2297:
1564:
578:
1163:
4975:
51:
4744:
1636:. 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
1693:
2251:
273:
5327:
4471:
1643:
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
1319:
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
1581:
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
1238:
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.
7435:
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
1974:
5827:
2600:
1901:
7482:
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
5118:
3293:
4739:{\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 }}\,.}
6030:
3781:
3124:
1518:
4441:
7228:
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.
3620:
5923:
3991:
2963:
1149:
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
2246:{\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}\,.}
5569:
4911:
7224:. 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
5696:
4824:
2456:
1741:
1539:, 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
5322:{\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 }}}\,,}
1550:
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
6601:
6542:
6495:
440:
397:
1131:
489:
354:
6094:
5394:
1312:. 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.
4921:
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
3139:
4966:
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.
8266:) 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),
3922:
3885:
5074:
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).
1514:. 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.
1444:
8515:
4239:
8389:
4189:
4136:
5937:
5069:
4092:
5655:
3631:
2978:
4344:
5928:
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).
3828:
3481:
2655:
1250:
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:
5842:
3467:
2371:
3930:
3431:
7495:
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.
2417:
214:
8473:
3398:
7527:
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".
2331:
1589:, the curvature at a point will be greatest (tightest) in one direction (north–south on Earth) and smallest (flattest) perpendicularly (east–west). The corresponding
8508:
5453:
4049:
937:
4274:
2813:
8016:
1577:) method for calculation of the Earth's radius simplified measuring the circumference compared to taking measurements from two locations distant from each other.
6679:
5477:
5418:
4995:
4294:
4014:
3848:
2274:
1031:
7674:
8218:
759:
7285:
of the World, soundly demonstrated the sphericity of the Earth, and affirmed the original measurement of 40,000 km (25,000 mi) by
Eratosthenes.
8501:
6548:
convention. Equatorial radius is conventionally used as the nominal value unless the polar radius is explicitly required. The nominal radius serves as a
927:
895:
5489:
4335:
4846:
5822:{\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 \,.}
1030:
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
905:
8395:
7572:
6841:
1600:
In summary, local variations in terrain prevent defining a single "precise" radius. One can only adopt an idealized model. Since the estimate by
8045:
2595:{\displaystyle N(\varphi )={\frac {a^{2}}{\sqrt {(a\cos \varphi )^{2}+(b\sin \varphi )^{2}}}}={\frac {a}{\sqrt {1-e^{2}\sin ^{2}\varphi }}}\,.}
1532:
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
8365:
7771:
4760:
885:
1616:
gained importance, true global models were developed which, while not as accurate for regional work, best approximate the Earth as a whole.
1896:{\displaystyle R(\varphi )={\sqrt {\frac {(a^{2}\cos \varphi )^{2}+(b^{2}\sin \varphi )^{2}}{(a\cos \varphi )^{2}+(b\sin \varphi )^{2}}}},}
7731:
7591:
7606:
7761:
8342:
1590:
666:
8289:
7947:
7915:
965:
6563:
6504:
6457:
4244:
The first and second radii of curvature correspond, respectively, to the Earth's meridional and prime-vertical radii of curvature.
402:
359:
3288:{\displaystyle A=a_{ij}=\sum _{\nu }{\frac {\partial r^{\nu }}{\partial w^{i}}}{\frac {\partial r^{\nu }}{\partial w^{j}}}=\left,}
1096:
454:
319:
7455:
6635:
6447:
6045:
5337:
1151:
7445:
The value of the radius is completely dependent upon the latitude in the case of an ellipsoid model, and nearly so on the geoid.
7274:
8136:
3890:
3853:
751:
288:
1294:
In the case of the geoid and ellipsoids, the fixed distance from any point on the model to the specified center is called
767:
1388:
8655:
8539:
6553:
1540:
8020:
7626:
7610:
7436:
center and orientation of the ellipsoid generally do not coincide with the earth's center of mass or axis of rotation.
1202:
6025:{\displaystyle M_{\mathrm {r} }\approx \left({\frac {a^{\frac {3}{2}}+b^{\frac {3}{2}}}{2}}\right)^{\frac {2}{3}}\,,}
4194:
4147:
1663:
and equals 6,378.1370 km (3,963.1906 mi). The equatorial radius is often used to compare Earth with other
8691:
8686:
7685:
4097:
2277:
1186:
6198:. This topographical average is 6,371.230 km (3,958.899 mi) with uncertainty of 10 m (33 ft).
2296:
7458:
5021:
3776:{\displaystyle B=b_{ij}=\sum _{\nu }n^{\nu }{\frac {\partial ^{2}r^{\nu }}{\partial w^{i}\partial w^{j}}}=\left,}
2423:
If one point had appeared due east of the other, one finds the approximate curvature in the east–west direction.
1683:
is the distance from its center to the North and South Poles, and equals 6,356.7523 km (3,949.9028 mi).
