b>54</b> (3): 395–405. <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/1980BGeod..54..395M">1980BGeod..54..395M</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%2FBF02521480">10.1007/BF02521480</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:198209711">198209711</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+G%C3%A9od%C3%A9sique&rft.atitle=Geodetic+Reference+System+1980&rft.volume=54&rft.issue=3&rft.pages=395-405&rft.date=1980-09&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A198209711%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1007%2FBF02521480&rft_id=info%3Abibcode%2F1980BGeod..54..395M&rft.aulast=Moritz&rft.aufirst=Helmut&rft_id=http%3A%2F%2Fgeoweb.mit.edu%2F~tah%2F12.221_2005%2Fgrs80_corr.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodetic+Reference+System+1980" class="Z3988"></span></span> </li> <li id="cite_note-Moritz1992-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Moritz1992_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoritz1992" class="citation journal cs1"><a href="/wiki/Helmut_Moritz" title="Helmut Moritz">Moritz, H.</a> (1992). "Geodetic Reference System 1980". <i>Bulletin Géodésique</i>. <b>66</b> (2). Springer Science and Business Media LLC: 187–192. <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/1992BGeod..66..187M">1992BGeod..66..187M</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%2Fbf00989270">10.1007/bf00989270</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0007-4632">0007-4632</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:122916060">122916060</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+G%C3%A9od%C3%A9sique&rft.atitle=Geodetic+Reference+System+1980&rft.volume=66&rft.issue=2&rft.pages=187-192&rft.date=1992&rft_id=info%3Adoi%2F10.1007%2Fbf00989270&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A122916060%23id-name%3DS2CID&rft.issn=0007-4632&rft_id=info%3Abibcode%2F1992BGeod..66..187M&rft.aulast=Moritz&rft.aufirst=H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodetic+Reference+System+1980" class="Z3988"></span></span> </li> <li id="cite_note-Moritz2000-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Moritz2000_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoritz2000" class="citation journal cs1"><a href="/wiki/Helmut_Moritz" title="Helmut Moritz">Moritz, Helmut</a> (March 2000). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160220054607/https://geodesy.geology.ohio-state.edu/course/refpapers/00740128.pdf">"Geodetic Reference System 1980"</a> <span class="cs1-format">(PDF)</span>. <i>Journal of Geodesy</i>. <b>74</b> (1): 128–162. <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%2FS001900050278">10.1007/S001900050278</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:195290884">195290884</a>. Archived from <a rel="nofollow" class="external text" href="https://geodesy.geology.ohio-state.edu/course/refpapers/00740128.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2016-02-20<span class="reference-accessdate">. Retrieved <span class="nowrap">2018-12-15</span></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=Geodetic+Reference+System+1980&rft.volume=74&rft.issue=1&rft.pages=128-162&rft.date=2000-03&rft_id=info%3Adoi%2F10.1007%2FS001900050278&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A195290884%23id-name%3DS2CID&rft.aulast=Moritz&rft.aufirst=Helmut&rft_id=https%3A%2F%2Fgeodesy.geology.ohio-state.edu%2Fcourse%2Frefpapers%2F00740128.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeodetic+Reference+System+1980" class="Z3988"></span></span> </li> </ol></div></div> <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=Geodetic_Reference_System_1980&action=edit&section=5" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20051225213554/http://www.gfy.ku.dk/~iag/HB2000/part4/grs80_corr.htm">GRS 80 Specification</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Geodetic_Reference_System_1980&oldid=1242002396">https://en.wikipedia.org/w/index.php?title=Geodetic_Reference_System_1980&oldid=1242002396</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a href="/wiki/Category:Geodesy" title="Category:Geodesy">Geodesy</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Articles_needing_additional_references_from_February_2009" title="Category:Articles needing additional references from February 2009">Articles needing additional references from February 2009</a></li><li><a href="/wiki/Category:All_articles_needing_additional_references" title="Category:All articles needing additional references">All articles needing additional references</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_May_2024" title="Category:Articles with unsourced statements from May 2024">Articles with unsourced statements from May 2024</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 24 August 2024, at 12:07<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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