An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations.
It is a spheroid (an ellipsoid of revolution) whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation. The ellipsoid is defined by the equatorial axis (a) and the polar axis (b); their radial difference is slightly more than 21 km, or 0.335% of a (which is not quite 6,400 km).
Many methods exist for determination of the axes of an Earth ellipsoid, ranging from meridian arcs up to modern satellite geodesy or the analysis and interconnection of continental geodetic networks. Amongst the different set of data used in national surveys are several of special importance: the Bessel ellipsoid of 1841, the international Hayford ellipsoid of 1924, and (for GPS positioning) the WGS84 ellipsoid.
There are two types of ellipsoid: mean and reference.
A data set which describes the global average of the Earth's surface curvature is called the mean Earth Ellipsoid. It refers to a theoretical coherence between the geographic latitude and the meridional curvature of the geoid. The latter is close to the mean sea level, and therefore an ideal Earth ellipsoid has the same volume as the geoid.
While the mean Earth ellipsoid is the ideal basis of global geodesy, for regional networks a so-called reference ellipsoid may be the better choice. When geodetic measurements have to be computed on a mathematical reference surface, this surface should have a similar curvature as the regional geoid; otherwise, reduction of the measurements will get small distortions.
This is the reason for the "long life" of former reference ellipsoids like the Hayford or the Bessel ellipsoid, despite the fact that their main axes deviate by several hundred meters from the modern values.
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The geoid (ˈdʒiː.oɪd) is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended through the continents (such as with very narrow hypothetical canals). According to Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth.
A geodetic control network (also geodetic network, reference network, control point network, or control network) is a network, often of triangles, which are measured precisely by techniques of control surveying, such as terrestrial surveying or satellite geodesy. A geodetic control network consists of stable, identifiable points with published datum values derived from observations that tie the points together.
The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum § Vertical datum). The term elevation is mainly used when referring to points on the Earth's surface, while altitude or geopotential height is used for points above the surface, such as an aircraft in flight or a spacecraft in orbit, and depth is used for points below the surface.