2286:
1553:
567:
1152:
4964:
40:
1682:
262:
4733:
1625:. 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
2240:
5316:
4460:
1632:
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
1308:
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
1507:
1570:
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 5 m (16 ft) of reference ellipsoid height, and to within 100 m (330 ft) of mean sea level (neglecting geoid
1227:
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.
7424:
In 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
1963:
5816:
2589:
1890:
7471:
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
5107:
3282:
4728:{\displaystyle R_{\mathrm {a} }(\varphi )={\frac {1}{\sqrt {K}}}={\frac {1}{2\pi }}\int _{0}^{2\pi }R_{\mathrm {c} }(\alpha )\,d\alpha \,={\sqrt {MN}}={\frac {a^{2}b}{(a\cos \varphi )^{2}+(b\sin \varphi )^{2}}}={\frac {a{\sqrt {1-e^{2}}}}{1-e^{2}\sin ^{2}\varphi }}\,.}
6019:
3770:
3113:
4430:
7217:
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.
3609:
5912:
3980:
2952:
1138:
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
2235:{\displaystyle M(\varphi )={\frac {(ab)^{2}}{{\big (}(a\cos \varphi )^{2}+(b\sin \varphi )^{2}{\big )}^{\frac {3}{2}}}}={\frac {a(1-e^{2})}{(1-e^{2}\sin ^{2}\varphi )^{\frac {3}{2}}}}={\frac {1-e^{2}}{a^{2}}}N(\varphi )^{3}\,.}
5558:
4900:
7213:. 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
5685:
4813:
2445:
1730:
1528:, positive above or outside the ellipsoid, negative below or inside. The geoid height variation is under 110 m (360 ft) on Earth. The geoid height can change abruptly due to earthquakes (such as the
5311:{\displaystyle R_{2}={\sqrt {{\frac {1}{2}}\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 }}}\,,}
1539:
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
6590:
6531:
6484:
429:
386:
1120:
478:
343:
6083:
5383:
1301:. 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.
4910:
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
3128:
4955:
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.
8255:) 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),
3911:
3874:
5063:
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 6,371.0088 km (3,958.7613 mi).
1503:. 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.
1433:
4228:
8378:
4178:
4125:
5926:
5058:
4081:
5644:
3620:
2967:
4333:
5917:
For integration limits of , the integrals for rectifying radius and mean radius evaluate to the same result, which, for Earth, amounts to 6,367.4491 km (3,956.5494 mi).
3817:
3470:
2644:
1239:
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:
5831:
3456:
2360:
3919:
3420:
7484:
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.
2406:
203:
8462:
3387:
8504:
7516:
Mamajek, E. E; Prsa, A; Torres, G; et al. (2015). "IAU 2015 Resolution B3 on
Recommended Nominal Conversion Constants for Selected Solar and Planetary Properties".
2320:
1578:, the curvature at a point will be greatest (tightest) in one direction (north–south on Earth) and smallest (flattest) perpendicularly (east–west). The corresponding
5442:
4038:
4263:
2802:
8005:
1566:) method for calculation of the Earth's radius simplified measuring the circumference compared to taking measurements from two locations distant from each other.
5466:
5407:
4283:
4003:
3837:
2263:
7663:
7274:
of the World, soundly demonstrated the sphericity of the Earth, and affirmed the original measurement of 40,000 km (25,000 mi) by
Eratosthenes.
6537:
convention. Equatorial radius is conventionally used as the nominal value unless the polar radius is explicitly required. The nominal radius serves as a
5478:
4835:
5811:{\displaystyle M_{\mathrm {r} }={\frac {2}{\pi }}\int _{0}^{\frac {\pi }{2}}{\sqrt {{a^{2}}\cos ^{2}\varphi +{b^{2}}\sin ^{2}\varphi }}\,d\varphi \,.}
1019:
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
8384:
7561:
8497:
1589:
In summary, local variations in terrain prevent defining a single "precise" radius. One can only adopt an idealized model. Since the estimate by
926:
8034:
2584:{\displaystyle N(\varphi )={\frac {a^{2}}{\sqrt {(a\cos \varphi )^{2}+(b\sin \varphi )^{2}}}}={\frac {a}{\sqrt {1-e^{2}\sin ^{2}\varphi }}}\,.}
1521:
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
6668:
4984:
4749:
1020:
1605:
gained importance, true global models were developed which, while not as accurate for regional work, best approximate the Earth as a whole.
1885:{\displaystyle R(\varphi )={\sqrt {\frac {(a^{2}\cos \varphi )^{2}+(b^{2}\sin \varphi )^{2}}{(a\cos \varphi )^{2}+(b\sin \varphi )^{2}}}},}
7720:
7580:
7595:
748:
8207:
8490:
7750:
4324:
916:
884:
6552:
6493:
6446:
4233:
The first and second radii of curvature correspond, respectively, to the Earth's meridional and prime-vertical radii of curvature.
894:
391:
348:
3277:{\displaystyle A=a_{ij}=\sum _{\nu }{\frac {\partial r^{\nu }}{\partial w^{i}}}{\frac {\partial r^{\nu }}{\partial w^{j}}}=\left,}
1085:
443:
308:
6830:
6034:
5326:
7434:
The value of the radius is completely dependent upon the latitude in the case of an ellipsoid model, and nearly so on the geoid.
8354:
7760:
3879:
3842:
874:
1283:
In the case of the geoid and ellipsoids, the fixed distance from any point on the model to the specified center is called
1377:
854:
8331:
1579:
655:
8009:
7425:
center and orientation of the ellipsoid generally do not coincide with the earth's center of mass or axis of rotation.
8278:
7936:
7904:
6014:{\displaystyle M_{\mathrm {r} }\approx \left({\frac {a^{\frac {3}{2}}+b^{\frac {3}{2}}}{2}}\right)^{\frac {2}{3}}\,,}
4183:
1594:
1270:
1266:
954:
4136:
1652:
and equals 6,378.1370 km (3,963.1906 mi). The equatorial radius is often used to compare Earth with other
7674:
7444:
6624:
6436:
4086:
1140:
6187:. This topographical average is 6,371.230 km (3,958.899 mi) with uncertainty of 10 m (33 ft).
7263:
5010:
3765:{\displaystyle B=b_{ij}=\sum _{\nu }n^{\nu }{\frac {\partial ^{2}r^{\nu }}{\partial w^{i}\partial w^{j}}}=\left,}
2412:
If one point had appeared due east of the other, one finds the approximate curvature in the east–west direction.
1672:
is the distance from its center to the North and South Poles, and equals 6,356.7523 km (3,949.9028 mi).
7644:"Department of Defense World Geodetic System 1984: Its Definition and Relationships with Local Geodetic Systems"
4046:
1175:
8125:
7855:
7780:
3108:{\displaystyle ds^{2}=\sum _{ij}a_{ij}dw^{i}dw^{j}=E\,d\varphi ^{2}+2F\,d\varphi \,d\lambda +G\,d\lambda ^{2},}
1593:, many models have been created. Historically, these models were based on regional topography, giving the best
740:
277:
6102:
The mathematical expressions above apply over the surface of the ellipsoid. The cases below considers Earth's
5591:
4425:{\displaystyle R_{\mathrm {c} }={\frac {1}{{\dfrac {\cos ^{2}\alpha }{M}}+{\dfrac {\sin ^{2}\alpha }{N}}}}\,.}
1582:
depends on the location and direction of measurement from that point. A consequence is that a distance to the
756:
8644:
8528:
7186:
6542:
3604:{\displaystyle 2D=\sum _{ij}b_{ij}dw^{i}dw^{j}=e\,d\varphi ^{2}+2f\,d\varphi \,d\lambda +g\,d\lambda ^{2},}
1529:
7725:
Numerical
Standards for Fundamental Astronomy: Astronomical Constants : Current Best Estimates (CBEs)
8294:
7615:
7599:
1191:
5907:{\displaystyle M_{\mathrm {r} }={\frac {2}{\pi }}\int _{0}^{\frac {\pi }{2}}\!M(\varphi )\,d\varphi \,.}
3777:
1166:, with north at the top. The light blue region is a circle. The outer edge of the dark blue line is an
8680:
8675:
7556:
3975:{\displaystyle N={\frac {\partial r}{\partial \varphi }}\times {\frac {\partial r}{\partial \lambda }}}
2608:
2266:
177:
7447:
7247:, left no doubt among medieval scholars that Earth is spherical, but they were wrong about its size.
5821:
The rectifying radius is equivalent to the meridional mean, which is defined as the average value of
3425:
2325:
1906:
The extrema geocentric radii on the ellipsoid coincide with the equatorial and polar radii. They are
1602:
719:
165:
8197:
8065:
3392:
2270:
8475:
8192:
7335:
6243:
5469:
2365:
686:
633:
184:
8440:
7451:
7302:
3461:
3289:
1586:
at the equator is slightly shorter in the north–south direction than in the east–west direction.
824:
784:
8091:
8639:
7728:
7577:
7345:
2958:
1451:
1309:
the Earth". While specific values differ, the concepts in this article generalize to any major
804:
7896:
7241:, but he accepted the lesser value attributed to Posidonius. His highly influential work, the
4440:
It is possible to combine the principal radii of curvature above in a non-directional manner.
2296:
8344:
8188:
7926:
7355:
5081:
4976:
2947:{\displaystyle (EG-F^{2})\,\kappa ^{2}-(eG+gE-2fF)\,\kappa +(eg-f^{2})=0=\det(A-\kappa \,B),}
2285:
1614:
1574:
Additionally, the radius can be estimated from the curvature of the Earth at a point. Like a
1235:. Strictly speaking, spheres are the only solids to have radii, but broader uses of the term
947:
864:
614:
53:
7888:
8049:
7966:
7317:. The expedition found that Newton's conjecture was correct: the Earth is flattened at the
7251:
7222:
6141:
5420:
5366:
4308:
4011:
2602:
1948:
1556:
764:
714:
640:
8240:
4239:
8:
8649:
8541:
8257:
Another Look at
Eratosthenes' and Posidonius' Determinations of the Earth's Circumference
7391:
7298:
7267:
7182:
6113:
6107:
5662:
5085:
1930:
1707:
1622:
1216:
1211:
1203:
1163:
1123:
1060:
676:
624:
8053:
7970:
6190:
1552:
7982:
7807:
Bowring, B. R. (October 1987). "Notes on the curvature in the prime vertical section".
7517:
7365:
7282:
7225:
recomputed Earth's radius, and found it to be close to that by
Eratosthenes, but later
7178:
5675:
of the ellipse described by any polar cross section of the ellipsoid. This requires an
5451:
5392:
5084:) is the radius of a hypothetical perfect sphere that has the same surface area as the
4446:
4268:
3988:
3822:
2248:
596:
566:
8061:
8586:
8436:
8350:
8327:
8274:
8121:
7986:
7932:
7900:
7889:
7756:
7611:
7459:
7360:
7322:
7318:
7294:
7255:
5676:
5072:
2659:
1718:
1443:
1135:
1068:
696:
681:
8482:
8252:
8222:
7286:
8169:
Drummond, William (1817). "On the
Science of the Egyptians and Chaldeans, Part I".
8057:
7974:
7816:
7370:
7271:
7230:
7190:
6360:
6293:
6256:
5658:
1322:
997:
940:
691:
8406:
7748:
5553:{\displaystyle {\frac {\int K\,dA}{A}}={\frac {4\pi }{A}}={\frac {1}{R_{2}^{2}}}.}
1059:
Other ways to define and measure the Earth's radius involve either the spheroid's
8321:
8145:
8006:"Discover-TheWorld.com – Guam – POINTS OF INTEREST – Don't Miss – Mariana Trench"
7707:
Map
Projections – A Working Manual (US Geological Survey Professional Paper 1395)
7584:
7565:
7412:
7290:
7238:
7210:
6345:
6180:
5649:
For Earth, the volumetric radius equals 6,371.0008 km (3,958.7564 mi).
4990:
4895:{\displaystyle R_{\mathrm {m} }={\frac {2}{{\dfrac {1}{M}}+{\dfrac {1}{N}}}}\,\!}
2598:
2274:
1669:
1645:
1518:
1207:
1195:
989:
21:
17:
7820:
5920:
The meridional mean is well approximated by the semicubic mean of the two axes,
8685:
8670:
8513:
7838:
7205:
6593:
6538:
6356:
6327:
5414:
For the Earth, the authalic radius is 6,371.0072 km (3,958.7603 mi).
4821:
2418:
1934:
1910:
of the ellipse and also coincide with minimum and maximum radius of curvature.
1907:
1598:
1251:
993:
904:
671:
645:
209:
6546:
3728:
3240:
1717:
is the distance from the Earth's center to a point on the spheroid surface at
8664:
8202:
7310:
7209:
that mathematicians had guessed the circumference of the Earth to be 400,000
6337:
5672:
3119:
1919:
539:
521:
8211:. Vol. 8 (11th ed.). Cambridge University Press. pp. 801–813.
