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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 calculation is essentially the conversion of the equatorial polar coordinates of Mecca (i.e. its longitude and latitude) to its polar coordinates (i.e. its qibla and distance) relative to a system whose reference meridian is the great circle through the given location and the Earth's poles and whose polar axis is the line through the ...
The WGS 84 datum surface is an oblate spheroid with equatorial radius a = 6 378 137 m at the equator and flattening f = 1 ⁄ 298.257 223 563. The refined value of the WGS 84 gravitational constant (mass of Earth's atmosphere included) is GM = 3.986 004 418 × 10 14 m 3 /s 2. The angular velocity of the Earth is defined to be ω = 72.921 15 × ...
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).
For example, if the measurements were hypothetically performed exactly over the equator plane and either geographical pole, the radii of curvature so obtained would be related to the equatorial radius and the polar radius, respectively a and b (see: Earth polar and equatorial radius of curvature).
A right-handed convention specifies a y axis 90° to the east in the fundamental plane; the z axis is the north polar axis. The reference frame does not rotate with the Earth, rather, the Earth rotates around the z axis. There are a number of rectangular variants of equatorial coordinates. All have:
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. The quantity f = (a−b)/a, where b is the semi-minor axis (polar radius), is a purely geometrical one.
The planet Earth has a rather slight equatorial bulge; its equatorial diameter is about 43 km (27 mi) greater than its polar diameter, with a difference of about 1 ⁄ 298 of the equatorial diameter. If Earth were scaled down to a globe with an equatorial diameter of 1 metre (3.3 ft), that difference would be only 3 mm (0.12 in).