Earth radius

 ( Radius ) 

, $\backslash mathcal\{R\}^\backslash mathrm\; N\_\{p\backslash mathrm\{E\}\}$ | units1 = SI base unit | inunits1 = | units2 = Metric system | inunits2 = | units3 = English units | inunits3 =

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 about to a minimum ( polar radius, denoted b) of nearly .

A globally-average value is usually considered to be 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 ( R) 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 ( R); and the volumetric radius, which is the radius of a sphere having the same volume as the ellipsoid ( R). All three values are about .

Other ways to define and measure the Earth's radius involve either the spheroid's radius of curvature or the actual topography. A few definitions yield values outside the range between the polar radius and radius because they account for localized effects.

A nominal Earth radius (denoted $\backslash mathcal\{R\}^\backslash mathrm\; N\_\backslash mathrm\{E\}$) is sometimes used as a unit of measurement in astronomy and geophysics, a conversion factor used when expressing planetary properties as multiples or fractions of a constant terrestrial radius; if the choice between equatorial or polar radii is not explicit, the equatorial radius is to be assumed, as recommended by the International Astronomical Union (IAU).

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Introduction Earth's rotation, internal density variations, and external cause its shape to deviate systematically from a perfect sphere.For details see figure of the Earth, geoid, and Earth tide. Local topography increases the variance, resulting in a surface of profound complexity. Our descriptions of Earth's surface must be simpler than reality in order to be tractable. Hence, we create models to approximate characteristics of Earth's surface, generally relying on the simplest model that suits the need.

Each of the models in common use involve some notion of the geometric radius. Strictly speaking, spheres are the only solids to have radii, but broader uses of the term radius are common in many fields, including those dealing with models of Earth. The following is a partial list of models of Earth's surface, ordered from exact to more approximate:

• The actual surface of Earth
• The geoid, defined by mean sea level at each point on the real surfaceThere is no single center to the geoid; it varies according to local Geodetic system conditions. Where there is land, the geoid is generally below ground; it represents where the sea level would be if water could reach it from the ocean via an imaginary canal.
• A spheroid, also called an ellipsoid of revolution, geocentric to model the entire Earth, or else geodetic for regional workIn a geocentric ellipsoid, the center of the ellipsoid coincides with some computed center of Earth, and best models the earth as a whole. Geodetic ellipsoids are better suited to regional idiosyncrasies of the geoid. A partial surface of an ellipsoid gets fitted to the region, in which case the center and orientation of the ellipsoid generally do not coincide with the earth's center of mass or axis of rotation.
• A sphere

In the case of the geoid and ellipsoids, the fixed distance from any point on the model to the specified center is called "a radius of the Earth" or "the radius of the Earth at that point".The value of the radius is completely dependent upon the latitude in the case of an ellipsoid model, and nearly so on the geoid. It is also common to refer to any mean radius of a spherical model as "the radius of the earth". When considering the Earth's real surface, on the other hand, it is uncommon to refer to a "radius", since there is generally no practical need. Rather, elevation above or below sea level is useful.

Regardless of the model, any of these geocentric radii falls between the polar minimum of about 6,357 km and the equatorial maximum of about 6,378 km (3,950 to 3,963 mi). Hence, the Earth deviates from a perfect sphere by only a third of a percent, which supports the spherical model in most contexts and justifies the term "radius of the Earth". While specific values differ, the concepts in this article generalize to any major planet.