1613:
730:
176:
7655:"Department of Defense World Geodetic System 1984: Its Definition and Relationships with Local Geodetic Systems"
5480:
4057:
8486:
8203:
7866:
7791:
3119:{\displaystyle ds^{2}=\sum _{ij}a_{ij}dw^{i}dw^{j}=E\,d\varphi ^{2}+2F\,d\varphi \,d\lambda +G\,d\lambda ^{2},}
1604:, many models have been created. Historically, these models were based on regional topography, giving the best
697:
7346:
7197:
6254:
6113:
The mathematical expressions above apply over the surface of the ellipsoid. The cases below considers Earth's
5602:
4436:{\displaystyle R_{\mathrm {c} }={\frac {1}{{\dfrac {\cos ^{2}\alpha }{M}}+{\dfrac {\sin ^{2}\alpha }{N}}}}\,.}
1593:
depends on the location and direction of measurement from that point. A consequence is that a distance to the
644:
7462:
7313:
3472:
795:
3615:{\displaystyle 2D=\sum _{ij}b_{ij}dw^{i}dw^{j}=e\,d\varphi ^{2}+2f\,d\varphi \,d\lambda +g\,d\lambda ^{2},}
1563:
8650:
7736:
Numerical
Standards for Fundamental Astronomy: Astronomical Constants : Current Best Estimates (CBEs)
7356:
2969:
1462:
815:
577:
8305:
8199:
7366:
5918:{\displaystyle M_{\mathrm {r} }={\frac {2}{\pi }}\int _{0}^{\frac {\pi }{2}}\!M(\varphi )\,d\varphi \,.}
5092:
4987:
3788:
1625:
1177:, with north at the top. The light blue region is a circle. The outer edge of the dark blue line is an
958:
875:
625:
64:
7567:
3986:{\displaystyle N={\frac {\partial r}{\partial \varphi }}\times {\frac {\partial r}{\partial \lambda }}}
2619:
8060:
7977:
7262:
7258:, left no doubt among medieval scholars that Earth is spherical, but they were wrong about its size.
7233:
6152:
5832:
The rectifying radius is equivalent to the meridional mean, which is defined as the average value of
4319:
3436:
2613:
2336:
1959:
1917:
The extrema geocentric radii on the ellipsoid coincide with the equatorial and polar radii. They are
865:
835:
775:
725:
651:
188:
8208:
8076:
3403:
8660:
8552:
7402:
7309:
7278:
6124:
6118:
5673:
5096:
2376:
1941:
1718:
1633:
1605:
1227:
1222:
1214:
1174:
1134:
1071:
687:
635:
195:
8451:
7993:
7528:
7376:
7293:
7189:
4457:
3300:
1597:
at the equator is slightly shorter in the north–south direction than in the east–west direction.
607:
8102:
7739:
7588:
1320:
the Earth". While specific values differ, the concepts in this article generalize to any major
8597:
8361:
8338:
8285:
8132:
7943:
7911:
7907:
7767:
7470:
7371:
7333:
7329:
7266:
7252:, but he accepted the lesser value attributed to Posidonius. His highly influential work, the
5083:
4451:
It is possible to combine the principal radii of curvature above in a non-directional manner.
2670:
2307:
1729:
1454:
1146:
1079:
707:
692:
8355:
7937:
2958:{\displaystyle (EG-F^{2})\,\kappa ^{2}-(eG+gE-2fF)\,\kappa +(eg-f^{2})=0=\det(A-\kappa \,B),}
1585:
Additionally, the radius can be estimated from the curvature of the Earth at a point. Like a
1246:. Strictly speaking, spheres are the only solids to have radii, but broader uses of the term
8068:
7985:
7899:
7827:
7381:
7282:
7241:
6371:
6304:
6267:
5669:
1333:
1008:
951:
702:
7328:. The expedition found that Newton's conjecture was correct: the Earth is flattened at the
5431:
5377:
4022:
1162:
8251:
7595:
7576:
7423:
7301:
7249:
7221:
7193:
6356:
6191:
5001:
4250:
2609:
2285:
1680:
1656:
1529:
1281:
1277:
1218:
1206:
1000:
32:
28:
8268:
Another Look at
Eratosthenes' and Posidonius' Determinations of the Earth's Circumference
8064:
7981:
4974:
50:
8696:
8681:
8524:
7849:
7818:
Bowring, B. R. (October 1987). "Notes on the curvature in the prime vertical section".
7236:
recomputed Earth's radius, and found it to be close to that by
Eratosthenes, but later
7216:
6604:
6549:
6367:
5686:
of the ellipse described by any polar cross section of the ellipsoid. This requires an
5462:
5403:
5095:) is the radius of a hypothetical perfect sphere that has the same surface area as the
4832:
4279:
3999:
3833:
2429:
2259:
1945:
1918:
1609:
1262:
1004:
915:
682:
656:
220:
8072:
8675:
8447:
8213:
7997:
7900:
7622:
7321:
6348:
5687:
5683:
3130:
550:
532:
8493:
8263:
8233:
8578:
8572:
8180:
Drummond, William (1817). "On the
Science of the Egyptians and Chaldeans, Part I".
7289:
7225:
7201:
6363:
6352:
6166:
2281:
1601:
510:
158:
17:
8417:
5564:{\displaystyle {\frac {\int K\,dA}{A}}={\frac {4\pi }{A}}={\frac {1}{R_{2}^{2}}}.}
1070:
Other ways to define and measure the Earth's radius involve either the spheroid's
8332:
8156:
8017:"Discover-TheWorld.com – Guam – POINTS OF INTEREST – Don't Miss – Mariana Trench"
7718:
Map
Projections – A Working Manual (US Geological Survey Professional Paper 1395)
5660:
For Earth, the volumetric radius equals 6,371.0008 km (3,958.7564 mi).
4906:{\displaystyle R_{\mathrm {m} }={\frac {2}{{\dfrac {1}{M}}+{\dfrac {1}{N}}}}\,\!}
8482:
8328:
7845:
7831:
7245:
7207:
5931:
The meridional mean is well approximated by the semicubic mean of the two axes,
1517:
1231:
1190:
597:
5425:
For the Earth, the authalic radius is 6,371.0072 km (3,958.7603 mi).
