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The Earth's meridional radius of curvature at the equator equals the meridian's semi-latus rectum: M e = b 2 / a = 6,335.439 km. The Earth's prime-vertical radius of curvature at the equator equals the equatorial radius, N e = a. The Earth's polar radius of curvature (either meridional or prime-vertical) is: M p =N p = a 2 / b ...
The Earth's radius is the distance from Earth's center to its surface, about 6,371 km (3,959 mi). While "radius" normally is a characteristic of perfect spheres, the Earth deviates from spherical by only a third of a percent, sufficiently close to treat it as a sphere in many contexts and justifying the term "the radius of the Earth".
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 ...
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.
Spherical Earth or Earth's curvature refers to the approximation of the figure of the Earth to a sphere. The concept of a spherical Earth gradually displaced earlier beliefs in a flat Earth during classical antiquity and the Middle Ages .
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Polar radius of curvature = / = 6 399 593.6259 m; Equatorial radius of curvature for a meridian = / = 6 335 439.3271 m; Meridian quadrant = 10 001 965.7292 m; Derived physical constants (rounded) Period of rotation (sidereal day) = / = 86 164.100 637 s
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.).