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Physics of Earth's deformation Rotation of a planet causes it to approximate an spheroid/spheroid with a bulge at the equator and flattening at the North Pole and , so that the equatorial radius is larger than the polar radius by approximately . The oblateness constant is given by

$q=\backslash frac\{a^3\; \backslash omega^2\}\{GM\},$

where is the angular frequency, is the gravitational constant, and is the mass of the planet. For the Earth , which is close to the measured inverse flattening . Additionally, the bulge at the equator shows slow variations. The bulge had been decreasing, but since 1998 the bulge has increased, possibly due to redistribution of ocean mass via currents. Satellites Reveal A Mystery Of Large Change In Earth's Gravity Field , Aug. 1, 2002, Goddard Space Flight Center. The variation in density and crustal thickness causes gravity to vary across the surface and in time, so that the mean sea level differs from the ellipsoid. This difference is the geoid height, positive above or outside the ellipsoid, negative below or inside. The geoid height variation is under on Earth. The geoid height can change abruptly due to earthquakes (such as the Sumatra-Andaman earthquake) or reduction in ice masses (such as Greenland). NASA's Grace Finds Greenland Melting Faster, 'Sees' Sumatra Quake, December 20, 2005, Goddard Space Flight Center.

Not all deformations originate within the Earth. Gravitational attraction from the Moon or Sun can cause the Earth's surface at a given point to vary by tenths of a meter over a nearly 12-hour period (see Earth tide).

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Radius and local conditions Given local and transient influences on surface height, the values defined below are based on a "general purpose" model, refined as globally precisely as possible within of reference ellipsoid height, and to within of mean sea level (neglecting geoid height).

Additionally, the radius can be estimated from the curvature of the Earth at a point. Like a torus, the curvature at a point will be greatest (tightest) in one direction (north–south on Earth) and smallest (flattest) perpendicularly (east–west). The corresponding radius of curvature depends on the location and direction of measurement from that point. A consequence is that a distance to the horizon at the equator is slightly shorter in the north–south direction than in the east–west direction.

In summary, local variations in terrain prevent defining a single "precise" radius. One can only adopt an idealized model. Since the estimate by Eratosthenes, many models have been created. Historically, these models were based on regional topography, giving the best reference ellipsoid for the area under survey. As satellite remote sensing and especially the Global Positioning System gained importance, true global models were developed which, while not as accurate for regional work, best approximate the Earth as a whole.

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Extrema: equatorial and polar radii The following radii are derived from the World Geodetic System 1984 (WGS-84) reference ellipsoid. 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. 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.

• The Earth's equatorial radius , or semi-major axis, is the distance from its center to the equator and equals . The equatorial radius is often used to compare Earth with other planets.
• The Earth's polar radius , or semi-minor axis is the distance from its center to the North and South Poles, and equals .

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Location-dependent radii

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Geocentric radius The geocentric radius is the distance from the Earth's center to a point on the spheroid surface at geodetic latitude , given by the formula

Mohinder S. Grewal (2025). 9781119547839, John Wiley & Sons. . ISBN 9781119547839

$R(\backslash varphi)=\backslash sqrt\{\backslash frac\{(a^2\backslash cos\backslash varphi)^2+(b^2\backslash sin\backslash varphi)^2\}\{(a\backslash cos\backslash varphi)^2+(b\backslash sin\backslash varphi)^2\}\},$

where and are, respectively, the equatorial radius and the polar radius.

The maximum and minimum geocentric radii on the ellipsoid coincide, respectively, with the equatorial and polar radii, at the vertices of the ellipse. However, the maximum and minimum radii of curvature coincide with the poles and Equator, in opposite regions than the geocentric radii, due to Earth's oblateness.

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Radii of curvature

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Principal radii of curvature There are two principal radii of curvature: along the meridional and prime-vertical .

