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The geoid is often expressed as a geoid undulation or geoidal height above a given reference ellipsoid, which is a slightly flattened sphere whose equatorial bulge is caused by the planet's rotation. Generally the geoidal height rises where the Earth's material is locally more dense and exerts greater gravitational force than the surrounding areas.
Functions of the form = () where (r, θ, φ) are the spherical coordinates which satisfy the partial differential equation (the Laplace equation) are called spherical harmonic functions. They take the forms:
The geoid, or mathematical mean sea surface, is defined not only on the seas, but also under land; it is the equilibrium water surface that would result, would sea water be allowed to move freely (e.g., through tunnels) under the land. Technically, an equipotential surface of the true geopotential, chosen to coincide (on average) with mean sea ...
A simple definition is as the shortest path between two points on a surface. However, it is frequently more useful to define them as paths with zero geodesic curvature—i.e., the analogue of straight lines on a curved surface. This definition encompasses geodesics traveling so far across the ellipsoid's surface that they start to return toward ...
The geometrical separation between it and the reference ellipsoid is called the geoidal undulation, or more usually the geoid-ellipsoid separation, N. It varies globally between ±110 m. 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.
Plant structures or organs fulfil specific functions, and those functions determine the structures that perform them. Among terrestrial (land) plants, the vascular and non-vascular plants (Bryophytes) evolved independently in terms of their adaptation to terrestrial life and are treated separately here (see Bryophytes). [6]
The reference surface is the geoid, an equigeopotential surface approximating the mean sea level as described above. For normal heights, the reference surface is the so-called quasi-geoid, which has a few-metre separation from the geoid due to the density assumption in its continuation under the continental masses. [11]
The geoid is a gently undulating surface due to the irregular mass distribution inside the Earth; it may be approximated however by an ellipsoid of revolution called the reference ellipsoid. The currently most widely used reference ellipsoid, that of the Geodetic Reference System 1980 , approximates the geoid to within a little over ±100 m.