6545:. (The notation is defined such that it can be easily generalized for other
6097:
1151:
8567:
8561:
8196:
7706:
7278:
7214:
7195:
The first published reference to the Earth's size appeared around 350
6352:
6341:
6155:
1590:
1049:, which is the radius of a sphere having the same volume as the ellipsoid (
499:
147:
7978:
4963:
1653:
39:
8471:
8317:
7834:
7752:
Global
Navigation Satellite Systems, Inertial Navigation, and Integration
7643:
7234:
7196:
6533:= 6,356.8 km (3,949.9 mi). These values correspond to the zero
1220:
1179:
586:
6486:, which is defined to be exactly 6,378.1 km (3,963.2 mi). The
5572:, which is the radius of a sphere of volume equal to the ellipsoid. The
8622:
8616:
8610:
8598:
7399:
7340:
6534:
6333:
6103:
4808:{\displaystyle K=\kappa _{1}\,\kappa _{2}={\frac {\det \,B}{\det \,A}}}
2428:
1541:
1480:
1343:
1339:
1224:
1223:
cause its shape to deviate systematically from a perfect sphere. Local
1171:
1156:
1131:
1064:
286:
6191:
Derived quantities: diameter, circumference, arc-length, area, volume
1231:
Each of the models in common use involve some notion of the geometric
8592:
8580:
8517:
8141:
7596:
Satellites Reveal A Mystery Of Large Change In Earth's
Gravity Field
7568:, by resolution of the XVII General Assembly of the IUGG in Canberra.
7411:
There is no single center to the geoid; it varies according to local
7200:
6248:
1533:
1262:
1183:
1127:
665:
591:
282:
7254:
believed that traveling 3,000 miles west from the west coast of the
1506:
7710:
p. 16–17. Washington D.C: United States Government Printing Office.
7522:
7306:
7243:
6197:
4236:
Geometrically, the second fundamental form gives the distance from
1626:
1329:
1258:
844:
661:
650:
296:
1681:
7612:
NASA's Grace Finds Greenland Melting Faster, 'Sees' Sumatra Quake
7455:
7350:
7314:
7229:
incorrectly attributed him a value about 3/4 of the actual size.
6604:
This table summarizes the accepted values of the Earth's radius.
4312:
1649:
1583:
1514:
1335:
1167:
1072:
724:
581:
558:
136:
1056:). All three values are about 6,371 kilometres (3,959 mi).
1034:) of three radii measured at two equator points and a pole; the
261:
8604:
8032:
7749:
Mohinder S. Grewal; Angus P. Andrews; Chris G. Bartone (2020).
7226:
7030:
7002:
6835:
6348:, can also be derived from Earth's equatorial and polar radii.
6088:
about 6,367.445 km (3,956.547 mi), can also be used.
4911:
1903:
are, respectively, the equatorial radius and the polar radius.
1618:
1310:
1277:
1232:
1067:. A few definitions yield values outside the range between the
834:
794:
732:
8323:
Before Galileo: The Birth of Modern Science in Medieval Europe
2601:
from the ellipsoid surface to the polar axis. The radius of a
1038:, which is the radius of a sphere with the same surface area (
7578:
IAU 2006 General Assembly: Result of the IAU Resolution votes
7395:
6585:{\displaystyle {\mathcal {R}}_{p\mathrm {J} }^{\mathrm {N} }}
6526:{\displaystyle {\mathcal {R}}_{p\mathrm {E} }^{\mathrm {N} }}
6479:{\displaystyle {\mathcal {R}}_{e\mathrm {E} }^{\mathrm {N} }}
6393:
6158:
is 6,352.8 km (3,947.4 mi) from the Earth's center.
6144:
is 6,384.4 km (3,967.1 mi) from the Earth's center.
6024:
which differs from the exact result by less than 1 μm (4
2796:
The principal curvatures are the roots of Equation (125) in:
1575:
1523:
1247:
1187:
985:
619:
424:{\displaystyle {\mathcal {R}}_{p\mathrm {E} }^{\mathrm {N} }}
381:{\displaystyle {\mathcal {R}}_{e\mathrm {E} }^{\mathrm {N} }}
154:
1115:{\displaystyle {\mathcal {R}}_{\mathrm {E} }^{\mathrm {N} }}
473:{\displaystyle {\mathcal {R}}_{\mathrm {E} }^{\mathrm {N} }}
338:{\displaystyle {\mathcal {R}}_{\mathrm {E} }^{\mathrm {N} }}
8097:
8035:"Mean radius, mass, and inertia for reference Earth models"
7957:
Moritz, H. (March 2000). "Geodetic Reference System 1980".
7259:
6078:{\displaystyle M_{\mathrm {r} }\approx {\frac {a+b}{2}}\,,}
5573:
5378:{\displaystyle \textstyle e={\sqrt {a^{2}-b^{2}}}{\big /}a}
5089:
2649:
1160:
921:
814:
27:
Distance from the Earth surface to a point near its center
7515:
4975:) and arithmetic mean Earth radii as defined in the 1984
2707:
Earth's prime-vertical radius of curvature at the equator
1685:
Three different radii as a function of Earth's latitude.
52:) and arithmetic mean Earth radii as defined in the 1984
8008:. Guam.discover-theworld.com. 1960-01-23. Archived from
1008:) of nearly 6,378 km (3,963 mi) to a minimum (
3906:{\displaystyle {\frac {\partial r}{\partial \lambda }}}
3869:{\displaystyle {\frac {\partial r}{\partial \varphi }}}
8380:
Méthode de déterminer si la terre est sphérique ou non
5330:
1608:
8512:
8443:
8342:
6555:
6496:
6449:
6171:
averages elevations everywhere, resulting in a value
6037:
5929:
5834:
5688:
5594:
5481:
5454:
5423:
5395:
5329:
5110:
5013:
4876:
4861:
4838:
4752:
4463:
4389:
4359:
4336:
4271:
4242:
4186:
4139:
4089:
4049:
4014:
3991:
3922:
3882:
3845:
3825:
3780:
3623:
3473:
3428:
3395:
3292:
3131:
2970:
2805:
2656:
Earth's meridional radius of curvature at the equator
2611:
2448:
2368:
2328:
2299:
2251:
1966:
1733:
1380:
1088:
988:
to a point on or near its surface. Approximating the
446:
394:
351:
311:
187:
8259:, Ql. J. of the Royal Astron. Soc., Vol. 16, p. 152.
7727:. IAU Division I Working Group. 2012. Archived from
6974:
WGS-84 ellipsoid, Radius of Sphere of Equal Volume (
8273:. New York: Springer-Verlag New York. p. 138.
1428:{\displaystyle q={\frac {a^{3}\omega ^{2}}{GM}}\,,}
1075:radius because they account for localized effects.
8456:
7853:
7778:
7755:(4 ed.). John Wiley & Sons. p. 512.
6945:WGS-84 ellipsoid, Radius of Sphere of Equal Area (
6584:
6525:
6478:
6077:
6013:
5906:
5810:
5671:, giving a sphere with circumference equal to the
5638:
5552:
5460:
5436:
5401:
5377:
5310:
5052:
4894:
4807:
4727:
4424:
4277:
4257:
4222:
4172:
4119:
4075:
4032:
3997:
3974:
3905:
3868:
3831:
3811:
3764:
3603:
3450:
3414:
3381:
3276:
3107:
2946:
2638:
2583:
2400:
2354:
2314:
2257:
2234:
1884:
1427:
1114:
472:
423:
380:
337:
197:
7297:instead, due to different interpretations of the
6217:). For the WGS84 ellipsoid, that's respectively:
5880:
5049:
4891:
1327:Rotation of a planet causes it to approximate an
1316:
8662:
8083:
7700:
7698:
7696:
7694:
5468:, over the surface of the ellipsoid. Using the
5448:, obtained by averaging the Gaussian curvature,
5101:. A closed-form solution exists for a spheroid:
4795:
4786:
2919:
5679:to find, given the polar and equatorial radii:
4223:{\displaystyle R_{2}={\frac {1}{\kappa _{2}}}.}
1924:
8346:Magellan and the First Voyage Around the World
7089:meridional radius of curvature at the equator
4293:
4173:{\displaystyle R_{1}={\frac {1}{\kappa _{1}}}}
3614:e, f, and g are elements of the shape tensor:
1547:
8498:
8187:
7952:
7950:
7948:
7691:
7262:. However, the 1492 enactment of that voyage
6890:WGS-84 ellipsoid, polar radius of curvature (
6201:is simply twice Earth's radius; for example,
4985:International Union of Geodesy and Geophysics
4120:{\displaystyle \kappa _{2}={\frac {e}{E}}\,,}
2597:can also be interpreted geometrically as the
2069:
2008:
1021:International Union of Geodesy and Geophysics
948:
8042:Physics of the Earth and Planetary Interiors
6916:WGS-84 ellipsoid, Mean radius of semi-axes (
6162:
1219:, internal density variations, and external
1023:(IUGG) provides three reference values: the
1016:) of nearly 6,357 km (3,950 mi).
8120:. John Wiley & Sons, Inc. p. 923.
7638:
7636:
7634:
7632:
7630:
7628:
7626:
7624:
5053:{\displaystyle R_{1}={\frac {2a+b}{3}}\,\!}
4040:for an oblate spheroid, the curvatures are
1693:is the meridional radius of curvature; and
1676:
8505:
8491:
8434:
8033:Frédéric Chambat; Bernard Valette (2001).
8028:
8026:
8000:
7998:
7996:
7945:
7895:. McGraw Hill Book Company, Inc. pp.
7511:
7509:
7507:
7505:
7503:
7501:
7450:rule (2): a planet assumes a shape due to
7258:would let him reach the eastern coasts of
6236:= 12,713.5046 km (7,899.8055 mi)
6226:= 12,756.2740 km (7,926.3812 mi)
5568:Another spherical model is defined by the
4076:{\displaystyle \kappa _{1}={\frac {g}{G}}}
2729:(either meridional or prime-vertical) is:
1933:: along the meridional and prime-vertical
1697:is the prime vertical radius of curvature.
1178:as the Earth. The red line represents the
955:
941:
922:Spatial Reference System Identifier (SRID)
917:International Terrestrial Reference System
260:
38:
8404:
7774:
7772:
7521:
6369:, or that of the reference ellipsoid, is
6127:
6071:
6007:
5900:
5893:
5804:
5797:
5632:
5491:
5304:
5048:
4958:
4890:
4798:
4789:
4769:
4721:
4564:
4557:
4418:
4130:and the principal radii of curvature are
4113:
3584:
3571:
3564:
3541:
3088:
3075:
3068:
3045:
2934:
2878:
2831:
2577:
2391:
2384:
2329:
2228:
1648:, is the distance from its center to the
1613:The following radii are derived from the
1479:, which is close to the measured inverse
1458:is the mass of the planet. For the Earth
1421:
8268:
8168:
8115:
8109:
8089:
7920:
7918:
7916:
7621:
7551:
7549:
7547:
7545:
7543:
7541:
7539:
7537:
7535:
7533:
7465:
7289:than to a sphere. However, around 1730,
7149:Average distance from center to surface
7129:Minimum (the floor of the Arctic Ocean)
5639:{\displaystyle R_{3}={\sqrt{a^{2}b}}\,.}
4962:
2650:Polar and equatorial radius of curvature
2284:
1680:
1597:for the area under survey. As satellite
1551:
1150:
8376:
8023:
7993:
7882:
7880:
7878:
7863:. Ohio State University, Columbus, Ohio
7833:
7806:
7800:
7788:. Ohio State University, Columbus, Ohio
7498:
6028:10 in); the mean of the two axes,
2269:of the earth. This is the radius that
1289:"the radius of the Earth at that point"
8663:
7956:
7857:Geometric Reference Systems in Geodesy
7782:Geometric Reference Systems in Geodesy
7769:
6184:
6169:topographical mean geocentric distance
6124:, which depends not only on latitude.
6091:
2425:Earth's transverse radius of curvature
1532:) or reduction in ice masses (such as
1304:Regardless of the model, any of these
190:
8486:
8140:
7924:
7913:
7530:
7237:gave empirical evidence supporting a
6270:, in terms of the equatorial radius,
5411:is the surface area of the spheroid.
3819:is the unit normal to the surface at
1913:
1000:), the radius ranges from a maximum (
984:) is the distance from the center of
8464:The Earth's Radius (and exoplanets)"
7886:
7875:
7301:involved. To settle the matter, the
7187:Earth's circumference § History
5652:
5563:
1701:
1291:. It is also common to refer to any
1186:, while the yellow area denotes the
16:For its historical development, see
8223:"Eratosthenes, the Greek Scientist"
7305:(1735–1739) measured one degree of
7285:argued that Earth was closer to an
7109:Maximum (the summit of Chimborazo)
7061:Spherical Earth Approx. of Radius (
6864:WGS-84 ellipsoid, semi-minor axis (
6599:
3464:for a surface (Equation (123) in):
2961:for a surface (Equation (112) in):
1609:Extrema: equatorial and polar radii
1269:to model the entire Earth, or else
927:Universal Transverse Mercator (UTM)
889:European Terrestrial Ref. Sys. 1989
13:
6775:radius of sphere of same surface (
6576:
6569:
6559:
6517:
6510:
6500:
6470:
6463:
6453:
6044:
5936:
5841:
5695:
5066:
4845:
4542:
4470:
4435:
4343:
3963:
3955:
3940:
3932:
3894:
3886:
3857:
3849:
3812:{\displaystyle n={\frac {N}{|N|}}}
3704:
3691:
3670:
3216:
3201:
3182:
3167:
1953:(in the north–south direction) at
1505:
1106:
1099:
1092:
799:Ordnance Survey Great Britain 1936
765:Discrete Global Grid and Geocoding
656:Horizontal position representation
464:
457:
450:
415:
408:
398:
372:
365:
355:
329:
322:
315:
14:
8697:
8428:
8090:Williams, David R. (2004-09-01),
7270:(1519–1522), which was the first
7264:brought his fleet to the Americas
6804:radius of sphere of same volume (
5576:denotes the volumetric radius as
5446:radius of (global) mean curvature
2727:Earth's polar radius of curvature
2639:{\displaystyle p=N\cos(\varphi )}
2280:
1254:at each point on the real surface
266:Cross section of Earth's Interior
8405:Levallois, Jean-Jacques (1986).
