Editing Geodesy (section)

== Geoid and reference ellipsoid ==
{{main|Geoid|Reference ellipsoid}}
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[[File:Geoid undulation 10k scale.jpg|220px|thumb|right|[[Geoid]], an approximation for the shape of the [[Earth]]; shown here with [[vertical exaggeration]] (10000 vertical scaling factor).]]
[[File:Surface of latitude ellipsoid cone.gif|220px|thumb|right|[[Ellipsoid]] - a mathematical representation of the [[Earth]]. When mapping in geodetic coordinates, a latitude circle forms a truncated cone.]]
[[File:WGS84_mean_Earth_radius.svg|thumb|upright=1.0|Equatorial ({{mvar|a}}), polar ({{mvar|b}}) and mean Earth radii as defined in the 1984 [[World Geodetic System]]]]

The [[geoid]] essentially is the figure of Earth abstracted from its [[Topography|topographical]] features. It is an idealized equilibrium surface of [[seawater]], the [[mean sea level]] surface in the absence of [[Ocean current|currents]] and [[Atmospheric pressure|air pressure]] variations, and continued under the continental masses. Unlike a [[reference ellipsoid]], the geoid is irregular and too complicated to serve as the computational [[Surface (mathematics)|surface]] for solving geometrical problems like point positioning. The geometrical separation between the geoid and a reference ellipsoid is called ''geoidal [[wiktionary:undulate|undulation]]'', and it varies globally between ±110 m based on the GRS 80 ellipsoid.

A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) ''a'' and flattening ''f''. The quantity ''f'' = {{sfrac|''a'' − ''b''|''a''}}, where ''b'' is the semi-minor axis (polar radius), is purely geometrical. The mechanical [[Flattening|ellipticity]] of Earth (dynamical flattening, symbol ''J''<sub>2</sub>) can be determined to high precision by observation of satellite [[Orbital perturbation analysis|orbit perturbations]]. 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.

The 1980 Geodetic Reference System ([[GRS80|GRS 80]]), adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics ([[IUGG]]), 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 [[Global Positioning System]] (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.

The geoid is a "realizable" surface, meaning it can be consistently located on Earth by suitable simple measurements from physical objects like a [[tide gauge]]. 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 [[Terrain|topographic surface]] of Earth — is also realizable.