The principal curvatures are the roots of Equation (125) in:

$(E\; G\; -\; F^2)\; \backslash kappa^2\; -\; (e\; G\; +\; g\; E\; -\; 2\; f\; F)\; \backslash kappa\; +\; (e\; g\; -\; f^2)\; =\; 0$

= \det(A - \kappa B),

where in the first fundamental form for a surface (Equation (112) in):

$ds^2\; =\; \backslash sum\_\{ij\}\; a\_\{ij\}\; dw^i\; dw^j\; =\; E\; \backslash ,d\backslash varphi^2\; +\; 2\; F\; \backslash ,d\backslash varphi\; \backslash ,d\backslash lambda\; +\; G\; \backslash ,d\backslash lambda^2,$

E, F, and G are elements of the metric tensor:

$A\; =\; a\_\{ij\}\; =\; \backslash sum\_\backslash nu\; \backslash frac\{\backslash partial\; r^\backslash nu\}\{\backslash partial\; w^i\}\; \backslash frac\{\backslash partial\; r^\backslash nu\}\{\backslash partial\; w^j\}$

= \begin{bmatrix} E & F \\ F & G \end{bmatrix},

$r\; =\; r^1,^T\; =\; x,^T$, $w^1\; =\; \backslash varphi$, $w^2\; =\; \backslash lambda,$

in the second fundamental form for a surface (Equation (123) in):

$2\; D\; =\; \backslash sum\_\{ij\}\; b\_\{ij\}\; dw^i\; dw^j\; =\; e\; \backslash ,d\backslash varphi^2\; +\; 2\; f\; \backslash ,d\backslash varphi\; \backslash ,d\backslash lambda\; +\; g\; \backslash ,d\backslash lambda^2,$

e, f, and g are elements of the shape tensor:

$B\; =\; b\_\{ij\}\; =\; \backslash sum\_\backslash nu\; n^\backslash nu\; \backslash frac\{\backslash partial\; ^2\; r^\backslash nu\}\{\backslash partial\; w^i\; \backslash partial\; w^j\}$

= \begin{bmatrix} e & f \\ f & g \end{bmatrix},

$n\; =\; \backslash frac\{N\}$

is the unit normal to the surface at $r$, and because $\backslash frac\{\backslash partial\; r\}\{\backslash partial\; \backslash varphi\}$ and $\backslash frac\{\backslash partial\; r\}\{\backslash partial\; \backslash lambda\}$ are tangents to the surface,

$N\; =\; \backslash frac\{\backslash partial\; r\}\{\backslash partial\; \backslash varphi\}\; \backslash times\; \backslash frac\{\backslash partial\; r\}\{\backslash partial\; \backslash lambda\}$

is normal to the surface at $r$.

With $F\; =\; f\; =\; 0$ for an oblate spheroid, the curvatures are

$\backslash kappa\_1\; =\; \backslash frac\{g\}\{G\}$ and $\backslash kappa\_2\; =\; \backslash frac\{e\}\{E\},$

and the principal radii of curvature are

$R\_1\; =\; \backslash frac\{1\}\{\backslash kappa\_1\}$ and $R\_2\; =\; \backslash frac\{1\}\{\backslash kappa\_2\}.$

The first and second radii of curvature correspond, respectively, to the Earth's meridional and prime-vertical radii of curvature.

Geometrically, the second fundamental form gives the distance from $r\; +\; dr$ to the plane tangent at $r$.

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Meridional In particular, the Earth's meridional radius of curvature (in the north–south direction) at is

$M(\backslash varphi)=\backslash frac\{(ab)^2\}\{\backslash big((a\backslash cos\backslash varphi)^2+(b\backslash sin\backslash varphi)^2\backslash big)^\backslash frac32\}$

=\frac{a(1-e^2)}{(1-e^2\sin^2\varphi)^\frac32} =\frac{1-e^2}{a^2} N(\varphi)^3, where $e$ is the eccentricity of the earth. This is the radius that Eratosthenes measured in his arc measurement.

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Prime vertical If one point had appeared due east of the other, one finds the approximate curvature in the east–west direction.East–west directions can be misleading. Point B, which appears due east from A, will be closer to the equator than A. Thus the curvature found this way is smaller than the curvature of a circle of constant latitude, except at the equator. West can be exchanged for east in this discussion. This Earth's prime vertical radius of curvature, also called the Earth's transverse radius of curvature, is defined perpendicular (orthogonal) to at geodetic latitude is defined as the radius of curvature in the plane that is normal to both the surface of the ellipsoid at, and the meridian passing through, the specific point of interest. and is

$N(\backslash varphi)=\backslash frac\{a^2\}\{\backslash sqrt\{(a\backslash cos\backslash varphi)^2+(b\backslash sin\backslash varphi)^2\}\}$

=\frac{a}{\sqrt{1-e^2\sin^2\varphi}}.