8295:"Almagest – Ptolemy (Elizabeth)"
7721:"Equatorial Radius of the Earth"
7445:International Astronomical Union
6437:International Astronomical Union
6430:
6176:
4315:(measured clockwise from north)
3118:E, F, and G are elements of the
1141:International Astronomical Union
715:Global Nav. Sat. Systems (GNSSs)
565:
8435:Merrifield, Michael R. (2010).
8398:
8370:
8336:
8311:
8287:
8262:
8245:
8233:
8215:
8181:
8162:
8134:
7847:
7827:
7742:
7713:
7656:
7605:
7475:
7309:at two locations, one near the
6629:nominal "zero tide" equatorial
6441:nominal equatorial Earth radius
5092:denotes the authalic radius as
4905:
3451:{\displaystyle w^{2}=\lambda ,}
2355:{\displaystyle \,e^{2}N(\phi )}
1293:
1182:100 km (62 mi) above
1146:
879:N. American Vertical Datum 1988
8343:Nancy Smiler Levinson (2001).
7589:
7571:
7558:Geodetic Reference System 1980
7437:
7428:
7418:
7405:
7384:
7183:Spherical Earth § History
5890:
5884:
4643:
4627:
4615:
4599:
4554:
4548:
4482:
4476:
3802:
3794:
3415:{\displaystyle w^{1}=\varphi }
3370:
3351:
3339:
3299:
2938:
2922:
2907:
2885:
2875:
2845:
2828:
2806:
2709:equals the equatorial radius,
2633:
2627:
2521:
2505:
2493:
2477:
2458:
2452:
2395:
2375:
2349:
2343:
2309:
2303:
2219:
2212:
2157:
2121:
2116:
2097:
2057:
2041:
2029:
2013:
1995:
1985:
1976:
1970:
1866:
1850:
1838:
1822:
1811:
1788:
1776:
1753:
1743:
1737:
1317:Physics of Earth's deformation
909:Internet link to a point 2010
839:Geodetic Reference System 1980
757:Quasi-Zenith Sat. Sys. (QZSS)
1:
8349:. Houghton Mifflin Harcourt.
8062:10.1016/S0031-9201(01)00200-X
7491:
6314:enters via the eccentricity,
5667:Another global radius is the
4305:azimuthal radius of curvature
3913:are tangents to the surface,
2779:
2401:{\displaystyle R=(X,\,Y,\,Z)}
1940:
1560:
899:Chinese obfuscated datum 2002
198:{\displaystyle {\mathsf {L}}}
20:. For its determination, see
8645:Orders of magnitude (length)
8529:Astronomical system of units
8198:"Earth, Figure of the"
6838:ellipsoid, semi-major axis (
6392:. Using the parameters from
4447:Gaussian radius of curvature
4298:
3985:is normal to the surface at
2427:, is defined perpendicular (
2322:. The length IQ is equal to
1931:principal radii of curvature
1925:Principal radii of curvature
849:Geographic point coord. 1983
7:
8457:{\displaystyle R_{\oplus }}
8383:(in French). Archived from
7854:Christopher Jekeli (2016).
7821:10.1179/sre.1987.29.226.195
7779:Christopher Jekeli (2016).
7616:Goddard Space Flight Center
7600:Goddard Space Flight Center
7328:
7191:Meridian arc § History
6720:polar radius of curvature (
6098:Earth § Size and shape
4294:Combined radii of curvature
3382:{\displaystyle r=^{T}=^{T}}
1548:Radius and local conditions
1243:The actual surface of Earth
1174:as the circle and the same
809:Systema Koordinat 1942 goda
10:
8702:
7891:Vector and Tensor Analysis
7843:. Oxford University Press.
7176:
7172:
6650:nominal "zero tide" polar
6488:nominal polar Earth radius
6310:), where the polar radius
6095:
5656:
5070:
2289:The length PQ, called the
1917:
1705:
1689:is the geocentric radius;
1530:Sumatra-Andaman earthquake
1320:
1201:
869:World Geodetic System 1984
15:
8632:
8537:
8524:
8377:Cassini, Jacques (1738).
8193:Helmert, Friedrich Robert
8150:. Vol. Book II 298 B
8116:Phillips, Warren (2004).
6396:ellipsoid of revolution,
6163:Topographical global mean
5669:Earth's rectifying radius
5570:Earth's volumetric radius
4325:Euler's curvature formula
1920:Spheroid § Curvature
1603:Global Positioning System
1299:"the radius of the earth"
1122:) is sometimes used as a
859:North American Datum 1983
829:South American Datum 1969
535:
517:
495:
491:
434:
302:
292:
276:
271:
259:
254:
208:
176:
160:
145:
135:
71:
61:
37:
32:
8476:University of Nottingham
7925:Torge, Wolfgang (2001).
7377:
6253:equatorial circumference
5444:also corresponds to the
5387:is the eccentricity and
4822:mean radius of curvature
4265:to the plane tangent at
2315:{\displaystyle N(\phi )}
1724:, given by the formula:
1706:Not to be confused with
1677:Location-dependent radii
1297:of a spherical model as
720:Global Pos. System (GPS)
687:Spatial reference system
8413:. pp. 277–284, 288
8299:projects.iq.harvard.edu
8269:Thurston, Hugh (1994).
8208:Encyclopædia Britannica
7452:hydrostatic equilibrium
7313:and the other near the
7303:French Geodesic Mission
5078:Earth's authalic radius
4979:revision (not to scale)
3462:second fundamental form
1285:"a radius of the Earth"
1155:A scale diagram of the
56:revision (not to scale)
8640:Cosmic distance ladder
8458:
8189:Clarke, Alexander Ross
7443:This follows from the
7346:Effective Earth radius
6592:for the nominal polar
6586:
6527:
6490:is defined exactly as
6480:
6128:Topographical extremes
6079:
6015:
5908:
5812:
5640:
5554:
5462:
5438:
5403:
5379:
5312:
5054:
4980:
4959:Arithmetic mean radius
4896:
4809:
4729:
4426:
4279:
4259:
4224:
4174:
4121:
4077:
4034:
3999:
3976:
3907:
3870:
3833:
3813:
3766:
3605:
3452:
3416:
3383:
3278:
3109:
2959:first fundamental form
2948:
2658:equals the meridian's
2640:
2585:
2409:
2402:
2356:
2316:
2259:
2236:
1886:
1698:
1567:
1510:
1452:gravitational constant
1429:
1338:and flattening at the
1199:
1116:
548:3,950 to 3,963 mi
530:6,357 to 6,378 km
474:
425:
382:
339:
199:
8459:
8407:"La Vie des sciences"
8171:The Classical Journal
7979:10.1007/s001900050278
7704:Snyder, J.P. (1987).
7614:, December 20, 2005,
7356:Geographical distance
7336:Earth's circumference
7203:reported in his book
6587:
6528:
6481:
6328:Ellipse#Circumference
6244:Earth's circumference
6080:
6016:
5909:
5813:
5641:
5555:
5463:
5439:
5437:{\displaystyle R_{2}}
5404:
5380:
5313:
5055:
4977:World Geodetic System
4966:
4897:
4810:
4730:
4427:
4280:
4260:
4225:
4175:
4122:
4078:
4035:
4033:{\displaystyle F=f=0}
4000:
3977:
3908:
3871:
3834:
3814:
3767:
3606:
3453:
3417:
3384:
3279:
3110:
2949:
2641:
2586:
2435:at geodetic latitude
2403:
2357:
2317:
2291:prime vertical radius
2288:
2260:
2237:
1887:
1684:
1615:World Geodetic System
1555:
1509:
1430:
1321:Further information:
1154:
1117:
615:Geographical distance
475:
426:
383:
340:
200:
54:World Geodetic System
8441:
7887:Lass, Harry (1950).
7462:are nearly balanced.
7252:Christopher Columbus
7223:Posidonius of Apamea
7221:Around 100 BC,
6553:
6494:
6447:
6355:, either based on a
6114:geocentric distances
6110:. As such, they are
6035:
5927:
5832:
5686:
5592:
5479:
5470:Gauss–Bonnet theorem
5452:
5421:
5417:The authalic radius
5393:
5327:
5108:
5011:
4836:
4750:
4461:
4334:
4309:Earth normal section
4269:
4258:{\displaystyle r+dr}
4240:
4184:
4137:
4087:
4047:
4012:
3989:
3920:
3880:
3843:
3823:
3778:
3621:
3471:
3426:
3393:
3290:
3129:
2968:
2803:
2609:
2603:parallel of latitude
2446:
2366:
2326:
2297:
2249:
1964:
1731:
1378:
1334:with a bulge at the
1086:
1080:nominal Earth radius
789:Sea Level Datum 1929
641:Geodetic coordinates
444:
392:
349:
309:
255:Nominal Earth radius
185:
166:coord transformation
8650:Conversion of units
8118:Mechanics of Flight
8054:2001PEPI..124..237C
7971:2000JGeod..74..128.
7555:Moritz, H. (1980).
7392:figure of the Earth
7299:Newtonian mechanics
7268:Magellan expedition
6581:
6522:
6475:
6425:10 cu mi)
6276:polar circumference
6203:equatorial diameter
6154:: the floor of the
6108:reference ellipsoid
6106:, above or below a
6092:Topographical radii
5879:
5733:
5663:Rectifying latitude
5544:
5086:reference ellipsoid
4987:(IUGG) defines the
4983:In geophysics, the
4914:ellipsoid; namely,
4535:
2421:radius of curvature
1951:radius of curvature
1945:In particular, the
1708:Geocentric distance
1623:reference ellipsoid
1601:and especially the
1595:reference ellipsoid
1580:radius of curvature
1366:oblateness constant
1353:is larger than the
1212:Reference ellipsoid
1204:Figure of the Earth
1164:reference ellipsoid
1124:unit of measurement
1111:
1061:radius of curvature
819:European Datum 1950
777:Standards (history)
677:Reference ellipsoid
625:Figure of the Earth
486:... is equal to ...
469:
420:
377:
334:
272:General information
8454:
7959:Journal of Geodesy
7671:earth-info.nga.mil
7583:2006-11-07 at the
7564:2016-02-20 at the
7460:centrifugal forces
7366:History of geodesy
7321:due to rotation's
7283:Christiaan Huygens
7179:History of geodesy
6673:equatorial radius
6616:Value (in meters)
6582:
6556:
6523:
6497:
6476:
6450:
6435:In astronomy, the
6421:10 km (2.5988
6075:
6011:
5904:
5860:
5808:
5714:
5636:
5550:
5530:
5458:
5434:
5399:
5375:
5374:
5308:
5050:
4981:
4892:
4885:
4870:
4805:
4744:Gaussian curvature
4725:
4518:
4422:
4413:
4383:
4323:, is derived from
4275:
4255:
4220:
4170:
4117:
4073:
4030:
3995:
3972:
3903:
3866:
3829:
3809:
3762:
3753:
3655:
3601:
3495:
3448:
3412:
3379:
3274:
3265:
3163:
3105:
2999:
2944:
2636:
2581:
2423:, also called the
2410:
2398:
2352:
2312:
2255:
2232:
1914:Radii of curvature
1882:
1699:
1568:
1511:
1425:
1200:
1112:
1089:
697:Vertical positions
545:
537:
527:
519:
505:
497:
470:
447:
421:
395:
378:
352:
335:
312:
195:
149:SI base units
67:terrestrial radius
8681:Planetary geology
8676:Planetary science
8658:
8657:
8587:Astronomical unit
8356:978-0-395-98773-5
7762:978-1-119-54783-9
7361:Osculating sphere
7323:centrifugal force
7256:Iberian Peninsula
7170:
7169:
7033:semi-minor axis (
7005:semi-major axis (
6292:, four times the
6185:volumetric radius
6069:
6004:
5990:
5983:
5965:
5877:
5858:
5795:
5731:
5712:
5677:elliptic integral
5653:Rectifying radius
5630:
5564:Volumetric radius
5545:
5520:
5502:
5461:{\displaystyle K}
5402:{\displaystyle A}
5362:
5302:
5301:
5282:
5280:
5252:
5232:
5210:
5203:
5169:
5134:
5073:Authalic latitude
5046:
4919:Equatorial radius
4888:
4884:
4869:
4803:
4719:
4682:
4653:
4576:
4516:
4498:
4497:
4416:
4412:
4382:
4290:
4289:
4278:{\displaystyle r}
4215:
4168:
4111:
4071:
3998:{\displaystyle r}
3970:
3947:
3901:
3864:
3832:{\displaystyle r}
3807:
3718:
3646:
3483:
3230:
3196:
3154:
2987:
2775:6,399.594 km
2701:6,335.439 km
2660:semi-latus rectum
2575:
2574:
2531:
2530:
2258:{\displaystyle e}
2207:
2172:
2168:
2086:
2082:
1877:
1876:
1719:geodetic latitude
1715:geocentric radius
1702:Geocentric radius
1639:equatorial radius
1513:The variation in
1444:angular frequency
1419:
1360:by approximately
1348:equatorial radius
1273:for regional work
1261:, also called an
1136:conversion factor
1047:volumetric radius
1002:equatorial radius
965:
964:
913:
912:
692:Spatial relations
682:Satellite geodesy
637:
553:
552:
435:Conversions
250:
249:
215:Equatorial radius
8693:
8507:
8500:
8493:
8484:
8483:
8479:
8463:
8461:
8460:
8455:
8453:
8452:
8422:
8421:
8419:
8418:
8402:
8396:
8395:
8393:
8392:
8374:
8368:
8367:
8365:
8363:
8340:
8334:
8315:
8309:
8308:
8306:
8305:
8291:
8285:
8284:
8266:
8260:
8249:
8243:
8237:
8231:
8230:
8219:
8213:
8212:
8200:
8185:
8179:
8178:
8166:
8160:
8159:
8157:
8155:
8138:
8132:
8131:
8113:
8107:
8106:
8105:
8104:
8093:Earth Fact Sheet
8087:
8081:
8080:
8078:
8076:
8070:
8064:. Archived from
8048:(3–4): 234–253.