1921:
of the ellipse and also coincide with minimum and maximum radius of curvature.
8633:
8627:
8621:
8609:
7410:
7351:
6545:
6344:
6114:
3739:
3251:
2439:
1728:
is the distance from the Earth's center to a point on the spheroid surface at
1692:
1552:
1491:
1354:
1350:
1235:
1182:
1167:
1142:
1075:
297:
7220:
that mathematicians had guessed the circumference of the Earth to be 400,000
8603:
8591:
8528:
8222:. Vol. 8 (11th ed.). Cambridge University Press. pp. 801–813.
8152:
7211:
6556:. (The notation is defined such that it can be easily generalized for other
6259:
1567:
1544:
1273:
1194:
1138:
676:
602:
293:
8207:
7717:
7206:
The first published reference to the Earth's size appeared around 350
1060:, which is the radius of a sphere having the same volume as the ellipsoid (
272:
7989:
7763:
Global
Navigation Satellite Systems, Inertial Navigation, and Integration
7654:
7317:
7305:
7297:
7254:
6544:= 6,356.8 km (3,949.9 mi). These values correspond to the zero
6208:
1930:
1637:
1340:
1269:
855:
672:
661:
307:
6497:, which is defined to be exactly 6,378.1 km (3,963.2 mi). The
5583:, which is the radius of a sphere of volume equal to the ellipsoid. The
7466:
7361:
7325:
6338:
4819:{\displaystyle K=\kappa _{1}\,\kappa _{2}={\frac {\det \,B}{\det \,A}}}
4323:
1660:
1594:
1525:
1346:
1234:
cause its shape to deviate systematically from a perfect sphere. Local
1178:
1083:
735:
592:
569:
147:
6202:
Derived quantities: diameter, circumference, arc-length, area, volume
1242:
Each of the models in common use involve some notion of the geometric
8615:
7607:
Satellites Reveal A Mystery Of Large Change In Earth's
Gravity Field
7579:, by resolution of the XVII General Assembly of the IUGG in Canberra.
7422:
There is no single center to the geoid; it varies according to local
7237:
7041:
7013:
6846:
6557:
4922:
1664:
1629:
1321:
1288:
1243:
845:
805:
743:
7265:
believed that traveling 3,000 miles west from the west coast of the
7721:
p. 16–17. Washington D.C: United States Government Printing Office.
7533:
4247:
Geometrically, the second fundamental form gives the distance from
7406:
6404:
6108:
4973:
2295:
1691:
1586:
1562:
1534:
1258:
1198:
996:
630:
165:
7623:
NASA's Grace Finds Greenland Melting Faster, 'Sees' Sumatra Quake
7240:
incorrectly attributed him a value about 3/4 of the actual size.
6615:
This table summarizes the accepted values of the Earth's radius.
8108:
7270:
5584:
5100:
1171:
1067:). All three values are about 6,371 kilometres (3,959 mi).
1045:) of three radii measured at two equator points and a pole; the
932:
825:
8497:
7760:
Mohinder S. Grewal; Angus P. Andrews; Chris G. Bartone (2020).
6359:, can also be derived from Earth's equatorial and polar radii.
6099:
about 6,367.445 km (3,956.547 mi), can also be used.
1914:
are, respectively, the equatorial radius and the polar radius.
1078:. A few definitions yield values outside the range between the
8334:
Before Galileo: The Birth of Modern Science in Medieval Europe
2612:
from the ellipsoid surface to the polar axis. The radius of a
1049:, which is the radius of a sphere with the same surface area (
7589:
IAU 2006 General Assembly: Result of the IAU Resolution votes
6596:{\displaystyle {\mathcal {R}}_{p\mathrm {J} }^{\mathrm {N} }}
6537:{\displaystyle {\mathcal {R}}_{p\mathrm {E} }^{\mathrm {N} }}
6490:{\displaystyle {\mathcal {R}}_{e\mathrm {E} }^{\mathrm {N} }}
6169:
is 6,352.8 km (3,947.4 mi) from the Earth's center.
6155:
is 6,384.4 km (3,967.1 mi) from the Earth's center.
6035:
which differs from the exact result by less than 1 μm (4
2807:
The principal curvatures are the roots of Equation (125) in:
435:{\displaystyle {\mathcal {R}}_{p\mathrm {E} }^{\mathrm {N} }}
392:{\displaystyle {\mathcal {R}}_{e\mathrm {E} }^{\mathrm {N} }}
6570:
6511:
6464:
1516:
1126:{\displaystyle {\mathcal {R}}_{\mathrm {E} }^{\mathrm {N} }}
1103:
484:{\displaystyle {\mathcal {R}}_{\mathrm {E} }^{\mathrm {N} }}
461:
409:
366:
349:{\displaystyle {\mathcal {R}}_{\mathrm {E} }^{\mathrm {N} }}
326:
8046:"Mean radius, mass, and inertia for reference Earth models"
7968:
Moritz, H. (March 2000). "Geodetic Reference System 1980".
6089:{\displaystyle M_{\mathrm {r} }\approx {\frac {a+b}{2}}\,,}
5389:{\displaystyle \textstyle e={\sqrt {a^{2}-b^{2}}}{\big /}a}
38:
Distance from the Earth surface to a point near its center
4986:) and arithmetic mean Earth radii as defined in the 1984
2718:
Earth's prime-vertical radius of curvature at the equator
1696:
Three different radii as a function of Earth's latitude.