N can also be interpreted geometrically as the normal distance from the ellipsoid surface to the polar axis. The radius of a parallel of latitude is given by $p=N\backslash cos(\backslash varphi)$.

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Combined radii of curvature

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Azimuthal

Earth's azimuthal radius of curvature of an Earth normal section at an azimuth (measured clockwise from north) and at latitude , is derived from Euler's curvature formula as follows:

$R\_\backslash mathrm\{c\}=\backslash frac\{1\}\{\backslash dfrac\{\backslash cos^2\backslash alpha\}\{M\}+\backslash dfrac\{\backslash sin^2\backslash alpha\}\{N\}\}$

or

$R\_\backslash mathrm\{c\}^\{-1\}=M^\{-1\}\backslash cos^2\backslash alpha\; +\; N^\{-1\}\backslash sin^2\backslash alpha,$

where $R\_\backslash mathrm\{c\}^\{-1\}$ is the azimuthal curvature of the ellipsoid.

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Non-directional (Gaussian and mean)

It is possible to combine the principal radii of curvature above in a non-directional manner.

Earth's Gaussian radius of curvature at latitude is

(2025). 9783110170726, Walter de Gruyter. . ISBN 9783110170726

$R\_\backslash text\{a\}(\backslash varphi)\; =\; \backslash frac\{1\}\{\backslash sqrt\{K\}\}\; =\; \backslash frac\{1\}\{2\backslash pi\}\backslash int\_\{0\}^\{2\backslash pi\}R\_\backslash text\{c\}(\backslash alpha)\backslash ,d\backslash alpha,$

or

$R\_\backslash text\{a\}(\backslash varphi)\; =\; \backslash sqrt\{MN\}\; =\; \backslash frac\{a^2b\}\{(a\backslash cos\backslash varphi)^2+(b\backslash sin\backslash varphi)^2\}$

= \frac{a\sqrt{1-e^2}}{1-e^2\sin^2\varphi}, where K is the Gaussian curvature, $K\; =\; \backslash kappa\_1\backslash ,\backslash kappa\_2.$ The Gaussian radius of curvature is defined in terms of the product of the principal radii of curvature and it integrates the azimuthal radius of curvature $R\_\backslash mathrm\{c\}$ over the full circle. It corresponds to the radius of the osculating sphere that best fits the ellipsoid locally.

Earth's radius of mean curvature at latitude is

$R\_\backslash text\{m\}\; =\; \backslash frac\{2\}\{\backslash dfrac\{1\}\{M\}\; +\; \backslash dfrac\{1\}\{N\}\}$

or

$R\_\backslash text\{m\}^\{-1\}\; =\; \backslash frac\{M^\{-1\}\; +\; N^\{-1\}\}\{2\}\; =\; \backslash frac\{1\}\{2\backslash pi\}\backslash int\_0^\{2\backslash pi\}\; R\_c^\{-1\}(\backslash theta)\; \backslash ;d\backslash theta.$

The mean curvature $R\_\backslash text\{m\}^\{-1\}$ equals the arithmetic mean of the two principal curvatures and integrates the azimuthal curvature $R\_\backslash mathrm\{c\}^\{-1\}$ over the full circle.