8039:
8030:
8021:
8020:
8018:
8017:
8002:
7991:
7990:
7954:
7943:
7942:
7922:
7911:
7910:
7894:
7884:
7873:
7872:
7870:
7868:
7862:
7851:
7845:
7844:
7831:
7825:
7824:
7815:(226): 195–196.
7804:
7798:
7797:
7795:
7793:
7787:
7776:
7767:
7766:
7746:
7740:
7739:
7737:
7736:
7717:
7711:
7702:
7689:
7688:
7686:
7685:
7679:
7673:. Archived from
7668:
7660:
7654:
7653:
7651:
7650:
7640:
7619:
7609:
7603:
7598:, Aug. 1, 2002,
7593:
7587:
7575:
7569:
7553:
7528:
7527:
7525:
7513:
7485:
7483:
7479:
7473:
7469:
7463:
7441:
7435:
7432:
7426:
7422:
7416:
7409:
7403:
7390:For details see
7388:
7371:Planetary radius
7295:prolate spheroid
7272:circumnavigation
7233:around 150
7231:Claudius Ptolemy
7164:
7162:
7159:
7156:
7140:
7139:
7136:
7120:
7119:
7116:
7100:
7099:
7096:
7080:
7078:
7075:
7052:
7051:
7047:
7044:
7021:
7019:
7016:
6993:
6991:
6988:
6964:
6962:
6959:
6935:
6933:
6930:
6906:
6904:
6901:
6880:
6878:
6875:
6854:
6852:
6849:
6823:
6821:
6818:
6794:
6792:
6789:
6765:
6763:
6760:
6736:
6734:
6731:
6710:
6708:
6705:
6694:semiminor axis (
6684:
6683:
6680:
6661:
6660:
6657:
6640:
6639:
6636:
6607:
6606:
6600:Published values
6591:
6589:
6588:
6583:
6580:
6579:
6573:
6572:
6563:
6562:
6532:
6530:
6529:
6524:
6521:
6520:
6514:
6513:
6504:
6503:
6485:
6483:
6482:
6477:
6474:
6473:
6467:
6466:
6457:
6456:
6426:
6424:
6420:
6414:
6413:
6411:
6407:
6399:
6398:a = 6,378.137 km
6391:
6389:
6386:
6384:
6383:
6380:
6377:
6361:geodesic polygon
6336:of more general
6294:quarter meridian
6257:circle perimeter
6237:
6227:
6177:IUGG mean radius
6175:larger than the
6174:
6140:: the summit of
6084:
6082:
6081:
6076:
6070:
6065:
6054:
6049:
6048:
6047:
6027:
6020:
6018:
6017:
6012:
6006:
6005:
5997:
5995:
5991:
5986:
5985:
5984:
5976:
5967:
5966:
5958:
5951:
5941:
5940:
5939:
5913:
5911:
5910:
5905:
5878:
5870:
5868:
5859:
5851:
5846:
5845:
5844:
5824:
5817:
5815:
5814:
5809:
5796:
5788:
5787:
5778:
5777:
5776:
5757:
5756:
5747:
5746:
5745:
5735:
5732:
5724:
5722:
5713:
5705:
5700:
5699:
5698:
5659:Quarter meridian
5645:
5643:
5642:
5637:
5631:
5629:
5624:
5620:
5619:
5609:
5604:
5603:
5584:
5559:
5557:
5556:
5551:
5546:
5543:
5538:
5526:
5521:
5516:
5508:
5503:
5498:
5483:
5467:
5465:
5464:
5459:
5443:
5441:
5440:
5435:
5433:
5432:
5410:
5408:
5406:
5405:
5400:
5386:
5384:
5382:
5381:
5376:
5370:
5369:
5363:
5361:
5360:
5348:
5347:
5338:
5317:
5315:
5314:
5309:
5303:
5300:
5289:
5288:
5283:
5281:
5276:
5269:
5268:
5255:
5253:
5248:
5247:
5238:
5233:
5228:
5227:
5218:
5216:
5211:
5209:
5205:
5204:
5202:
5198:
5189:
5178:
5170:
5165:
5164:
5155:
5150:
5149:
5135:
5127:
5125:
5120:
5119:
5100:
5059:
5057:
5056:
5051:
5047:
5042:
5028:
5023:
5022:
5003:
4950:
4948:
4942:
4932:
4930:
4924:
4901:
4899:
4898:
4893:
4889:
4887:
4886:
4877:
4871:
4862:
4855:
4850:
4849:
4848:
4828:
4814:
4812:
4811:
4806:
4804:
4802:
4793:
4784:
4779:
4778:
4768:
4767:
4734:
4732:
4731:
4726:
4720:
4718:
4711:
4710:
4701:
4700:
4684:
4683:
4681:
4680:
4665:
4659:
4654:
4652:
4651:
4650:
4623:
4622:
4597:
4593:
4592:
4582:
4577:
4569:
4547:
4546:
4545:
4534:
4526:
4517:
4515:
4504:
4499:
4493:
4489:
4475:
4474:
4473:
4453:
4431:
4429:
4428:
4423:
4417:
4415:
4414:
4408:
4401:
4400:
4390:
4384:
4378:
4371:
4370:
4360:
4353:
4348:
4347:
4346:
4322:
4319:and at latitude
4318:
4284:
4282:
4281:
4276:
4264:
4262:
4261:
4256:
4229:
4227:
4226:
4221:
4216:
4214:
4213:
4201:
4196:
4195:
4179:
4177:
4176:
4171:
4169:
4167:
4166:
4154:
4149:
4148:
4126:
4124:
4123:
4118:
4112:
4104:
4099:
4098:
4082:
4080:
4079:
4074:
4072:
4064:
4059:
4058:
4039:
4037:
4036:
4031:
4004:
4002:
4001:
3996:
3981:
3979:
3978:
3973:
3971:
3969:
3961:
3953:
3948:
3946:
3938:
3930:
3912:
3910:
3909:
3904:
3902:
3900:
3892:
3884:
3875:
3873:
3872:
3867:
3865:
3863:
3855:
3847:
3838:
3836:
3835:
3830:
3818:
3816:
3815:
3810:
3808:
3806:
3805:
3797:
3788:
3771:
3769:
3768:
3763:
3758:
3754:
3719:
3717:
3716:
3715:
3703:
3702:
3689:
3688:
3687:
3678:
3677:
3667:
3665:
3664:
3654:
3642:
3641:
3610:
3608:
3607:
3602:
3597:
3596:
3554:
3553:
3534:
3533:
3521:
3520:
3508:
3507:
3494:
3457:
3455:
3454:
3449:
3438:
3437:
3421:
3419:
3418:
3413:
3405:
3404:
3388:
3386:
3385:
3380:
3378:
3377:
3347:
3346:
3337:
3336:
3324:
3323:
3311:
3310:
3283:
3281:
3280:
3275:
3270:
3266:
3231:
3229:
3228:
3227:
3214:
3213:
3212:
3199:
3197:
3195:
3194:
3193:
3180:
3179:
3178:
3165:
3162:
3150:
3149:
3114:
3112:
3111:
3106:
3101:
3100:
3058:
3057:
3038:
3037:
3025:
3024:
3012:
3011:
2998:
2983:
2982:
2953:
2951:
2950:
2945:
2906:
2905:
2841:
2840:
2827:
2826:
2789:Extended content
2785:
2784:
2774:
2770:
2767:
2766:
2764:
2763:
2758:
2755:
2721:
2700:
2696:
2693:
2692:
2690:
2689:
2684:
2681:
2645:
2643:
2642:
2637:
2590:
2588:
2587:
2582:
2576:
2567:
2566:
2557:
2556:
2541:
2537:
2532:
2529:
2528:
2501:
2500:
2476:
2475:
2474:
2465:
2438:
2434:
2407:
2405:
2404:
2399:
2361:
2359:
2358:
2353:
2339:
2338:
2321:
2319:
2318:
2313:
2273:measured in his
2264:
2262:
2261:
2256:
2241:
2239:
2238:
2233:
2227:
2226:
2208:
2206:
2205:
2196:
2195:
2194:
2178:
2173:
2171:
2170:
2169:
2161:
2149:
2148:
2139:
2138:
2119:
2115:
2114:
2092:
2087:
2085:
2084:
2083:
2075:
2073:
2072:
2065:
2064:
2037:
2036:
2012:
2011:
2004:
2003:
2002:
1983:
1956:
1902:
1898:
1891:
1889:
1888:
1883:
1878:
1875:
1874:
1873:
1846:
1845:
1820:
1819:
1818:
1800:
1799:
1784:
1783:
1765:
1764:
1751:
1750:
1723:
1696:
1692:
1688:
1667:
1643:
1565:
1562:
1502:
1500:
1498:
1497:
1492:
1489:
1478:
1476:
1474:
1473:
1468:
1465:
1457:
1449:
1441:
1434:
1432:
1431:
1426:
1420:
1418:
1410:
1409:
1408:
1399:
1398:
1388:
1370:
1363:
1359:
1352:
1330:oblate ellipsoid
1323:Equatorial bulge
1217:Earth's rotation
1121:
1119:
1118:
1113:
1110:
1109:
1103:
1102:
1096:
1095:
998:oblate ellipsoid
957:
950:
943:
781:
780:
760:
752:
744:
736:
728:
668:
627:
569:
555:
554:
549:
546:
538:
531:
528:
520:
513:
511:
506:
498:
479:
477:
476:
471:
468:
467:
461:
460:
454:
453:
430:
428:
427:
422:
419:
418:
412:
411:
402:
401:
387:
385:
384:
379:
376:
375:
369:
368:
359:
358:
344:
342:
341:
336:
333:
332:
326:
325:
319:
318:
264:
252:
251:
245:
243:
237:
228:
226:
220:
204:
202:
201:
196:
194:
193:
168:
150:
42:
30:
29:
8701:
8700:
8696:
8695:
8694:
8692:
8691:
8690:
8661:
8660:
8659:
8654:
8628:
8576:
8573:
8556:
8550:
8547:
8533:
8520:
8514:Units of length
8511:
8448:
8444:
8442:
8439:
8438:
8431:
8426:
8425:
8416:
8414:
8403:
8399:
8390:
8388:
8375:
8371:
8361:
8359:
8357:
8341:
8337:
8316:
8312:
8303:
8301:
8293:
8292:
8288:
8281:
8271:Early astronomy
8267:
8263:
8253:in Fragment 202
8250:
8246:
8238:
8234:
8221:
8220:
8216:
8186:
8182:
8167:
8163:
8153:
8151:
8139:
8135:
8128:
8114:
8110:
8102:
8100:
8088:
8084:
8074:
8072:
8071:on 30 July 2020
8068:
8037:
8031:
8024:
8015:
8013:
8004:
8003:
7994:
7955:
7946:
7939:
7923:
7914:
7907:
7885:
7876:
7866:
7864:
7860:
7852:
7848:
7832:
7828:
7805:
7801:
7791:
7789:
7785:
7777:
7770:
7763:
7747:
7743:
7734:
7732:
7719:
7718:
7714:
7703:
7692:
7683:
7681:
7677:
7666:
7662:
7661:
7657:
7648:
7646:
7642:
7641:
7622:
7610:
7606:
7594:
7590:
7585:Wayback Machine
7576:
7572:
7566:Wayback Machine
7554:
7531:
7514:
7499:
7494:
7489:
7488:
7481:
7480:
7476:
7470:
7466:
7442:
7438:
7433:
7429:
7423:
7419:
7410:
7406:
7389:
7385:
7380:
7375:
7331:
7291:Jacques Cassini
7287:oblate spheroid
7239:spherical Earth
7193:
7175:
7160:
7157:
7154:
7152:
7137:
7134:
7132:
7117:
7114:
7112:
7097:
7094:
7092:
7076:
7073:
7071:
7066:
7049:
7045:
7042:
7040:
7017:
7014:
7012:
6989:
6986:
6984:
6979:
6960:
6957:
6955:
6950:
6931:
6928:
6926:
6921:
6902:
6899:
6897:
6876:
6873:
6871:
6850:
6847:
6845:
6819:
6816:
6814:
6809:
6790:
6787:
6785:
6780:
6761:
6758:
6756:
6751:
6732:
6729:
6727:
6706:
6703:
6701:
6681:
6678:
6676:
6658:
6655:
6653:
6637:
6634:
6632:
6602:
6575:
6574:
6568:
6564:
6558:
6557:
6554:
6551:
6550:
6516:
6515:
6509:
6505:
6499:
6498:
6495:
6492:
6491:
6469:
6468:
6462:
6458:
6452:
6451:
6448:
6445:
6444:
6433:
6422:
6418:
6416:
6409:
6405:
6403:
6401:
6397:
6387:
6381:
6378:
6375:
6374:
6372:
6370:
6300:
6290:
6283:
6264:
6231:
6221:
6193:
6181:authalic radius
6172:
6165:
6152:
6138:
6130:
6122:
6100:
6094:
6055:
6053:
6043:
6042:
6038:
6036:
6033:
6032:
6025:
5996:
5975:
5971:
5957:
5953:
5952:
5950:
5946:
5945:
5935:
5934:
5930:
5928:
5925:
5924:
5869:
5864:
5850:
5840:
5839:
5835:
5833:
5830:
5829:
5822:
5783:
5779:
5772:
5768:
5767:
5752:
5748:
5741:
5737:
5736:
5734:
5723:
5718:
5704:
5694:
5693:
5689:
5687:
5684:
5683:
5665:
5655:
5625:
5615:
5611:
5610:
5608:
5599:
5595:
5593:
5590:
5589:
5583:
5577:
5566:
5539:
5534:
5525:
5509:
5507:
5484:
5482:
5480:
5477:
5476:
5453:
5450:
5449:
5428:
5424:
5422:
5419:
5418:
5394:
5391:
5390:
5388:
5365:
5364:
5356:
5352:
5343:
5339:
5337:
5328:
5325:
5324:
5322:
5293:
5287:
5261:
5257:
5256:
5254:
5243:
5239:
5237:
5223:
5219:
5217:
5215:
5194:
5190:
5179:
5177:
5160:
5156:
5154:
5145:
5141:
5140:
5136:
5126:
5124:
5115:
5111:
5109:
5106:
5105:
5099:
5093:
5075:
5069:
5067:Authalic radius
5029:
5027:
5018:
5014:
5012:
5009:
5008:
5002:
4996:
4991:arithmetic mean
4961:
4946:
4944:
4940:
4928:
4926:
4922:
4908:
4875:
4860:
4859:
4854:
4844:
4843:
4839:
4837:
4834:
4833:
4826:
4794:
4785:
4783:
4774:
4770:
4763:
4759:
4751:
4748:
4747:
4706:
4702:
4696:
4692:
4685:
4676:
4672:
4664:
4660:
4658:
4646:
4642:
4618:
4614:
4598:
4588:
4584:
4583:
4581:
4568:
4541:
4540:
4536:
4527:
4522:
4508:
4503:
4488:
4469:
4468:
4464:
4462:
4459:
4458:
4451:
4438:
4436:Non-directional
4396:
4392:
4391:
4388:
4366:
4362:
4361:
4358:
4357:
4352:
4342:
4341:
4337:
4335:
4332:
4331:
4320:
4316:
4301:
4296:
4291:
4270:
4267:
4266:
4241:
4238:
4237:
4209:
4205:
4200:
4191:
4187:
4185:
4182:
4181:
4162:
4158:
4153:
4144:
4140:
4138:
4135:
4134:
4103:
4094:
4090:
4088:
4085:
4084:
4063:
4054:
4050:
4048:
4045:
4044:
4013:
4010:
4009:
3990:
3987:
3986:
3962:
3954:
3952:
3939:
3931:
3929:
3921:
3918:
3917:
3893:
3885:
3883:
3881:
3878:
3877:
3856:
3848:
3846:
3844:
3841:
3840:
3824:
3821:
3820:
3801:
3793:
3792:
3787:
3779:
3776:
3775:
3752:
3751:
3746:
3740:
3739:
3734:
3727:
3723:
3711:
3707:
3698:
3694:
3690:
3683:
3679:
3673:
3669:
3668:
3666:
3660:
3656:
3650:
3634:
3630:
3622:
3619:
3618:
3592:
3588:
3549:
3545:
3529:
3525:
3516:
3512:
3500:
3496:
3487:
3472:
3469:
3468:
3433:
3429:
3427:
3424:
3423:
3400:
3396:
3394:
3391:
3390:
3373:
3369:
3342:
3338:
3332:
3328:
3319:
3315:
3306:
3302:
3291:
3288:
3287:
3264:
3263:
3258:
3252:
3251:
3246:
3239:
3235:
3223:
3219:
3215:
3208:
3204:
3200:
3198:
3189:
3185:
3181:
3174:
3170:
3166:
3164:
3158:
3142:
3138:
3130:
3127:
3126:
3096:
3092:
3053:
3049:
3033:
3029:
3020:
3016:
3004:
3000:
2991:
2978:
2974:
2969:
2966:
2965:
2901:
2897:
2836:
2832:
2822:
2818:
2804:
2801:
2800:
2790:
2782:
2772:
2768:
2759:
2756:
2751:
2750:
2748:
2746:
2739:
2733:
2716:
2710:
2698:
2694:
2685:
2682:
2677:
2676:
2674:
2672:
2666:
2652:
2610:
2607:
2606:
2599:normal distance
2562:
2558:
2552:
2548:
2536:
2524:
2520:
2496:
2492:
2470:
2466:
2464:
2447:
2444:
2443:
2436:
2432:
2367:
2364:
2363:
2334:
2330:
2327:
2324:
2323:
2298:
2295:
2294:
2283:
2275:arc measurement
2250:
2247:
2246:
2222:
2218:
2201:
2197:
2190:
2186:
2179:
2177:
2160:
2156:
2144:
2140:
2134:
2130:
2120:
2110:
2106:
2093:
2091:
2074:
2068:
2067:
2066:
2060:
2056:
2032:
2028:
2007:
2006:
2005:
1998:
1994:
1984:
1982:
1965:
1962:
1961:
1954:
1943:
1935:normal sections
1927:
1922:
1916:
1900:
1896:
1869:
1865:
1841:
1837:
1821:
1814:
1810:
1795:
1791:
1779:
1775:
1760:
1756:
1752:
1749:
1732:
1729:
1728:
1721:
1711:
1704:
1694:
1690:
1686:
1679:
1670:semi-minor axis
1665:
1646:semi-major axis
1641:
1611:
1563:
1550:
1493:
1490:
1487:
1486:
1484:
1483:
1469:
1466:
1463:
1462:
1460:
1459:
1455:
1447:
1439:
1411:
1404:
1400:
1394:
1390:
1389:
1387:
1379:
1376:
1375:
1368:
1361:
1357:
1350:
1325:
1319:
1265:of revolution,
1214:
1208:Earth ellipsoid
1202:Main articles:
1196:low Earth orbit
1149:
1105:
1104:
1098:
1097:
1091:
1090:
1087:
1084:
1083:
1055:
1044:
1036:authalic radius
1033:
990:figure of Earth
983:
976:
961:
932:
931:
778:
770:
769:
758:
750:
742:
734:
726:
710:
702:
701:
660:
610:
602:
601:
577:
547:
544:
536:
529:
526:
518:
509:
507:
504:
496:
463:
462:
456:
455:
449:
448:
445:
442:
441:
414:
413:
407:
403:
397:
396:
393:
390:
389:
371:
370:
364:
360:
354:
353:
350:
347:
346:
328:
327:
321:
320:
314:
313:
310:
307:
306:
267:
241:
239:
235:
230:
224:
222:
218:
189:
188:
186:
183:
182:
169:
164:
163:
162:Behaviour under
148:
131:
121:
111:
104:
89:
82:
74:
64:
57:
28:
25:
22:Arc measurement
18:Spherical Earth
12:
11:
5:
8699:
8689:
8688:
8683:
8678:
8673:
8656:
8655:
8653:
8652:
8647:
8642:
8637:
8633:
8630:
8629:
8627:
8626:
8620:
8614:
8608:
8602:
8596:
8590:
8584:
8578:
8574:
8571:
8565:
8559:
8554:
8548:
8545:
8538:
8535:
8534:
8532:
8531:
8525:
8522:
8521:
8510:
8509:
8502:
8495:
8487:
8481:
8480:
8451:
8447:
8430:
8429:External links
8427:
8424:
8423:
8397:
8369:
8355:
8335:
8332:978-1468308501
8310:
8286:
8279:
8261:
8244:
8232:
8227:Britannica.com
8214:
8203:Chisholm, Hugh
8180:
8161:
8147:On the Heavens
8133:
8126:
8108:
8082:
8022:
7992:
7965:(1): 128–133.
7944:
7937:
7912:
7905:
7874:
7846:
7826:
7799:
7768:
7761:
7741:
7712:
7690:
7655:
7620:
7604:
7588:
7570:
7529:
7496:
7495:
7493:
7490:
7487:
7486:
7474:
7464:
7436:
7427:
7417:
7404:
7382:
7381:
7379:
7376:
7374:
7373:
7368:
7363:
7358:
7353:
7348:
7343:
7338:
7332:
7330:
7327:
7206:On the Heavens
7174:
7171:
7168:
7167:
7165:
7150:
7147:
7144:
7143:
7141:
7130:
7127:
7124:
7123:
7121:
7110:
7107:
7104:
7103:
7101:
7090:
7087:
7084:
7083:
7081:
7069:
7064:
7059:
7056:
7055:
7053:
7038:
7028:
7025:
7024:
7022:
7010:
7000:
6997:
6996:
6994:
6982:
6977:
6972:
6968:
6967:
6965:
6953:
6948:
6943:
6939:
6938:
6936:
6924:
6919:
6914:
6910:
6909:
6907:
6895:
6888:
6884:
6883:
6881:
6869:
6862:
6858:
6857:
6855:
6843:
6833:
6827:
6826:
6824:
6812:
6807:
6802:
6798:
6797:
6795:
6783:
6778:
6773:
6769:
6768:
6766:
6754:
6749:
6744:
6740:
6739:
6737:
6725:
6718:
6714:
6713:
6711:
6699:
6692:
6688:
6687:
6685:
6674:
6671:
6665:
6664:
6662:
6651:
6648:
6644:
6643:
6641:
6630:
6627:
6621:
6620:
6617:
6614:
6611:
6601:
6598:
6594:Jupiter radius
6578:
6571:
6567:
6561:
6539:unit of length
6519:
6512:
6508:
6502:
6472:
6465:
6461:
6455:
6432:
6429:
6367:Earth's volume
6357:map projection
6338:surface curves
6298:
6288:
6281:
6262:
6255:is simply the
6240:
6239:
6229:
6211:polar diameter
6192:
6189:
6164:
6161:
6160:
6159:
6150:
6145:
6136:
6129:
6126:
6120:
6112:topographical
6093:
6090:
6086:
6085:
6074:
6068:
6064:
6061:
6058:
6052:
6046:
6041:
6022:
6021:
6010:
6003:
6000:
5994:
5989:
5982:
5979:
5974:
5970:
5964:
5961:
5956:
5949:
5944:
5938:
5933:
5915:
5914:
5903:
5899:
5896:
5892:
5889:
5886:
5883:
5876:
5873:
5867:
5863:
5857:
5854:
5849:
5843:
5838:
5819:
5818:
5807:
5803:
5800:
5794:
5791:
5786:
5782:
5775:
5771:
5766:
5763:
5760:
5755:
5751:
5744:
5740:
5730:
5727:
5721:
5717:
5711:
5708:
5703:
5697:
5692:
5654:
5651:
5647:
5646:
5635:
5628:
5623:
5618:
5614:
5607:
5602:
5598:
5581:
5565:
5562:
5561:
5560:
5549:
5542:
5537:
5533:
5529:
5524:
5519:
5515:
5512:
5506:
5501:
5497:
5494:
5490:
5487:
5457:
5431:
5427:
5398:
5373:
5368:
5359:
5355:
5351:
5346:
5342:
5336:
5333:
5319:
5318:
5307:
5299:
5296:
5292:
5286:
5279:
5275:
5272:
5267:
5264:
5260:
5251:
5246:
5242:
5236:
5231:
5226:
5222:
5214:
5208:
5201:
5197:
5193:
5188:
5185:
5182:
5176:
5173:
5168:
5163:
5159:
5153:
5148:
5144:
5139:
5133:
5130:
5123:
5118:
5114:
5097:
5068:
5065:
5061:
5060:
5045:
5041:
5038:
5035:
5032:
5026:
5021:
5017:
5000:
4960:
4957:
4953:
4952:
4934:
4907:
4904:
4903:
4902:
4883:
4880:
4874:
4868:
4865:
4858:
4853:
4847:
4842:
4801:
4797:
4792:
4788:
4782:
4777:
4773:
4766:
4762:
4758:
4755:
4736:
4735:
4724:
4717:
4714:
4709:
4705:
4699:
4695:
4691:
4688:
4679:
4675:
4671:
4668:
4663:
4657:
4649:
4645:
4641:
4638:
4635:
4632:
4629:
4626:
4621:
4617:
4613:
4610:
4607:
4604:
4601:
4596:
4591:
4587:
4580:
4575:
4572:
4567:
4563:
4560:
4556:
4553:
4550:
4544:
4539:
4533:
4530:
4525:
4521:
4514:
4511:
4507:
4502:
4496:
4492:
4487:
4484:
4481:
4478:
4472:
4467:
4437:
4434:
4433:
4432:
4421:
4411:
4407:
4404:
4399:
4395:
4387:
4381:
4377:
4374:
4369:
4365:
4356:
4351:
4345:
4340:
4300:
4297:
4295:
4292:
4288:
4287:
4274:
4254:
4251:
4248:
4245:
4231:
4230:
4219:
4212:
4208:
4204:
4199:
4194:
4190:
4165:
4161:
4157:
4152:
4147:
4143:
4128:
4127:
4116:
4110:
4107:
4102:
4097:
4093:
4070:
4067:
4062:
4057:
4053:
4029:
4026:
4023:
4020:
4017:
3994:
3983:
3982:
3968:
3965:
3960:
3957:
3951:
3945:
3942:
3937:
3934:
3928:
3925:
3899:
3896:
3891:
3888:
3862:
3859:
3854:
3851:
3839:, and because
3828:
3804:
3800:
3796:
3791:
3786:
3783:
3773:
3772:
3761:
3757:
3750:
3747:
3745:
3742:
3741:
3738:
3735:
3733:
3730:
3729:
3726:
3722:
3714:
3710:
3706:
3701:
3697:
3693:
3686:
3682:
3676:
3672:
3663:
3659:
3653:
3649:
3645:
3640:
3637:
3633:
3629:
3626:
3612:
3611:
3600:
3595:
3591:
3587:
3583:
3580:
3577:
3574:
3570:
3567:
3563:
3560:
3557:
3552:
3548:
3544:
3540:
3537:
3532:
3528:
3524:
3519:
3515:
3511:
3506:
3503:
3499:
3493:
3490:
3486:
3482:
3479:
3476:
3447:
3444:
3441:
3436:
3432:
3411:
3408:
3403:
3399:
3376:
3372:
3368:
3365:
3362:
3359:
3356:
3353:
3350:
3345:
3341:
3335:
3331:
3327:
3322:
3318:
3314:
3309:
3305:
3301:
3298:
3295:
3285:
3284:
3273:
3269:
3262:
3259:
3257:
3254:
3253:
3250:
3247:
3245:
3242:
3241:
3238:
3234:
3226:
3222:
3218:
3211:
3207:
3203:
3192:
3188:
3184:
3177:
3173:
3169:
3161:
3157:
3153:
3148:
3145:
3141:
3137:
3134:
3116:
3115:
3104:
3099:
3095:
3091:
3087:
3084:
3081:
3078:
3074:
3071:
3067:
3064:
3061:
3056:
3052:
3048:
3044:
3041:
3036:
3032:
3028:
3023:
3019:
3015:
3010:
3007:
3003:
2997:
2994:
2990:
2986:
2981:
2977:
2973:
2955:
2954:
2943:
2940:
2937:
2933:
2930:
2927:
2924:
2921:
2918:
2915:
2912:
2909:
2904:
2900:
2896:
2893:
2890:
2887:
2884:
2881:
2877:
2874:
2871:
2868:
2865:
2862:
2859:
2856:
2853:
2850:
2847:
2844:
2839:
2835:
2830:
2825:
2821:
2817:
2814:
2811:
2808:
2792:
2791:
2788:
2783:
2781:
2778:
2777:
2776:
2744:
2737:
2714:
2703:
2702:
2670:
2651:
2648:
2635:
2632:
2629:
2626:
2623:
2620:
2617:
2614:
2592:
2591:
2580:
2573:
2570:
2565:
2561:
2555:
2551:
2547:
2544:
2540:
2535:
2527:
2523:
2519:
2516:
2513:
2510:
2507:
2504:
2499:
2495:
2491:
2488:
2485:
2482:
2479:
2473:
2469:
2463:
2460:
2457:
2454:
2451:
2419:prime-vertical
2397:
2394:
2390:
2387:
2383:
2380:
2377:
2374:
2371:
2351:
2348:
2345:
2342:
2337:
2333:
2311:
2308:
2305:
2302:
2282:
2281:Prime vertical
2279:
2254:
2243:
2242:
2231:
2225:
2221:
2217:
2214:
2211:
2204:
2200:
2193:
2189:
2185:
2182:
2176:
2167:
2164:
2159:
2155:
2152:
2147:
2143:
2137:
2133:
2129:
2126:
2123:
2118:
2113:
2109:
2105:
2102:
2099:
2096:
2090:
2081:
2078:
2071:
2063:
2059:
2055:
2052:
2049:
2046:
2043:
2040:
2035:
2031:
2027:
2024:
2021:
2018:
2015:
2010:
2001:
1997:
1993:
1990:
1987:
1981:
1978:
1975:
1972:
1969:
1942:
1939:
1929:There are two
1926:
1923:
1915:
1912:
1893:
1892:
1881:
1872:
1868:
1864:
1861:
1858:
1855:
1852:
1849:
1844:
1840:
1836:
1833:
1830:
1827:
1824:
1817:
1813:
1809:
1806:
1803:
1798:
1794:
1790:
1787:
1782:
1778:
1774:
1771:
1768:
1763:
1759:
1755:
1748:
1745:
1742:
1739:
1736:
1703:
1700:
1678:
1675:
1674:
1673:
1658:
1657:
1610:
1607:
1599:remote sensing
1549:
1546:
1436:
1435:
1424:
1417:
1414:
1407:
1403:
1397:
1393:
1386:
1383:
1346:, so that the
1318:
1315:
1281:
1280:
1274:
1255:
1252:mean sea level
1244:
1170:with the same
1148:
1145:
1108:
1101:
1094:
1063:or the actual
1053:
1042:
1031:
994:Earth spheroid
981:
974:
963:
962:
960:
959:
952:
945:
937:
934:
933:
930:
929:
924:
919:
911:
910:
907:
901:
900:
897:
891:
890:
887:
881:
880:
877:
871:
870:
867:
861:
860:
857:
851:
850:
847:
841:
840:
837:
831:
830:
827:
821:
820:
817:
811:
810:
807:
801:
800:
797:
791:
790:
787:
779:
776:
775:
772:
771:
768:
767:
762:
754:
746:
738:
730:
722:
717:
711:
708:
707:
704:
703:
700:
699:
694:
689:
684:
679:
674:
672:Map projection
669:
658:
653:
648:
646:Geodetic datum
643:
638:
622:
617:
611:
608:
607:
604:
603:
600:
599:
594:
589:
584:
578:
575:
574:
571:
570:
562:
561:
551:
550:
542:
533:
532:
524:
515:
514:
502:
493:
492:
489:
488:
483:
466:
459:
452:
437:
436:
432:
431:
417:
410:
406:
400:
374:
367:
363:
357:
331:
324:
317:
304:
300:
299:
294:
290:
289:
280:
274:
273:
269:
268:
265:
257:
256:
248:
247:
212:
206:
205:
192:
180:
174:
173:
170:
161:
158:
157:
152:
143:
142:
139:
133:
132:
126:
116:
109:
102:
87:
80:
75:
73:Common symbols
72:
69:
68:
65:
62:
59:
58:
43:
35:
34:
26:
9:
6:
4:
3:
2:
8698:
8687:
8684:
8682:
8679:
8677:
8674:
8672:
8669:
8668:
8666:
8651:
8648:
8646:
8643:
8641:
8638:
8635:
8634:
8631:
8624:
8621:
8618:
8615:
8612:
8609:
8606:
8603:
8600:
8597:
8594:
8591:
8588:
8585:
8582:
8579:
8569:
8566:
8563:
8560:
8557:
8543:
8540:
8539:
8536:
8530:
8527:
8526:
8523:
8519:
8515:
8508:
8503:
8501:
8496:
8494:
8489:
8488:
8485:
8477:
8473:
8469:
8468:Sixty Symbols
8465:
8449:
8445:
8433:
8432:
8412:
8408:
8401:
8387:on 2018-01-27
8386:
8382:
8381:
8373:
8358:
8352:
8348:
8347:
8339:
8333:
8329:
8325:
8324:
8319:
8314:
8300:
8296:
8290:
8282:
8280:0-387-94107-X
8276:
8272:
8265:
8258:
8254:
8248:
8242:
8236:
8228:
8224:
8218:
8210:
8209:
8204:
8199:
8194:
8190:
8184:
8176:
8172:
8165:
8149:
8148:
8143:
8137:
8129:
8123:
8119:
8112:
8099:
8095:
8094:
8086:
8067:
8063:
8059:
8055:
8051:
8047:
8043:
8036:
8029:
8027:
8012:on 2012-09-10
8011:
8007:
8001:
7999:
7997:
7988:
7984:
7980:
7976:
7972:
7968:
7964:
7960:
7953:
7951:
7949:
7940:
7938:9783110170726
7934:
7930:
7929:
7921:
7919:
7917:
7908:
7906:9780070365209
7902:
7898:
7893:
7892:
7883:
7881:
7879:
7859:
7858:
7850:
7842:
7841:
7836:
7830:
7822:
7818:
7814:
7810:
7809:Survey Review
7803:
7784:
7783:
7775:
7773:
7764:
7758:
7754:
7753:
7745:
7731:on 2016-08-26
7730:
7726:
7722:
7716:
7709:
7708:
7701:
7699:
7697:
7695:
7680:on 2020-08-04
7676:
7672:
7665:
7659:
7645:
7639:
7637:
7635:
7633:
7631:
7629:
7627:
7625:
7617:
7613:
7608:
7601:
7597:
7592:
7586:
7582:
7579:
7574:
7567:
7563:
7560:
7559:
7552:
7550:
7548:
7546:
7544:
7542:
7540:
7538:
7536:
7534:
7524:
7519:
7512:
7510:
7508:
7506:
7504:
7502:
7497:
7478:
7468:
7461:
7457:
7453:
7449:
7446:
7440:
7431:
7421:
7414:
7408:
7401:
7397:
7393:
7387:
7383:
7372:
7369:
7367:
7364:
7362:
7359:
7357:
7354:
7352:
7349:
7347:
7344:
7342:
7339:
7337:
7334:
7333:
7326:
7324:
7320:
7316:
7312:
7311:Arctic Circle
7308:
7304:
7300:
7296:
7293:argued for a
7292:
7288:
7284:
7280:
7277:Around 1690,
7275:
7273:
7269:
7265:
7261:
7257:
7253:
7248:
7246:
7245:
7240:
7236:
7232:
7228:
7224:
7219:
7216:
7212:
7208:
7207:
7202:
7198:
7192:
7188:
7184:
7180:
7166:
7151:
7148:
7146:
7145:
7142:
7131:
7128:
7126:
7125:
7122:
7111:
7108:
7106:
7105:
7102:
7091:
7088:
7086:
7085:
7082:
7070:
7067:
7060:
7058:
7057:
7054:
7039:
7036:
7032:
7029:
7027:
7026:
7023:
7011:
7008:
7004:
7001:
6999:
6998:
6995:
6983:
6980:
6973:
6970:
6969:
6966:
6954:
6951:
6944:
6941:
6940:
6937:
6925:
6922:
6915:
6912:
6911:
6908:
6896:
6893:
6889:
6886:
6885:
6882:
6870:
6867:
6863:
6860:
6859:
6856:
6844:
6841:
6837:
6834:
6832:
6829:
6828:
6825:
6813:
6810:
6803:
6800:
6799:
6796:
6784:
6781:
6774:
6771:
6770:
6767:
6755:
6752:
6746:mean radius (
6745:
6742:
6741:
6738:
6726:
6723:
6719:
6716:
6715:
6712:
6700:
6697:
6693:
6690:
6689:
6686:
6675:
6672:
6670:
6667:
6666:
6663:
6652:
6649:
6646:
6645:
6642:
6631:
6628:
6626:
6623:
6622:
6618:
6615:
6612:
6609:
6608:
6605:
6597:
6595:
6565:
6548:
6544:
6540:
6536:
6506:
6489:
6459:
6442:
6438:
6431:Nominal radii
6428:
6395:
6368:
6364:
6362:
6358:
6354:
6351:Likewise for
6349:
6347:
6343:
6342:meridian arcs
6339:
6335:
6331:
6330:for details.