63:) and arithmetic mean Earth radii as defined in the 1984
8019:. Guam.discover-theworld.com. 1960-01-23. Archived from
1019:) of nearly 6,378 km (3,963 mi) to a minimum (
3917:{\displaystyle {\frac {\partial r}{\partial \lambda }}}
3880:{\displaystyle {\frac {\partial r}{\partial \varphi }}}
8391:
Méthode de déterminer si la terre est sphérique ou non
5341:
8454:
6566:
6507:
6460:
6182:
averages elevations everywhere, resulting in a value
6048:
5940:
5845:
5699:
5605:
5492:
5465:
5434:
5406:
5340:
5121:
5024:
4887:
4872:
4849:
4763:
4474:
4400:
4370:
4347:
4282:
4253:
4197:
4150:
4100:
4060:
4025:
4002:
3933:
3893:
3856:
3836:
3791:
3634:
3484:
3439:
3406:
3303:
3142:
2981:
2816:
2667:
Earth's meridional radius of curvature at the equator
2622:
2459:
2379:
2339:
2310:
2262:
1977:
1744:
1391:
1099:
999:
to a point on or near its surface. Approximating the
457:
405:
362:
322:
198:
8270:, Ql. J. of the Royal Astron. Soc., Vol. 16, p. 152.
7738:. IAU Division I Working Group. 2012. Archived from
6985:
WGS-84 ellipsoid, Radius of Sphere of Equal Volume (
8284:. New York: Springer-Verlag New York. p. 138.
1439:{\displaystyle q={\frac {a^{3}\omega ^{2}}{GM}}\,,}
1086:radius because they account for localized effects.
546:
528:
506:
445:
313:
303:
287:
282:
265:
219:
187:
171:
156:
146:
82:
72:
43:
8467:
7766:(4 ed.). John Wiley & Sons. p. 512.
6956:WGS-84 ellipsoid, Radius of Sphere of Equal Area (
6595:
6536:
6489:
6088:
6024:
5917:
5821:
5682:, giving a sphere with circumference equal to the
5649:
5563:
5471:
5447:
5412:
5388:
5321:
5063:
4905:
4818:
4738:
4435:
4288:
4268:
4233:
4183:
4130:
4086:
4043:
4008:
3985:
3916:
3879:
3842:
3822:
3775:
3614:
3461:
3425:
3392:
3287:
3118:
2957:
2649:
2594:
2411:
2365:
2325:
2268:
2245:
1895:
1438:
1125:
483:
434:
391:
348:
208:
7308:instead, due to different interpretations of the
6228:). For the WGS84 ellipsoid, that's respectively:
5891:
5060:
4902:
1338:Rotation of a planet causes it to approximate an
7711:
7709:
7707:
7705:
5479:, over the surface of the ellipsoid. Using the
5459:, obtained by averaging the Gaussian curvature,
5112:. A closed-form solution exists for a spheroid:
4806:
4797:
2930:
5690:to find, given the polar and equatorial radii:
4234:{\displaystyle R_{2}={\frac {1}{\kappa _{2}}}.}
8357:Magellan and the First Voyage Around the World
7100:meridional radius of curvature at the equator
4184:{\displaystyle R_{1}={\frac {1}{\kappa _{1}}}}
3625:e, f, and g are elements of the shape tensor:
8509:
7963:
7961:
7959:
7273:. However, the 1492 enactment of that voyage
6901:WGS-84 ellipsoid, polar radius of curvature (
6212:is simply twice Earth's radius; for example,
4996:International Union of Geodesy and Geophysics
4131:{\displaystyle \kappa _{2}={\frac {e}{E}}\,,}
2608:can also be interpreted geometrically as the
2080:
2019:
1032:International Union of Geodesy and Geophysics
959:
8:
8053:Physics of the Earth and Planetary Interiors
6927:WGS-84 ellipsoid, Mean radius of semi-axes (
1230:, internal density variations, and external
1034:(IUGG) provides three reference values: the
1027:) of nearly 6,357 km (3,950 mi).
8131:. John Wiley & Sons, Inc. p. 923.
7649:
7647:
7645:
7643:
7641:
7639:
7637:
7635:
5064:{\displaystyle R_{1}={\frac {2a+b}{3}}\,\!}
4051:for an oblate spheroid, the curvatures are
1704:is the meridional radius of curvature; and
8516:
8502:
8494:
8044:Frédéric Chambat; Bernard Valette (2001).
8039:
8037:
8011:
8009:
8007:
7906:. McGraw Hill Book Company, Inc. pp.
7522:
7520:
7518:
7516:
7514:
7512:
7461:rule (2): a planet assumes a shape due to
7269:would let him reach the eastern coasts of
6617:
6247:= 12,713.5046 km (7,899.8055 mi)
6237:= 12,756.2740 km (7,926.3812 mi)
5579:Another spherical model is defined by the
4087:{\displaystyle \kappa _{1}={\frac {g}{G}}}
2795:
2740:(either meridional or prime-vertical) is:
1944:: along the meridional and prime-vertical
1708:is the prime vertical radius of curvature.