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Equatorial radii of curvature

Earth's meridional radius of curvature at the equator equals the meridian's semi-latus rectum:

$M(0\backslash text\{°\})=\backslash frac\{b^2\}\{a\}=\backslash ell=6,335.439\; \backslash text\{\; km.\}$

Earth's prime-vertical radius of curvature at the equator equals the equatorial radius,

$N(0\backslash text\{°\})=a$

Earth's Gaussian radius of curvature at the equator simplifies to the polar radius ( the equatorial radius):

$R\_\backslash text\{a\}(0\backslash text\{°\})=b$

Earth's mean radius of curvature at the equator involves the semi-latus rectum:

$R\_\backslash text\{m\}(0\backslash text\{°\})=2\; (a\; \backslash cdot\; \backslash ell)/(a\; +\; \backslash ell)\; =\; 6,356.716\; \backslash text\{\; km.\}$

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Polar radii of curvature

Earth's radius of curvature at the poles (either meridional or prime-vertical) is

$M(90\backslash text\{°\})=N(90\backslash text\{°\})=\backslash frac\{a^2\}\{b\}=6,399.594\; \backslash text\{\; km.\}$

Earth's Gaussian or mean radii of curvature at the poles also equal the principal radii of curvature at the poles ( the polar radius):

$R\_\backslash text\{a\}(90\backslash text\{°\})=R\_\backslash text\{m\}(90\backslash text\{°\})=\backslash frac\{a^2\}\{b\}$

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Global radii

The Earth can be modeled as a sphere in many ways. This section describes the common ways. The various radii derived here use the notation and dimensions noted above for the Earth as derived from the WGS-84 ellipsoid; namely,

Equatorial radius: = ()

Polar radius: = ()

A sphere being a gross approximation of the spheroid, which itself is an approximation of the geoid, units are given here in kilometers rather than the millimeter resolution appropriate for geodesy.

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Arithmetic mean radius

In geophysics, the International Union of Geodesy and Geophysics (IUGG) defines the Earth's arithmetic mean radius (denoted ) to beMoritz, H. (1980). Geodetic Reference System 1980 , by resolution of the XVII General Assembly of the IUGG in Canberra.

$R\_1\; =\; \backslash frac\{2a+b\}\{3\}.$

The factor of two accounts for the biaxial symmetry in Earth's spheroid, a specialization of triaxial ellipsoid. For Earth, the arithmetic mean radius is published by IUGG and NGA as .

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Authalic radius

Earth's authalic radius (meaning "equal area") is the radius of a hypothetical perfect sphere that has the same surface area as the reference ellipsoid. The IUGG denotes the authalic radius as . A closed-form solution exists for a spheroid:Snyder, J. P. (1987). Map Projections – A Working Manual (US Geological Survey Professional Paper 1395) p. 16–17. Washington D.C: United States Government Printing Office.

$R\_2$

=\sqrt{\frac12\left(a^2+\frac{b^2}{e}\ln{\frac{1+e}{b/a}} \right) } =\sqrt{\frac{a^2}2+\frac{b^2}2\frac{\tanh^{-1}e}e} =\sqrt{\frac{A}{4\pi}}, where is the eccentricity, and is the surface area of the spheroid.

For the Earth, the authalic radius is .

The authalic radius $R\_2$ also corresponds to the radius of (global) mean curvature, obtained by averaging the Gaussian curvature, $K$, over the surface of the ellipsoid. Using the Gauss–Bonnet theorem, this gives

$\backslash frac\{\backslash int\; K\; \backslash ,dA\}\{A\}\; =\; \backslash frac\{4\backslash pi\}\{A\}\; =\; \backslash frac\{1\}\{R\_2^2\}.$

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Volumetric radius

Another spherical model is defined by the Earth's volumetric radius, which is the radius of a sphere of volume equal to the ellipsoid. The IUGG denotes the volumetric radius as .

$R\_3\; =\; \backslash sqrt3\{a^2b\}.$

For Earth, the volumetric radius equals .

