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Earth radius

Earth radius (denoted as R🜨 or ) 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, the radius ranges from a maximum of nearly 6,378 km (3,963 mi) (equatorial radius, denoted a) to a minimum of nearly 6,357 km (3,950 mi) (polar radius, denoted b).

For its historical development, see Spherical Earth. For its determination, see Arc measurement.

Earth radius

R🜨, ,

   6.3781×106 m[1]

   6,357 to 6,378 km

   3,950 to 3,963 mi

A nominal Earth radius is sometimes used as a unit of measurement in astronomy and geophysics, which is recommended by the International Astronomical Union to be the equatorial value.[1]


A globally-average value is usually considered to be 6,371 kilometres (3,959 mi) with a 0.3% variability (±10 km) for the following reasons. The International Union of Geodesy and Geophysics (IUGG) provides three reference values: the mean radius (R1) of three radii measured at two equator points and a pole; the authalic radius, which is the radius of a sphere with the same surface area (R2); and the volumetric radius, which is the radius of a sphere having the same volume as the ellipsoid (R3).[2] All three values are about 6,371 kilometres (3,959 mi).


Other ways to define and measure the Earth's radius involve the radius of curvature. A few definitions yield values outside the range between the polar radius and equatorial radius because they include local or geoidal topography or because they depend on abstract geometrical considerations.

The actual surface of Earth

The , defined by mean sea level at each point on the real surface[b]

geoid

A , also called an ellipsoid of revolution, geocentric to model the entire Earth, or else geodetic for regional work[c]

spheroid

A

sphere

The Earth's equatorial radius a, or ,[8]: 11  is the distance from its center to the equator and equals 6,378.1370 km (3,963.1906 mi).[9] The equatorial radius is often used to compare Earth with other planets.

semi-major axis

The following radii are derived from the World Geodetic System 1984 (WGS-84) reference ellipsoid.[6] It is an idealized surface, and the Earth measurements used to calculate it have an uncertainty of ±2 m in both the equatorial and polar dimensions.[7] Additional discrepancies caused by topographical variation at specific locations can be significant. When identifying the position of an observable location, the use of more precise values for WGS-84 radii may not yield a corresponding improvement in accuracy.


The value for the equatorial radius is defined to the nearest 0.1 m in WGS-84. The value for the polar radius in this section has been rounded to the nearest 0.1 m, which is expected to be adequate for most uses. Refer to the WGS-84 ellipsoid if a more precise value for its polar radius is needed.

Maximum Rt: the summit of is 6,384.4 km (3,967.1 mi) from the Earth's center.

Chimborazo

Minimum Rt: the floor of the is 6,352.8 km (3,947.4 mi) from the Earth's center.[17]

Arctic Ocean

2a = 12,756.2740 km (7,926.3812 mi),

2b = 12,713.5046 km (7,899.8055 mi).

Earth's diameter is simply twice Earth's radius; for example, equatorial diameter (2a) and polar diameter (2b). For the WGS84 ellipsoid, that's respectively:


Earth's circumference equals the perimeter length. The equatorial circumference is simply the circle perimeter: Ce=2πa, in terms of the equatorial radius, a. The polar circumference equals Cp=4mp, four times the quarter meridian mp=aE(e), where the polar radius b enters via the eccentricity, e=(1−b2/a2)0.5; see Ellipse#Circumference for details.


Arc length of more general surface curves, such as meridian arcs and geodesics, can also be derived from Earth's equatorial and polar radii.


Likewise for surface area, either based on a map projection or a geodesic polygon.


Earth's volume, or that of the reference ellipsoid, is V = 4/3Ï€a2b. Using the parameters from WGS84 ellipsoid of revolution, a = 6,378.137 km and b = 6356.7523142 km, V = 1.08321×1012 km3 (2.5988×1011 cu mi).[19]

Merrifield, Michael R. (2010). . Sixty Symbols. Brady Haran for the University of Nottingham.

" The Earth's Radius (and exoplanets)"