1189:as the Earth. The red line represents the
966:
952:
933:Spatial Reference System Identifier (SRID)
928:International Terrestrial Reference System
565:
271:
262:
49:
8459:
8453:
7785:
7783:
7532:
6586:
6585:
6579:
6575:
6569:
6568:
6565:
6527:
6526:
6520:
6516:
6510:
6509:
6506:
6480:
6479:
6473:
6469:
6463:
6462:
6459:
6380:, or that of the reference ellipsoid, is
6082:
6064:
6054:
6053:
6047:
6018:
6007:
5986:
5968:
5961:
5946:
5945:
5939:
5911:
5904:
5880:
5875:
5861:
5851:
5850:
5844:
5815:
5808:
5794:
5783:
5778:
5763:
5752:
5747:
5745:
5734:
5729:
5715:
5705:
5704:
5698:
5643:
5636:
5626:
5619:
5610:
5604:
5550:
5545:
5536:
5518:
5502:
5493:
5491:
5464:
5439:
5433:
5405:
5376:
5375:
5367:
5354:
5348:
5339:
5315:
5298:
5272:
5265:
5254:
5248:
5234:
5228:
5226:
5205:
5188:
5171:
5165:
5156:
5137:
5135:
5126:
5120:
5059:
5038:
5029:
5023:
4901:
4886:
4871:
4865:
4855:
4854:
4848:
4809:
4800:
4794:
4785:
4780:
4774:
4762:
4732:
4717:
4707:
4687:
4675:
4669:
4657:
4629:
4599:
4592:
4579:
4575:
4568:
4552:
4551:
4538:
4533:
4514:
4499:
4480:
4479:
4473:
4429:
4407:
4399:
4377:
4369:
4363:
4353:
4352:
4346:
4281:
4252:
4220:
4211:
4202:
4196:
4173:
4164:
4155:
4149:
4141:and the principal radii of curvature are
4124:
4114:
4105:
4099:
4074:
4065:
4059:
4024:
4001:
3963:
3940:
3932:
3894:
3892:
3857:
3855:
3835:
3812:
3804:
3798:
3790:
3738:
3722:
3709:
3694:
3684:
3677:
3671:
3661:
3645:
3633:
3603:
3595:
3582:
3575:
3560:
3552:
3540:
3527:
3511:
3498:
3483:
3444:
3438:
3411:
3405:
3384:
3353:
3343:
3330:
3317:
3302:
3250:
3234:
3219:
3209:
3200:
3185:
3175:
3169:
3153:
3141:
3107:
3099:
3086:
3079:
3064:
3056:
3044:
3031:
3015:
3002:
2989:
2980:
2945:
2912:
2889:
2847:
2842:
2833:
2815:
2621:
2588:
2573:
2563:
2547:
2535:
2507:
2481:
2475:
2458:
2402:
2395:
2378:
2345:
2340:
2338:
2309:
2261:
2239:
2233:
2212:
2201:
2188:
2171:
2155:
2145:
2121:
2102:
2085:
2079:
2078:
2071:
2043:
2018:
2017:
2009:
1993:
1976:
1880:
1852:
1825:
1806:
1790:
1771:
1760:
1743:
1659:, is the distance from its center to the
1624:The following radii are derived from the
1490:, which is close to the measured inverse
1469:is the mass of the planet. For the Earth
1432:
1415:
1405:
1398:
1390:
1116:
1115:
1109:
1108:
1102:
1101:
1098:
474:
473:
467:
466:
460:
459:
456:
425:
424:
418:
414:
408:
407:
404:
382:
381:
375:
371:
365:
364:
361:
339:
338:
332:
331:
325:
324:
321:
200:
199:
197:
7931:
7929:
7927:
7562:
7560:
7558:
7556:
7554:
7552:
7550:
7548:
7546:
7544:
7300:than to a sphere. However, around 1730,
7160:Average distance from center to surface
7140:Minimum (the floor of the Arctic Ocean)
5650:{\displaystyle R_{3}={\sqrt{a^{2}b}}\,.}
2661:Polar and equatorial radius of curvature
1608:for the area under survey. As satellite
1161:
7893:
7891:
7889:
7874:. Ohio State University, Columbus, Ohio
7799:. Ohio State University, Columbus, Ohio
7508:
7394:
6039:10 in); the mean of the two axes,
2798:
2280:of the earth. This is the radius that
1300:"the radius of the Earth at that point"
568:
7868:Geometric Reference Systems in Geodesy
7793:Geometric Reference Systems in Geodesy
6195:
6180:topographical mean geocentric distance
6135:, which depends not only on latitude.
2436:Earth's transverse radius of curvature
1543:) or reduction in ice masses (such as
1315:Regardless of the model, any of these
201:
40:
7248:gave empirical evidence supporting a
6281:, in terms of the equatorial radius,
5422:is the surface area of the spheroid.
3830:is the unit normal to the surface at
1011:), the radius ranges from a maximum (
995:) is the distance from the center of
7:
8475:The Earth's Radius (and exoplanets)"
7312:involved. To settle the matter, the
7198:Earth's circumference § History
1302:. It is also common to refer to any
1197:, while the yellow area denotes the
791:
27:For its historical development, see
8234:"Eratosthenes, the Greek Scientist"
7316:(1735–1739) measured one degree of
7296:argued that Earth was closer to an
7120:Maximum (the summit of Chimborazo)
7072:Spherical Earth Approx. of Radius (
6875:WGS-84 ellipsoid, semi-minor axis (
3475:for a surface (Equation (123) in):
2972:for a surface (Equation (112) in):
1620:Extrema: equatorial and polar radii
1280:to model the entire Earth, or else
938:Universal Transverse Mercator (UTM)
900:European Terrestrial Ref. Sys. 1989
6786:radius of sphere of same surface (
6587:
6580:
6528:
6521:
6481:
6474:
6055:
5947:
5852:
5706:
4856:
4553:
4481:
4354:
3974:
3966:
3951:
3943:
3905:
3897:
3868:
3860:
3823:{\displaystyle n={\frac {N}{|N|}}}
3715:
3702:
3681:
3227:
3212:
3193:
3178:
1964:(in the north–south direction) at
1117:
1110:
810:Ordnance Survey Great Britain 1936
776:Discrete Global Grid and Geocoding
667:Horizontal position representation
475:
468:
426:
419:
383:
376:
340:
333:
25:
8101:Williams, David R. (2004-09-01),
7281:(1519–1522), which was the first
7275:brought his fleet to the Americas
6815:radius of sphere of same volume (
5587:denotes the volumetric radius as
5457:radius of (global) mean curvature
2738:Earth's polar radius of curvature
2650:{\displaystyle p=N\cos(\varphi )}
1265:at each point on the real surface
449:
277:Cross section of Earth's Interior
8416:Levallois, Jean-Jacques (1986).