6329:
6325:
6321:
6317:
6313:
6309:
6305:
6301:
6295:
6291:
6284:
6277:
6273:
6269:
6265:
6258:
6254:
6250:
6246:
6245:
6235:
6230:
6225:
6220:
6219:
6218:
6216:
6212:
6208:
6204:
6200:
6199:
6188:
6186:
6182:
6178:
6170:
6157:
6153:
6146:
6143:
6139:
6132:
6131:
6125:
6123:
6116:
6115:
6109:
6105:
6099:
6089:
6072:
6066:
6062:
6059:
6056:
6050:
6039:
6031:
6030:
6029:
6008:
6001:
5998:
5992:
5987:
5980:
5977:
5972:
5968:
5962:
5959:
5954:
5947:
5942:
5931:
5923:
5922:
5921:
5918:
5901:
5897:
5894:
5887:
5881:
5874:
5871:
5865:
5861:
5855:
5852:
5847:
5836:
5828:
5827:
5826:
5805:
5801:
5798:
5792:
5789:
5784:
5780:
5773:
5769:
5764:
5761:
5758:
5753:
5749:
5742:
5738:
5728:
5725:
5719:
5715:
5709:
5706:
5701:
5690:
5682:
5681:
5680:
5678:
5674:
5670:
5664:
5660:
5650:
5633:
5626:
5621:
5616:
5612:
5605:
5600:
5596:
5588:
5587:
5586:
5580:
5575:
5571:
5547:
5540:
5535:
5531:
5527:
5522:
5517:
5513:
5510:
5504:
5499:
5495:
5492:
5488:
5485:
5475:
5474:
5473:
5472:, this gives
5471:
5455:
5447:
5429:
5425:
5415:
5412:
5396:
5371:
5357:
5353:
5349:
5344:
5340:
5334:
5331:
5305:
5297:
5294:
5290:
5284:
5277:
5273:
5270:
5265:
5262:
5258:
5249:
5244:
5240:
5234:
5229:
5224:
5220:
5212:
5206:
5199:
5195:
5191:
5186:
5183:
5180:
5174:
5171:
5166:
5161:
5157:
5151:
5146:
5142:
5137:
5131:
5128:
5121:
5116:
5112:
5104:
5103:
5102:
5096:
5091:
5087:
5083:
5079:
5074:
5064:
5043:
5039:
5036:
5033:
5030:
5024:
5019:
5015:
5007:
5006:
5005:
4999:
4994:
4992:
4986:
4978:
4974:
4970:
4965:
4956:
4949:.7523 km
4938:
4935:
4931:.1370 km
4920:
4917:
4916:
4915:
4913:
4881:
4878:
4872:
4866:
4863:
4856:
4851:
4840:
4832:
4831:
4830:
4824:
4823:
4816:
4799:
4790:
4780:
4775:
4771:
4764:
4760:
4756:
4753:
4745:
4741:
4722:
4715:
4712:
4707:
4703:
4697:
4693:
4689:
4686:
4677:
4673:
4669:
4666:
4661:
4655:
4647:
4639:
4636:
4633:
4630:
4624:
4619:
4611:
4608:
4605:
4602:
4594:
4589:
4585:
4578:
4573:
4570:
4565:
4561:
4558:
4551:
4537:
4531:
4528:
4523:
4519:
4512:
4509:
4505:
4500:
4494:
4490:
4485:
4479:
4465:
4457:
4456:
4455:
4449:
4448:
4441:
4419:
4409:
4405:
4402:
4397:
4393:
4385:
4379:
4375:
4372:
4367:
4363:
4354:
4349:
4338:
4330:
4329:
4328:
4326:
4314:
4310:
4306:
4286:
4272:
4252:
4249:
4246:
4243:
4234:
4217:
4210:
4206:
4202:
4197:
4192:
4188:
4163:
4159:
4155:
4150:
4145:
4141:
4133:
4132:
4131:
4114:
4108:
4105:
4100:
4095:
4091:
4068:
4065:
4060:
4055:
4051:
4043:
4042:
4041:
4027:
4024:
4021:
4018:
4015:
4006:
3992:
3966:
3958:
3949:
3943:
3935:
3926:
3923:
3916:
3915:
3914:
3897:
3889:
3860:
3852:
3826:
3798:
3789:
3784:
3781:
3759:
3755:
3748:
3743:
3736:
3731:
3724:
3720:
3712:
3708:
3699:
3695:
3684:
3680:
3674:
3661:
3657:
3651:
3647:
3643:
3638:
3635:
3631:
3627:
3624:
3617:
3616:
3615:
3598:
3593:
3589:
3585:
3581:
3578:
3575:
3572:
3568:
3565:
3561:
3558:
3555:
3550:
3546:
3542:
3538:
3535:
3530:
3526:
3522:
3517:
3513:
3509:
3504:
3501:
3497:
3491:
3488:
3484:
3480:
3477:
3474:
3467:
3466:
3465:
3463:
3458:
3445:
3442:
3439:
3434:
3430:
3409:
3406:
3401:
3397:
3374:
3366:
3363:
3360:
3357:
3354:
3348:
3343:
3333:
3329:
3325:
3320:
3316:
3312:
3307:
3303:
3296:
3293:
3271:
3267:
3260:
3255:
3248:
3243:
3236:
3232:
3224:
3220:
3209:
3205:
3190:
3186:
3175:
3171:
3159:
3155:
3151:
3146:
3143:
3139:
3135:
3132:
3125:
3124:
3123:
3121:
3120:metric tensor
3102:
3097:
3093:
3089:
3085:
3082:
3079:
3076:
3072:
3069:
3065:
3062:
3059:
3054:
3050:
3046:
3042:
3039:
3034:
3030:
3026:
3021:
3017:
3013:
3008:
3005:
3001:
2995:
2992:
2988:
2984:
2979:
2975:
2971:
2964:
2963:
2962:
2960:
2957:where in the
2941:
2935:
2931:
2928:
2925:
2916:
2913:
2910:
2902:
2898:
2894:
2891:
2888:
2882:
2879:
2872:
2869:
2866:
2863:
2860:
2857:
2854:
2851:
2848:
2842:
2837:
2833:
2823:
2819:
2815:
2812:
2809:
2799:
2798:
2797:
2794:
2793:
2787:
2786:
2762:
2754:
2743:
2736:
2732:
2731:
2730:
2728:
2723:
2720:
2713:
2708:
2688:
2680:
2669:
2665:
2664:
2663:
2661:
2657:
2647:
2630:
2624:
2621:
2618:
2615:
2612:
2604:
2600:
2596:
2578:
2571:
2568:
2563:
2559:
2553:
2549:
2545:
2542:
2538:
2533:
2525:
2517:
2514:
2511:
2508:
2502:
2497:
2489:
2486:
2483:
2480:
2471:
2467:
2461:
2455:
2449:
2442:
2441:
2440:
2430:
2426:
2422:
2420:
2413:
2392:
2388:
2385:
2381:
2378:
2372:
2369:
2346:
2340:
2335:
2331:
2306:
2300:
2292:
2287:
2278:
2276:
2272:
2268:
2252:
2229:
2223:
2215:
2209:
2202:
2198:
2191:
2187:
2183:
2180:
2174:
2165:
2162:
2153:
2150:
2145:
2141:
2135:
2131:
2127:
2124:
2111:
2107:
2103:
2100:
2094:
2088:
2079:
2076:
2061:
2053:
2050:
2047:
2044:
2038:
2033:
2025:
2022:
2019:
2016:
1999:
1991:
1988:
1979:
1973:
1967:
1960:
1959:
1958:
1952:
1950:
1938:
1936:
1932:
1921:
1911:
1909:
1904:
1879:
1870:
1862:
1859:
1856:
1853:
1847:
1842:
1834:
1831:
1828:
1825:
1815:
1807:
1804:
1801:
1796:
1792:
1785:
1780:
1772:
1769:
1766:
1761:
1757:
1746:
1740:
1734:
1727:
1726:
1725:
1720:
1716:
1709:
1683:
1671:
1664:
1660:
1659:
1655:
1651:
1647:
1640:
1636:
1635:
1634:
1630:
1628:
1624:
1620:
1616:
1606:
1604:
1600:
1596:
1592:
1587:
1585:
1581:
1577:
1572:
1558:
1554:
1545:
1543:
1537:
1535:
1531:
1527:
1525:
1520:
1516:
1508:
1504:
1496:
1482:
1472:
1453:
1445:
1422:
1415:
1412:
1405:
1401:
1395:
1391:
1384:
1381:
1374:
1373:
1372:
1367:
1356:
1349:
1345:
1341:
1337:
1333:
1331:
1324:
1314:
1312:
1307:
1302:
1300:
1296:
1295:
1290:
1286:
1279:
1275:
1272:
1268:
1264:
1260:
1256:
1253:
1250:, defined by
1249:
1245:
1242:
1241:
1240:
1238:
1234:
1229:
1226:
1222:
1218:
1213:
1209:
1205:
1197:
1193:
1190:range of the
1189:
1185:
1181:
1177:
1173:
1169:
1165:
1162:
1158:
1153:
1144:
1142:
1137:
1133:
1129:
1125:
1081:
1076:
1074:
1070:
1066:
1062:
1057:
1052:
1048:
1041:
1037:
1030:
1026:
1022:
1017:
1015:
1011:
1007:
1003:
999:
995:
991:
987:
980:
973:
969:
958:
953:
951:
946:
944:
939:
938:
936:
935:
928:
925:
923:
920:
918:
915:
914:
908:
906:
903:
902:
898:
896:
893:
892:
888:
886:
883:
882:
878:
876:
873:
872:
868:
866:
863:
862:
858:
856:
853:
852:
848:
846:
843:
842:
838:
836:
833:
832:
828:
826:
823:
822:
818:
816:
813:
812:
808:
806:
803:
802:
798:
796:
793:
792:
788:
786:
783:
782:
774:
773:
766:
763:
761:
755:
753:
747:
745:
739:
737:
733:BeiDou (BDS)
731:
729:
723:
721:
718:
716:
713:
712:
706:
705:
698:
695:
693:
690:
688:
685:
683:
680:
678:
675:
673:
670:
667:
663:
659:
657:
654:
652:
649:
647:
644:
642:
639:
635:
634:circumference
631:
626:
623:
621:
618:
616:
613:
612:
606:
605:
598:
595:
593:
590:
588:
585:
583:
580:
579:
573:
572:
568:
564:
563:
560:
557:
556:
543:
541:
540:English units
534:
525:
523:
522:Metric system
516:
503:
501:
494:
490:
487:
484:
482:
439:
438:
433:
404:
361:
305:
301:
298:
295:
291:
288:
284:
281:
279:
275:
270:
263:
258:
253:
244:.7523 km
233:
227:.1370 km
216:
213:
211:
207:
181:
179:
175:
171:
167:
159:
156:
153:
151:
144:
140:
138:
134:
129:
125:
119:
115:
108:
101:
97:
93:
86:
79:
76:
70:
66:
60:
55:
51:
47:
41:
36:
31:
23:
19:
8568:Solar radius
8562:Light-second
8552:
8542:Earth radius
8467:
8415:. Retrieved
8410:
8400:
8389:. Retrieved
8385:the original
8379:
8372:
8360:. Retrieved
8345:
8338:
8322:
8313:
8302:. Retrieved
8298:
8289:
8270:
8264:
8256:
8247:
8241:fragment 202
8239:Posidonius,
8235:
8226:
8217:
8206:
8183:
8174:
8170:
8164:
8152:. Retrieved
8146:
8136:
8117:
8111:
8101:, retrieved
8092:
8085:
8073:. Retrieved
8066:the original
8045:
8041:
8014:. Retrieved
8010:the original
7962:
7958:
7927:
7890:
7865:. Retrieved
7856:
7849:
7839:
7829:
7812:
7808:
7802:
7790:. Retrieved
7781:
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7744:
7733:. Retrieved
7729:the original
7724:
7715:
7705:
7682:. Retrieved
7675:the original
7670:
7658:
7647:. Retrieved
7607:
7591:
7573:
7557:
7477:
7467:
7439:
7430:
7420:
7407:
7386:
7279:Isaac Newton
7276:
7249:
7242:
7220:
7215:Eratosthenes
7204:
7194:
7062:
7034:
7006:
6975:
6946:
6917:
6891:
6865:
6839:
6805:
6776:
6747:
6721:
6695:
6613:Description
6603:
6487:
6440:
6439:denotes the
6434:
6366:
6365:
6353:surface area
6350:
6332:
6323:
6319:
6315:
6311:
6307:
6303:
6296:
6286:
6279:
6275:
6271:
6267:
6260:
6252:
6251:length. The
6242:
6241:
6233:
6223:
6214:
6210:
6206:
6202:
6195:
6194:
6168:
6166:
6156:Arctic Ocean
6148:
6134:
6118:
6111:
6101:
6087:
6023:
5919:
5916:
5820:
5668:
5666:
5648:
5578:
5569:
5567:
5445:
5416:
5413:
5320:
5094:
5082:"equal area"
5077:
5076:
5062:
4997:
4988:
4982:
4972:
4968:
4967:Equatorial (
4954:
4937:Polar radius
4936:
4918:
4909:
4906:Global radii
4825:at latitude
4819:
4817:
4743:
4739:
4737:
4450:at latitude
4444:
4442:
4439:
4327:as follows:
4304:
4303:The Earth's
4302:
4235:
4232:
4129:
4007:
3984:
3774:
3613:
3459:
3286:
3117:
2956:
2795:
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2752:
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2734:
2726:
2724:
2718:
2711:
2706:
2704:
2686:
2678:
2667:
2655:
2653:
2605:is given by
2594:
2593:
2424:
2416:
2414:
2411:
2290:
2271:Eratosthenes
2267:eccentricity
2244:
1946:
1944:
1928:
1905:
1894:
1714:
1712:
1663:polar radius
1662:
1661:The Earth's
1638:
1637:The Earth's
1631:
1612:
1591:Eratosthenes
1588:
1584:true horizon
1573:
1569:
1538:
1522:
1512:
1494:
1470:
1437:
1371:is given by
1365:
1355:polar radius
1354:
1347:
1328:
1326:
1305:
1303:
1298:
1292:
1288:
1284:
1282:
1236:
1230:
1221:tidal forces
1215:
1176:eccentricity
1159:of the 2003
1147:Introduction
1079:
1077:
1058:
1050:
1046:
1039:
1035:
1028:
1024:
1018:
1013:
1010:polar radius
1009:
1005:
1001:
978:
971:
970:(denoted as
968:Earth radius
967:
966:
709:Technologies
664: /
629:
576:Fundamentals
500:SI base unit
485:
480:
293:Unit of
232:Polar radius
231:
214:
137:SI unit
127:
123:
117:
113:
106:
99:
95:
91:
84:
77:
49:
45:
44:Equatorial (
33:Earth radius
8472:Brady Haran
8318:John Freely
8251:Cleomedes (
8075:18 November
7835:Bomford, G.
