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Earth radius (denoted as R 🜨 or R E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equatorial radius, denoted a) of nearly 6,378 km (3,963 mi) to a minimum (polar radius, denoted b) of nearly 6,357 km (3,950 mi).
More complex surfaces have radii of curvature that vary over the surface. The radius of curvature describes the radius of the sphere that best approximates the surface at that point. Oblate ellipsoids have a constant radius of curvature east to west along parallels, if a graticule is drawn on the surface, but varying curvature in any other ...
Later arc measurements aimed at determining the flattening of the Earth ellipsoid by measuring at different geographic latitudes. The first of these was the French Geodesic Mission , commissioned by the French Academy of Sciences in 1735–1738, involving measurement expeditions to Lapland ( Maupertuis et al.) and Peru ( Pierre Bouguer et al.).
Radius of curvature and center of curvature. In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or ...
Geodetic latitude and geocentric latitude have different definitions. Geodetic latitude is defined as the angle between the equatorial plane and the surface normal at a point on the ellipsoid, whereas geocentric latitude is defined as the angle between the equatorial plane and a radial line connecting the centre of the ellipsoid to a point on the surface (see figure).
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.
On an ellipsoid of revolution, for short meridian arcs, their length can be approximated using the Earth's meridional radius of curvature and the circular arc formulation. For longer arcs, the length follows from the subtraction of two meridian distances, the distance from the equator to a point at a latitude φ.
Geodesy is the scientific discipline that deals with the measurement and representation of the earth, its gravitational field and geodynamic phenomena (polar motion, earth tides, and crustal motion) in three-dimensional, time-varying space. The geoid is essentially the figure of the Earth abstracted from its topographic features. It is an ...