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Rectifying radius

Another global radius is the Earth's rectifying radius, giving a sphere with circumference equal to the circumference of the ellipse described by any polar cross section of the ellipsoid. This requires an elliptic integral to find, given the polar and equatorial radii:

$M\_\backslash text\{r\}\; =\; \backslash frac\{2\}\{\backslash pi\}\; \backslash int\_0^\{\backslash frac\{\backslash pi\}\{2\}\}\; \backslash sqrt\{a^2\; \backslash cos^2\backslash varphi\; +\; b^2\; \backslash sin^2\backslash varphi\}\; \backslash ,d\backslash varphi.$

The rectifying radius is equivalent to the meridional mean, which is defined as the average value of :

$M\_\backslash text\{r\}\; =\; \backslash frac\{2\}\{\backslash pi\}\; \backslash int\_0^\{\backslash frac\{\backslash pi\}\{2\}\}\; M(\backslash varphi)\; \backslash ,d\backslash varphi.$

For integration limits of 0,, the integrals for rectifying radius and mean radius evaluate to the same result, which, for Earth, amounts to .

The meridional mean is well approximated by the semicubic mean of the two axes,

$M\_\backslash text\{r\}\; \backslash approx\; \backslash left(\backslash frac\{a^\backslash frac32\; +\; b^\backslash frac32\}\{2\}\backslash right)^\backslash frac23,$

which differs from the exact result by less than ; the mean of the two axes,

$M\_\backslash text\{r\}\; \backslash approx\; \backslash frac\{a\; +\; b\}\{2\},$

about , can also be used.

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Topographical radii

The mathematical expressions above apply over the surface of the ellipsoid. The cases below considers Earth's topography, above or below a reference ellipsoid. As such, they are topographical geocentric distances, R_t, which depends not only on latitude.

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Topographical extremes

• Maximum R_t: the summit of Chimborazo is from the Earth's center.
• Minimum R_t: the floor of the Arctic Ocean is from the Earth's center.

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Topographical global mean

The topographical mean geocentric distance averages elevations everywhere, resulting in a value larger than the IUGG mean radius, the authalic radius, or the volumetric radius. This topographical average is with uncertainty of .

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Derived quantities: diameter, circumference, arc-length, area, volume

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

,

.

Earth's circumference equals the perimeter length. The equatorial circumference is simply the circle perimeter: C_e = 2 πa, in terms of the equatorial radius a:

The polar circumference equals C_p = 4 m_p, four times the quarter meridian m_p = aE( e):

The polar radius b enters via the eccentricity e = (1 − b²/ a²)^0.5; see Ellipse#Circumference for details.

Arc length of more general , such as and Earth 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 $V\; =\; \backslash tfrac\{4\}\{3\}\backslash pi\; a^2\; b.$ Using the parameters from WGS84 ellipsoid of revolution, and , it results in:

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Nominal radii

In astronomy, the International Astronomical Union denotes the nominal equatorial Earth radius as $\backslash mathcal\{R\}^\backslash text\{N\}\_\backslash text\{eE\}$, which is defined to be exactly . The nominal polar Earth radius is defined exactly as $\backslash mathcal\{R\}^\backslash text\{N\}\_\backslash text\{pE\}$ = . These values correspond to the zero Earth tide convention. Equatorial radius is conventionally used as the nominal value unless the polar radius is explicitly required. The nominal radius serves as a unit of length for astronomy. (The notation is defined such that it can be easily generalized for other planets; e.g., $\backslash mathcal\{R\}^\backslash text\{N\}\_\backslash text\{pJ\}$ for the nominal polar Jupiter radius.)

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Published values

This table summarizes the accepted values of the Earth's radius.