8306:"Almagest – Ptolemy (Elizabeth)"
7732:"Equatorial Radius of the Earth"
7456:International Astronomical Union
6448:International Astronomical Union
6187:
4326:(measured clockwise from north)
3129:E, F, and G are elements of the
1152:International Astronomical Union
726:Global Nav. Sat. Systems (GNSSs)
576:
8446:Merrifield, Michael R. (2010).
7320:at two locations, one near the
6640:nominal "zero tide" equatorial
6452:nominal equatorial Earth radius
5103:denotes the authalic radius as
3462:{\displaystyle w^{2}=\lambda ,}
2366:{\displaystyle \,e^{2}N(\phi )}
1304:
1193:100 km (62 mi) above
890:N. American Vertical Datum 1988
8354:Nancy Smiler Levinson (2001).
7569:Geodetic Reference System 1980
7194:Spherical Earth § History
5901:
5895:
4654:
4638:
4626:
4610:
4565:
4559:
4493:
4487:
3813:
3805:
3426:{\displaystyle w^{1}=\varphi }
3381:
3362:
3350:
3310:
2949:
2933:
2918:
2896:
2886:
2856:
2839:
2817:
2720:equals the equatorial radius,
2644:
2638:
2532:
2516:
2504:
2488:
2469:
2463:
2406:
2386:
2360:
2354:
2320:
2314:
2230:
2223:
2168:
2132:
2127:
2108:
2068:
2052:
2040:
2024:
2006:
1996:
1987:
1981:
1877:
1861:
1849:
1833:
1822:
1799:
1787:
1764:
1754:
1748:
1328:Physics of Earth's deformation
920:Internet link to a point 2010
850:Geodetic Reference System 1980
768:Quasi-Zenith Sat. Sys. (QZSS)
1:
8360:. Houghton Mifflin Harcourt.
8073:10.1016/S0031-9201(01)00200-X
6325:enters via the eccentricity,
5678:Another global radius is the
4316:azimuthal radius of curvature
3924:are tangents to the surface,
2412:{\displaystyle R=(X,\,Y,\,Z)}
1571:
910:Chinese obfuscated datum 2002
209:{\displaystyle {\mathsf {L}}}
31:. For its determination, see
8656:Orders of magnitude (length)
8540:Astronomical system of units
8209:"Earth, Figure of the"
6849:ellipsoid, semi-major axis (
6403:. Using the parameters from
4458:Gaussian radius of curvature
3996:is normal to the surface at
2438:, is defined perpendicular (
2333:. The length IQ is equal to
1942:principal radii of curvature
1936:Principal radii of curvature
860:Geographic point coord. 1983
8468:{\displaystyle R_{\oplus }}
8394:(in French). Archived from
7865:Christopher Jekeli (2016).
7832:10.1179/sre.1987.29.226.195
7790:Christopher Jekeli (2016).
7627:Goddard Space Flight Center
7611:Goddard Space Flight Center
7202:Meridian arc § History
6731:polar radius of curvature (
6109:Earth § Size and shape
4305:Combined radii of curvature
3393:{\displaystyle r=^{T}=^{T}}
1559:Radius and local conditions
1327:
1254:The actual surface of Earth
1185:as the circle and the same
820:Systema Koordinat 1942 goda
8713:
7902:Vector and Tensor Analysis
7854:. Oxford University Press.
7187:
6661:nominal "zero tide" polar
6499:nominal polar Earth radius
6321:), where the polar radius
6106:
5667:
5081:
2300:The length PQ, called the
1928:
1716:
1700:is the geocentric radius;
1541:Sumatra-Andaman earthquake
1331:
1212:
880:World Geodetic System 1984
26:
8643:
8548:
8535:
8388:Cassini, Jacques (1738).
8204:Helmert, Friedrich Robert
8161:. Vol. Book II 298 B
8127:Phillips, Warren (2004).
6407:ellipsoid of revolution,
6174:Topographical global mean
5680:Earth's rectifying radius
5581:Earth's volumetric radius
4336:Euler's curvature formula
1931:Spheroid § Curvature
1614:Global Positioning System
1310:"the radius of the earth"
1133:) is sometimes used as a
870:North American Datum 1983
840:South American Datum 1969
502:
270:
48:
8487:University of Nottingham
7936:Torge, Wolfgang (2001).
6264:equatorial circumference
5455:also corresponds to the
5398:is the eccentricity and
4833:mean radius of curvature
4276:to the plane tangent at
2326:{\displaystyle N(\phi )}
1735:, given by the formula:
1717:Not to be confused with
1688:Location-dependent radii
1308:of a spherical model as
731:Global Pos. System (GPS)
698:Spatial reference system
8424:. pp. 277–284, 288
8310:projects.iq.harvard.edu
8280:Thurston, Hugh (1994).
