# نصف قطر الأرض

القطر الأرضي هو وحدة قياس تستخدم في القياسات الكبيرة، وهي تساوي قطر الأرض الذي يبلغ طوله 12,750 كيلومتر. وعلى سبيل المثال، يبلغ قطر الزهرة 12100 كلم أي 0.95 قطر أرضي.

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## مقدمة

Scale drawing of the oblateness of the 2003 IERS reference ellipsoid. The outer edge of the dark blue line is an ellipse with the same eccentricity as that of the Earth, with north at the top. For comparison, the outer edge of light blue area is a circle of diameter equal to the minor axis. The red line denotes the Karman line and the yellow area, the range of the International Space Station.
مقال رئيسي: صورة الأرض

### فيزياء انبعاج الأرض

Rotation of a planet causes it to approximate an oblate ellipsoid/spheroid with a bulge at the equator and flattening at the North and South Poles, so that the equatorial radius a is larger than the polar radius b by approximately aq. The oblateness constant q is given by

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

where ω is the angular frequency, G is the gravitational constant, and M is the mass of the planet.[أ] For the Earth 1/q ≈ 289, which is close to the measured inverse flattening 1/f ≈ 298.257. 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.[2]

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 110 م (360 قدم) 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).[3]

Not all deformations originate within the Earth. The gravity of the Moon and Sun cause the Earth's surface at a given point to undulate by tenths of meters over a nearly 12-hour period (see Earth tide).

### نصف القطر والأحوال المحلية

البيروني's (973–1048) method for calculation of the Earth's radius improved accuracy.

## أنصاف الأقطار المعتمدة على الموقع

The distance from the Earth's center to a point on the spheroid surface at geodetic latitude φ is:

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

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

• Maximum: The summit of Chimborazo is 6,384.4 kم (3,967.1 ميل) from the Earth's center.
• Minimum: The floor of the Arctic Ocean is approximately 6,352.8 kم (3,947.4 ميل) from the Earth's center.[4]

#### Principal sections

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

##### Meridional

In particular, the Earth's radius of curvature in the (north–south) meridian at φ is:

${\displaystyle M(\varphi )={\frac {(ab)^{2}}{{\big (}(a\cos \varphi )^{2}+(b\sin \varphi )^{2}{\big )}^{\frac {3}{2}}}}\,.}$

This is the radius that Eratosthenes measured.

Three different radii as a function of Earth's latitude. R is the geocentric radius; M is the meridional radius of curvature; and N is the prime vertical radius of curvature.

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

b2/a = 6,335.439 km

The Earth's polar radius of curvature is:

a2/b = 6,399.594 km

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#### Directional

The Earth's radius of curvature along a course at an azimuth (measured clockwise from north) α at φ is derived from Euler's curvature formula as follows:[5]:97

${\displaystyle R_{\mathrm {c} }={\frac {1}{{\dfrac {\cos ^{2}\alpha }{M}}+{\dfrac {\sin ^{2}\alpha }{N}}}}\,.}$

#### Combinations

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

## Notes

1. ^ This follows from the International Astronomical Union definition rule (2): a planet assumes a shape due to hydrostatic equilibrium where gravity and centrifugal forces are nearly balanced.[1]

## References

1. ^
2. ^ Satellites Reveal A Mystery Of Large Change In Earth's Gravity Field , Aug. 1, 2002, Goddard Space Flight Center. Archived April 28, 2010, at the Wayback Machine.
3. ^
4. ^ "Discover-TheWorld.com - Guam - POINTS OF INTEREST - Don't Miss - Mariana Trench". Guam.discover-theworld.com. 1960-01-23. Retrieved 2013-09-16.
5. ^ خطأ استشهاد: وسم <ref> غير صحيح؛ لا نص تم توفيره للمراجع المسماة Torge