The models chosen to approximate the surface.
From the point of view of the geometry of our planet - the earth is a body of irregular shape. Despite its proximity to the spherical shape, the shape of the Earth's pear-shaped, flattened at the poles and wider at the equator (slideshow). To carry out mathematical calculations required mathematical surface closely matches the shape of the earth, and the closest approximation (approximation - the replacement of complex forms easier) to a first approximation to the corresponding shape of the Earth actually gives the geoid.
Geoid is called an equipotential surface in the gravity field of the Earth which coincides with the mean sea level (MSL) extended continuously through the continents. Thus, the geoid surface differs from the physical surface of the earth absence mountains.
Equipotential surface - the physical surface of the earth in a force field which all points have the same potential.
The geoid is expressed mathematically by using the coefficients of the spherical harmonics. For example, the geoid WGS 84 Earth Gravitational Model (EGM 96), uses a spherical harmonic coefficients for the polynomials of order up to 360. For the full equation EGM 96 geoid requires a 60,000 coefficients. It is clear that using all of them to calculate the surface too hard.
The geoid is currently under construction on satellite data. Interestingly, the raising of the geoid and troughs do not coincide with the topography of the Earth. This suggests that there is a compensation masses (Isostasy) on a continental scale.
Because the exact position of the geoid determination at a given point can not be used for this purpose, conventionally constructed taking into account the average (normal) models of the gravitational field of the earth surface is called quasigeoid.
Quasi-geoid is imaginary surface which close in geoid form, created on the surface of the common terrestrial ellipsoid with the height anomalies. Quasigeoid surface recedes from the surface of the geoid to within a few centimeters in the plains and up to 2 meters in the mountain. Quasigeoid are measured from the surface of the earth's surface heights of the points listed on the maps.
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