IAU	nominal "zero tide" equatorial
IAU	nominal "zero tide" polar
IUGG	equatorial radius
IUGG	semiminor axis ( b)
IUGG	polar radius of curvature ( c)
IUGG	mean radius ( R1)
IUGG	radius of sphere of same surface ( R2)
IUGG	radius of sphere of same volume ( R3)
NGA	WGS-84 ellipsoid, semi-major axis ( a)
NGA	WGS-84 ellipsoid, semi-minor axis ( b)
NGA	WGS-84 ellipsoid, polar radius of curvature ( c)
NGA	WGS-84 ellipsoid, Mean radius of semi-axes ( R1)
NGA	WGS-84 ellipsoid, Radius of Sphere of Equal Area ( R2)
NGA	WGS-84 ellipsoid, Radius of Sphere of Equal Volume ( R3)
	GRS 80 semi-major axis ( a)
	GRS 80 semi-minor axis ( b)
	Spherical Earth Approx. of Radius ( RE)		(2025). 9780471334583, John Wiley & Sons, Inc.. ISBN 9780471334583
	meridional radius of curvature at the equator
	Maximum (the summit of Chimborazo)
	Minimum (the floor of the Arctic Ocean)
	Average distance from center to surface

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History

The first published reference to the Earth's size appeared around 350 Anno Domini, when Aristotle reported in his book On the Heavens that mathematicians had guessed the circumference of the Earth to be 400,000 stadia. Scholars have interpreted Aristotle's figure to be anywhere from highly accurate to almost double the true value. The first known scientific measurement and calculation of the circumference of the Earth was performed by Eratosthenes in about 240 BC. Estimates of the error of Eratosthenes's measurement range from 0.5% to 17%. For both Aristotle and Eratosthenes, uncertainty in the accuracy of their estimates is due to modern uncertainty over which stadion length they meant.

Around 100 BC, Posidonius of Apamea recomputed Earth's radius, and found it to be close to that by Eratosthenes,Posidonius, fragment 202 but later Strabo incorrectly attributed him a value about 3/4 of the actual size.Cleomedes ( in Fragment 202) stated that if the distance is measured by some other number the result will be different, and using 3,750 instead of 5,000 produces this estimation: 3,750 x 48 = 180,000; see Fischer I., (1975), Another Look at Eratosthenes' and Posidonius' Determinations of the Earth's Circumference, Ql. J. of the Royal Astron. Soc., Vol. 16, p. 152. Claudius Ptolemy around 150 Anno Domini gave empirical evidence supporting a spherical Earth,

Hugh Thurston (1994). 038794107X, Springer-Verlag New York. 038794107X

but he accepted the lesser value attributed to Posidonius. His highly influential work, the Almagest, left no doubt among medieval scholars that Earth is spherical, but they were wrong about its size.

By 1490, Christopher Columbus believed that traveling 3,000 miles west from the west coast of the Iberian Peninsula would let him reach the eastern coasts of Asia.John Freely, Before Galileo: The Birth of Modern Science in Medieval Europe (2013), However, the 1492 enactment of that voyage brought his fleet to the Americas. The Magellan expedition (1519–1522), which was the first circumnavigation of the World, soundly demonstrated the sphericity of the Earth,

Nancy Smiler Levinson (2025). 9780395987735, Houghton Mifflin Harcourt. . ISBN 9780395987735

and affirmed the original measurement of by Eratosthenes.

Around 1690, Isaac Newton and Christiaan Huygens argued that Earth was closer to an oblate spheroid than to a sphere. However, around 1730, Jacques Cassini argued for a prolate spheroid instead, due to different interpretations of the Newtonian mechanics involved. To settle the matter, the French Geodesic Mission (1735–1739) measured one degree of latitude at two locations, one near the Arctic Circle and the other near the equator. The expedition found that Newton's conjecture was correct: the Earth is flattened at the poles due to rotation's centrifugal force.

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See also

• Earth ellipsoid
• Earth mass
• Earth's circumference
• Effective Earth radius
• Geodesy
• Geographical distance
• History of geodesy
• Planetary radius
• Timeline of Earth estimates

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Notes

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External links

Categories: Radius, Planetary Science, Planetary Geology, Radii, Units Of Measurement In Astronomy

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