Editing Geodetic datum (section)

== Earth reference ellipsoid ==
{{main|Reference ellipsoid}}

=== Defining and derived parameters ===
{{further|Reference ellipsoid#Ellipsoid parameters}}

The ellipsoid is completely parameterised by the semi-major axis <math>a</math> and the flattening <math>f</math>.

{| class="wikitable"
! Parameter
! Symbol
|-
| Semi-major axis
| <math>a</math>
|-
| Reciprocal of flattening
| <math>\frac{1}{f}</math>
|}

From <math>a</math> and <math>f</math> it is possible to derive the semi-minor axis <math>b</math>, first eccentricity <math>e</math> and second eccentricity <math>e'</math> of the ellipsoid

{| class="wikitable"
! Parameter
! Value
|-
| Semi-minor axis
| <math>b = a(1 - f)</math>
|-
| First eccentricity squared
| <math>e^2 = 1 - \frac{b^2}{a^2} = f(2 - f)</math>
|-
| Second eccentricity squared
| <math>{e'}^2 = \frac{a^2}{b^2} - 1 = \frac{f(2 - f)}{(1 - f)^2}</math>
|}

=== Parameters for some geodetic systems ===
{{Main|Earth ellipsoid#Historical Earth ellipsoids}}

The two main reference ellipsoids used worldwide are the GRS{{nbsp}}80<ref>{{Cite web |url=http://www.icsm.gov.au/gda/gda-v_2.4.pdf |title=Geocentric Datum of Australia Technical Manual |date=2 December 2014 |website=Intergovernmental Committee on Surveying and Mapping |access-date=2017-02-20 |archive-url=https://web.archive.org/web/20180320125650/http://www.icsm.gov.au/gda/gda-v_2.4.pdf |archive-date=2018-03-20 |url-status=dead }}</ref>
and the WGS{{nbsp}}84.<ref>{{Cite web |url=http://earth-info.nga.mil/GandG/publications/tr8350.2/tr8350_2.html |title= NGA: DoD World Geodetic System 1984  |access-date=2007-03-01 |archive-date=2017-07-04 |archive-url=https://web.archive.org/web/20170704192233/http://earth-info.nga.mil/GandG/publications/tr8350.2/tr8350_2.html |url-status=dead }}</ref>

A more comprehensive list of geodetic systems can be found [http://www.geo.upm.es/postgrado/CarlosLopez/materiales/cursos/www.ncgia.ucsb.edu/education/curricula/giscc/units/u015/tables/table01.html here].

==== Geodetic Reference System 1980 (GRS{{nbsp}}80) ====

{| class="wikitable"
|+ GRS{{nbsp}}80 parameters
! Parameter
! Notation
! Value
|-
| Semi-major axis
| <math>a</math>
| {{val|6378137|u=m}}
|-
| Reciprocal of flattening
| <math>\frac{1}{f}</math>
| {{val|298.257222101}}
|}

==== World Geodetic System 1984 (WGS{{nbsp}}84) ====

The Global Positioning System (GPS) uses the World Geodetic System 1984 (WGS{{nbsp}}84) to determine the location of a point near the surface of Earth.

{| class="wikitable"
|+ WGS{{nbsp}}84 defining parameters
! Parameter
! Notation
! Value
|-
| Semi-major axis
| <math>a</math>
| {{val|6378137.0|u=m}}
|-
| Reciprocal of flattening
| <math>\frac{1}{f}</math>
| {{val|298.257223563}}
|}

{| class="wikitable"
|+ WGS{{nbsp}}84 derived geometric constants
! Constant
! Notation
! Value
|-
| Semi-minor axis
| <math>b</math>
| {{val|6356752.3142|u=m}}
|-
| First eccentricity squared
| <math>e^2</math>
| {{val|6.69437999014|e=−3}}
|-
| Second eccentricity squared
| <math>{e'}^2</math>
| {{val|6.73949674228|e=−3}}
|}