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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).
The curvature is the reciprocal of radius of curvature. That is, the curvature is =, where R is the radius of curvature [5] (the whole circle has this curvature, it can be read as turn 2π over the length 2π R). This definition is difficult to manipulate and to express in formulas.
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 combinations thereof. [1][2][3]
In the journal Acta Eruditorum (1691), Jacob Bernoulli used a system with a point on a line, called the pole and polar axis respectively. Coordinates were specified by the distance from the pole and the angle from the polar axis. Bernoulli's work extended to finding the radius of curvature of curves expressed in these coordinates.
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 direction. For an oblate ellipsoid, the polar radius of curvature r p {\displaystyle r_{p}} is larger than the equatorial
Polar coordinates centered at the center. In polar coordinates, ... The radius of curvature at the co-vertices , is: . The diagram shows an easy ...
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
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 ...