7472:discussion.
7415:conditions.
6417:V = 1.08321
6247:equals the
4307:, along an
1564: 1050
1344:South Poles
1294:mean radius
1180:Karman line
1071:radius and
1045:); and the
1025:mean radius
587:Geodynamics
278:Unit system
63:Other names
8665:Categories
8623:gigaparsec
8617:megaparsec
8611:kiloparsec
8599:light-year
8417:2019-05-22
8391:2023-02-09
8304:2022-11-05
8154:5 November
8127:0471334588
8103:2007-03-17
8016:2013-09-16
7735:2016-08-10
7684:2008-12-31
7649:2018-10-17
7523:1510.07674
7492:References
7448:definition
7400:Earth tide
7341:Earth mass
7177:See also:
6535:Earth tide
6340:, such as
6334:Arc length
6173:230 m
6142:Chimborazo
6104:topography
6096:See also:
5657:See also:
5071:See also:
4971:), polar (
2780:Derivation
2429:orthogonal
1949:meridional
1941:Meridional
1918:See also:
1559:'s (973 –
1542:Earth tide
1481:flattening
1306:geocentric
1267:geocentric
1225:topography
1172:minor axis
1157:oblateness
1132:geophysics
1073:equatorial
1065:topography
1012:, denoted
1004:, denoted
287:geophysics
48:), polar (
8593:terametre
8581:gigametre
8518:Astronomy
8450:⊕
8142:Aristotle
7987:195290884
7250:By 1490,
7201:Aristotle
6543:astronomy
6346:geodesics
6249:perimeter
6183:, or the
6051:≈
5943:≈
5898:φ
5888:φ
5872:π
5862:∫
5856:π
5802:φ
5793:φ
5790:
5762:φ
5759:
5726:π
5716:∫
5710:π
5673:perimeter
5514:π
5486:∫
5350:−
5298:π
5271:
5263:−
5175:
5080:(meaning
4995:(denoted
4772:κ
4761:κ
4716:φ
4713:
4690:−
4670:−
4640:φ
4637:
4612:φ
4609:
4562:α
4552:α
4532:π
4520:∫
4513:π
4480:φ
4406:α
4403:
4376:α
4373:
4299:Azimuthal
4207:κ
4160:κ
4092:κ
4052:κ
3967:λ
3964:∂
3956:∂
3950:×
3944:φ
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3933:∂
3898:λ
3895:∂
3887:∂
3861:φ
3858:∂
3850:∂
3705:∂
3692:∂
3685:ν
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3662:ν
3652:ν
3648:∑
3590:λ
3576:λ
3569:φ
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3443:λ
3410:φ
3217:∂
3210:ν
3202:∂
3183:∂
3176:ν
3168:∂
3160:ν
3156:∑
3094:λ
3080:λ
3073:φ
3051:φ
2989:∑
2932:κ
2929:−
2895:−
2880:κ
2864:−
2843:−
2834:κ
2816:−
2631:φ
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2572:φ
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2546:−
2518:φ
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2490:φ
2487:
2456:φ
2347:ϕ
2307:ϕ
2216:φ
2184:−
2154:φ
2151:
2128:−
2104:−
2054:φ
2051:
2026:φ
2023:
1974:φ
1863:φ
1860:
1835:φ
1832:
1808:φ
1805:
1773:φ
1770:
1741:φ
1571:height).
1557:Al-Biruni
1534:Greenland
1501:≈ 298.257
1402:ω
1332:/spheroid
1263:ellipsoid
1184:sea level
1128:astronomy
1082:(denoted
666:Longitude
592:Geomatics
512:10 m
283:astronomy
178:Dimension
8636:See also
8575:☉
8516:used in
8474:for the
8326:(2013),
8195:(1911).
7837:(1952).
7581:Archived
7562:Archived
7413:geodetic
7329:See also
7307:latitude
7244:Almagest
6549:; e.g.,
6412: km
6198:diameter
6196:Earth's
6147:Minimum
6133:Maximum
5004:) to be
4989:Earth's
4820:Earth's
4445:Earth's
2439:and is:
2417:Earth's
1947:Earth's
1908:vertices
1633:needed.
1627:accuracy
1271:geodetic
1259:spheroid
1188:altitude
845:ISO 6709
743:(Europe)
741:Galileo
727:(Russia)
725:GLONASS
662:Latitude
651:Geodesic
609:Concepts
345:,
297:distance
8411:Gallica
8362:31 July
8229:. 2016.
8205:(ed.).
8050:Bibcode
7967:Bibcode
7928:Geodesy
7840:Geodesy
7456:gravity
7351:Geodesy
7315:equator
7199:, when
7173:History
6610:Agency
6547:planets
6385:
6373:
6326:); see
6278:equals
5409:
5389:
5385:
5323:
4742:is the
4313:azimuth
3460:in the
2765:
2749:
2691:
2675:
2265:is the
1654:planets
1650:equator
1519:crustal
1515:density
1499:
1485:
1475:
1461:
1450:is the
1442:is the
1336:equator
1168:ellipse
1143:(IAU).
905:Geo URI
875:NAVD 88
785:NGVD 29
759:(Japan)
751:(India)
735:(China)
597:History
582:Geodesy
559:Geodesy
440:1
8605:parsec
8353:
8330:
8277:
8177:: 159.
8124:
7985:
7935:
7903:
7867:13 May
7792:13 May
7759:
7664:"Info"
7454:where
7398:, and
7266:. The
7227:Strabo
7211:stadia
7189:, and
7031:GRS 80
7003:GRS 80
6836:WGS-84
6274:. The
6209:) and
6179:, the
5321:where
5088:. The
4993:radius
4912:WGS-84
4738:Where
4311:at an
2773:
2769:
2699:
2695:
2245:where
1895:where
1619:WGS-84
1617:1984 (
1526:height
1454:, and
1438:where
1364:. The
1311:planet
1278:sphere
1237:radius
1233:radius
1210:, and
992:by an
895:GCJ-02
885:ETRS89
865:WGS 84
855:NAD 83
835:GRS 80
795:OSGB36
749:NAVIC
630:radius
508:6.3781
481:in ...
303:Symbol
172:scalar
141:meters
8686:Radii
8671:Earth
8625:(Gpc)
8619:(Mpc)
8613:(kpc)
8201:. In
8069:(PDF)
8038:(PDF)
7983:S2CID
7899:–77.
7861:(PDF)
7786:(PDF)
7678:(PDF)
7667:(PDF)
7518:arXiv
7396:geoid
7378:Notes
7319:poles
7079:.0195
6992:.7900
6963:.1809
6934:.7714
6905:.6258
6879:.3142
6822:.7900
6801:IUGG
6793:.1810
6772:IUGG
6764:.7714
6743:IUGG
6735:.6259
6717:IUGG
6709:.3141
6691:IUGG
6394:WGS84
6359:or a
4008:With
2431:) to
2415:This
2293:, is
1668:, or
1644:, or
1576:torus
1524:geoid
1477:≈ 289
1340:North
1248:geoid
1069:polar
986:Earth
825:SAD69
805:SK-42
620:Geoid
210:Value
8607:(pc)
8601:(ly)
8595:(Tm)
8589:(au)
8583:(Gm)
8564:(ls)
8364:2010
8351:ISBN
8328:ISBN
8275:ISBN
8156:2017
8122:ISBN
8098:NASA
8077:2017
7933:ISBN
7901:ISBN
7869:2023
7794:2023
7757:ISBN
7458:and
7281:and
7260:Asia
7048:.314
6971:NGA
6942:NGA
6913:NGA
6887:NGA
6861:NGA
6669:IUGG
6647:IAU
6619:Ref
6541:for
6410:3142
6408:.752
6402:b =
6400:and
6371:V =
6344:and
6318:=(1−
6167:The
5661:and
5574:IUGG
5259:tanh
5090:IUGG
4829:is:
4818:The
4454:is:
4443:The
4180:and
4083:and
3876:and
2725:The
2705:The
2654:The
1957:is:
1937:.
1899:and
1713:The
1517:and
1342:and
1246:The
1161:IERS
1134:, a
1130:and
996:(an
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632:and
8551:or
8058:doi
8046:124
7975:doi
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4350:=
4344:c
4339:R
4321:φ
4317:α
4273:r
4253:r
4250:d
4247:+
4244:r
4218:.
4211:2
4203:1
4198:=
4193:2
4189:R
4164:1
4156:1
4151:=
4146:1
4142:R
4115:,
4109:E
4106:e
4101:=
4096:2
4069:G
4066:g
4061:=
4056:1
4028:0
4025:=
4022:f
4019:=
4016:F
3993:r
3959:r
3936:r
3927:=
3924:N
3890:r
3853:r
3827:r
3803:|
3799:N
3795:|
3790:N
3785:=
3782:n
3760:,
3756:]
3749:g
3744:f
3737:f
3732:e
3725:[
3721:=
3713:j
3709:w
3700:i
3696:w
3681:r
3675:2
3658:n
3644:=
3639:j
3636:i
3632:b
3628:=
3625:B
3599:,
3594:2
3586:d
3582:g
3579:+
3573:d
3566:d
3562:f
3559:2
3556:+
3551:2
3543:d
3539:e
3536:=
3531:j
3527:w
3523:d
3518:i
3514:w
3510:d
3505:j
3502:i
3498:b
3492:j
3489:i
3481:=
3478:D
3475:2
3446:,
3440:=
3435:2
3431:w
3407:=
3402:1
3398:w
3375:T
3371:]
3367:z
3364:,
3361:y
3358:,
3355:x
3352:[
3349:=
3344:T
3340:]
3334:3
3330:r
3326:,
3321:2
3317:r
3313:,
3308:1
3304:r
3300:[
3297:=
3294:r
3272:,
3268:]
3261:G
3256:F
3249:F
3244:E
3237:[
3233:=
3225:j
3221:w
3206:r
3191:i
3187:w
3172:r
3152:=
3147:j
3144:i
3140:a
3136:=
3133:A
3103:,
3098:2
3090:d
3086:G
3083:+
3077:d
3070:d
3066:F
3063:2
3060:+
3055:2
3047:d
3043:E
3040:=
3035:j
3031:w
3027:d
3022:i
3018:w
3014:d
3009:j
3006:i
3002:a
2996:j
2993:i
2985:=
2980:2
2976:s
2972:d
2942:,
2939:)
2936:B
2926:A
2923:(
2917:=
2914:0
2911:=
2908:)
2903:2
2899:f
2892:g
2889:e
2886:(
2883:+
2876:)
2873:F
2870:f
2867:2
2861:E
2858:g
2855:+
2852:G
2849:e
2846:(
2838:2
2829:)
2824:2
2820:F
2813:G
2810:E
2807:(
2771:=
2761:b
2757:/
2753:a
2747:=
2745:p
2742:N
2740:=
2738:p
2735:M
2719:a
2715:e
2712:N
2697:=
2687:a
2683:/
2679:b
2673:=
2671:e
2668:M
2634:)
2628:(
2619:N
2616:=
2613:p
2595:N
2579:.
2564:2
2554:2
2550:e
2543:1
2539:a
2534:=
2526:2
2522:)
2509:b
2506:(
2503:+
2498:2
2494:)
2481:a
2478:(
2472:2
2468:a
2462:=
2459:)
2453:(
2450:N
2437:φ
2433:M
2408:.
2396:)
2393:Z
2389:,
2386:Y
2382:,
2379:X
2376:(
2373:=
2370:R
2350:)
2344:(
2341:N
2336:2
2332:e
2310:)
2304:(
2301:N
2253:e
2230:.
2224:3
2220:)
2213:(
2210:N
2203:2
2199:a
2192:2
2188:e
2181:1
2175:=
2166:2
2163:3
2158:)
2146:2
2136:2
2132:e
2125:1
2122:(
2117:)
2112:2
2108:e
2101:1
2098:(
2095:a
2089:=
2080:2
2077:3
2070:)
2062:2
2058:)
2045:b
2042:(
2039:+
2034:2
2030:)
2017:a
2014:(
2009:(
2000:2
1996:)
1992:b
1989:a
1986:(
1980:=
1977:)
1971:(
1968:M
1955:φ
1901:b
1897:a
1880:,
1871:2
1867:)
1854:b
1851:(
1848:+
1843:2
1839:)
1826:a
1823:(
1816:2
1812:)
1797:2
1793:b
1789:(
1786:+
1781:2
1777:)
1762:2
1758:a
1754:(
1747:=
1744:)
1738:(
1735:R
1722:φ
1710:.
1695:N
1691:M
1687:R
1666:b
1656:.
1642:a
1495:f
1491:/
1488:1
1471:q
1467:/
1464:1
1456:M
1448:G
1440:ω
1423:,
1416:M
1413:G
1406:2
1396:3
1392:a
1385:=
1382:q
1369:q
1358:b
1351:a
1198:.
1107:N
1100:E
1093:R
1054:3
1051:R
1043:2
1040:R
1032:1
1029:R
1027:(
1014:b
1006:a
982:E
979:R
972:R
956:e
949:t
942:v
636:)
628:(
510:×
465:N
458:E
451:R
416:N
409:E
405:p
399:R
373:N
366:E
362:e
356:R
330:N
323:E
316:R
246:)
240:6
236:b
223:6
219:a
191:L
155:m
130:E
128:p
124:R
120:E
118:e
114:R
110:E
107:b
103:E
100:a
96:b
92:a
88:E
85:R
78:R
50:b
46:a
24:.
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