8219:Encyclopædia Britannica
7463:hydrostatic equilibrium
7324:and the other near the
7314:French Geodesic Mission
5089:Earth's authalic radius
4990:revision (not to scale)
3473:second fundamental form
1296:"a radius of the Earth"
1166:A scale diagram of the
67:revision (not to scale)
8651:Cosmic distance ladder
8469:
8200:Clarke, Alexander Ross
7454:This follows from the
7357:Effective Earth radius
6603:for the nominal polar
6597:
6538:
6501:is defined exactly as
6491:
6139:Topographical extremes
6090:
6026:
5919:
5823:
5651:
5565:
5473:
5449:
5414:
5390:
5323:
5065:
4991:
4970:Arithmetic mean radius
4907:
4820:
4740:
4437:
4290:
4270:
4235:
4185:
4132:
4088:
4045:
4010:
3987:
3918:
3881:
3844:
3824:
3777:
3616:
3463:
3427:
3394:
3289:
3120:
2970:first fundamental form
2959:
2669:equals the meridian's
2651:
2596:
2420:
2413:
2367:
2327:
2270:
2247:
1897:
1709:
1578:
1521:
1463:gravitational constant
1440:
1349:and flattening at the
1210:
1127:
559:3,950 to 3,963 mi
541:6,357 to 6,378 km
485:
436:
393:
350:
210:
8470:
8418:"La Vie des sciences"
8182:The Classical Journal
7990:10.1007/s001900050278
7715:Snyder, J.P. (1987).
7625:, December 20, 2005,
7367:Geographical distance
7347:Earth's circumference
7214:reported in his book
6598:
6539:
6492:
6339:Ellipse#Circumference
6255:Earth's circumference
6091:
6027:
5920:
5824:
5652:
5566:
5474:
5450:
5448:{\displaystyle R_{2}}
5415:
5391:
5324:
5066:
4988:World Geodetic System
4977:
4908:
4821:
4741:
4438:
4291:
4271:
4236:
4186:
4133:
4089:
4046:
4044:{\displaystyle F=f=0}
4011:
3988:
3919:
3882:
3845:
3825:
3778:
3617:
3464:
3428:
3395:
3290:
3121:
2960:
2652:
2597:
2446:at geodetic latitude
2414:
2368:
2328:
2302:prime vertical radius
2299:
2271:
2248:
1898:
1695:
1626:World Geodetic System
1566:
1520:
1441:
1332:Further information:
1165:
1128:
626:Geographical distance
486:
437:
394:
351:
211:
65:World Geodetic System
8452:
7898:Lass, Harry (1950).
7473:are nearly balanced.
7263:Christopher Columbus
7234:Posidonius of Apamea
7232:Around 100 BC,
6564:
6505:
6458:
6366:, either based on a
6125:geocentric distances
6121:. As such, they are
6046:
5938:
5843:
5697:
5603:
5490:
5481:Gauss–Bonnet theorem
5463:
5432:
5428:The authalic radius
5404:
5338:
5119:
5022:
4847:
4761:
4472:
4345:
4320:Earth normal section
4280:
4269:{\displaystyle r+dr}
4251:
4195:
4148:
4098:
4058:
4023:
4000:
3931:
3891:
3854:
3834:
3789:
3632:
3482:
3437:
3404:
3301:
3140:
2979:
2814:
2620:
2614:parallel of latitude
2457:
2377:
2337:
2308:
2260:
1975:
1742:
1389:
1345:with a bulge at the
1097:
1091:nominal Earth radius
800:Sea Level Datum 1929
652:Geodetic coordinates
455:
403:
360:
320:
266:Nominal Earth radius
196:
177:coord transformation
8661:Conversion of units
8129:Mechanics of Flight
8065:2001PEPI..124..237C
7982:2000JGeod..74..128.
7566:Moritz, H. (1980).
7403:figure of the Earth
7310:Newtonian mechanics
7279:Magellan expedition
6592:
6533:
6486:
6436:10 cu mi)
6287:polar circumference
6214:equatorial diameter
6165:: the floor of the
6119:reference ellipsoid
6117:, above or below a
6103:Topographical radii
5890:
5744:
5674:Rectifying latitude
5555:
5097:reference ellipsoid
4998:(IUGG) defines the
4994:In geophysics, the
4925:ellipsoid; namely,
4546:
2432:radius of curvature
1962:radius of curvature
1956:In particular, the
1719:Geocentric distance
1634:reference ellipsoid
1612:and especially the
1606:reference ellipsoid
1591:radius of curvature
1377:oblateness constant
1364:is larger than the
1223:Reference ellipsoid
1215:Figure of the Earth
1175:reference ellipsoid
1135:unit of measurement
1122:
1072:radius of curvature
830:European Datum 1950
788:Standards (history)
688:Reference ellipsoid
636:Figure of the Earth
497:... is equal to ...
480:
431:
388:
345:
283:General information
18:Earth's radius
8465:
7970:Journal of Geodesy
7682:earth-info.nga.mil
7594:2006-11-07 at the
7575:2016-02-20 at the
7471:centrifugal forces
7377:History of geodesy
7332:due to rotation's
7294:Christiaan Huygens
7190:History of geodesy
6684:equatorial radius
6627:Value (in meters)
6593:
6567:
6534:
6508:
6487:
6461:
6446:In astronomy, the
6432:10 km (2.5988
6086:
6022:
5915:
5871:
5819:
5725:
5647:
5561:
5541:
5469:
5445:
5410:
5386:
5385:
5319:
5061:
4992:
4903:
4896:
4881:
4816:
4755:Gaussian curvature
4736:
4529:
4433:
4424:
4394:
4334:, is derived from
4286:
4266:
4231:
4181:
4128:
4084:
4041:
4006:
3983:
3914:
3877:
3840:
3820:
3773:
3764:
3666:
3612:
3506:
3459:
3423:
3390:
3285:
3276:
3174:
3116:
3010:
2955:
2647:
2592:
2434:, also called the
2421:
2409:
2363:
2323:
2266:
2243:
1925:Radii of curvature
1893:
1710:
1579:
1522:
1436:
1211:
1123:
1100:
708:Vertical positions
556:
548:
538:
530:
516:
508:
481:
458:
432:
406:
389:
363:
346:
323:
206:
160:SI base units
78:terrestrial radius
8692:Planetary geology
8687:Planetary science
8669:
8668:
8598:Astronomical unit
8367:978-0-395-98773-5
7773:978-1-119-54783-9
7372:Osculating sphere
7334:centrifugal force
7267:Iberian Peninsula
7181:
7180:
7044:semi-minor axis (
7016:semi-major axis (
6303:, four times the
6196:volumetric radius
6080:
6015:
6001:
5994:
5976:
5888:
5869:
5806:
5742:
5723:
5688:elliptic integral
5664:Rectifying radius
5641:
5575:Volumetric radius
5556:
5531:
5513:
5472:{\displaystyle K}
5413:{\displaystyle A}
5373:
5313:
5312:
5293:
5291:
5263:
5243:
5221:
5214:
5180:
5145:
5084:Authalic latitude
5057:
4930:Equatorial radius
4899:
4895:
4880:
4814:
4730:
4693:
4664:
4587:
4527:
4509:
4508:
4427:
4423:
4393:
4301:
4300:
4289:{\displaystyle r}
4226:
4179:
4122:
4082:
4009:{\displaystyle r}
3981:
3958:
3912:
3875:
3843:{\displaystyle r}
3818:
3729:
3657:
3494:
3241:
3207:
3165:
2998:
2786:6,399.594 km
2712:6,335.439 km
2671:semi-latus rectum
2586:
2585:
2542:
2541:
2269:{\displaystyle e}
2218:
2183:
2179:
2097:
2093:
1888:
1887:
1730:geodetic latitude
1726:geocentric radius
1713:Geocentric radius
1650:equatorial radius
1524:The variation in
1455:angular frequency
1430:
1371:by approximately
1359:equatorial radius
1284:for regional work
1272:, also called an
1147:conversion factor
1058:volumetric radius
1013:equatorial radius
976:
975:
924:
923:
703:Spatial relations
693:Satellite geodesy
648:
564:
563:
446:Conversions
261:
260:
226:Equatorial radius
16:(Redirected from
8704:
8518:
8511:
8504:
8495:
8490:
8474:
8472:
8471:
8466:
8464:
8463:
8433:
8432:
8430:
8429:
8413:
8407:
8406:
8404:
8403:
8385:
8379:
8378:
8376:
8374:
8351:
8345:
8326:
8320:
8319:
8317:
8316:
8302:
8296:
8295:
8277:
8271:
8260:
8254:
8248:
8242:
8241:
8230:
8224:
8223:
8211:
8196:
8190:
8189:
8177:
8171:
8170:
8168:
8166:
8149:
8143:
8142:
8124:
8118:
8117:
8116:
8115:
8104:Earth Fact Sheet
8098:
8092:
8091:
8089:
8087:
8081:
8075:. Archived from
8059:(3–4): 234–253.
8050:
8041:
8032:
8031:
8029:
8028:
8013:
8002:
8001:
7965:
7954:
7953:
7933:
7922:
7921:
7905:
7895:
7884:
7883:
7881:
7879:
7873:
7862:
7856:
7855:
7842:
7836:
7835:
7826:(226): 195–196.
7815:
7809:
7808:
7806:
7804:
7798:
7787:
7778:
7777:
7757:
7751:
7750:
7748:
7747:
7728:
7722:
7713:
7700:
7699:
7697:
7696:
7690:
7684:. Archived from
7679:
7671:
7665:
7664:
7662:
7661:
7651:
7630:
7620:
7614:
7609:, Aug. 1, 2002,
7604:
7598:
7586:
7580:
7564:
7539:
7538:
7536:
7524:
7496:
7494:
7490:
7484:
7480:
7474:
7452:
7446:
7443:
7437:
7433:
7427:
7420:
7414:
7401:For details see
7399:
7382:Planetary radius
7306:prolate spheroid
7283:circumnavigation
7244:around 150
7242:Claudius Ptolemy
7175:
7173:
7170:
7167:
7151:
7150:
7147:
7131:
7130:
7127:
7111:
7110:
7107:
7091:
7089:
7086:
7063:
7062:
7058:
7055:
7032:
7030:
7027:
7004:
7002:
6999:
6975:
6973:
6970:
6946:
6944:
6941:
6917:
6915:
6912:
6891:
6889:
6886:
6865:
6863:
6860:
6834:
6832:
6829:
6805:
6803:
6800:
6776:
6774:
6771:
6747:
6745:
6742:
6721:
6719:
6716:
6705:semiminor axis (
6695:
6694:
6691:
6672:
6671:
6668:
6651:
6650:
6647:
6618:
6611:Published values
6602:
6600:
6599:
6594:
6591:
6590:
6584:
6583:
6574:
6573:
6543:
6541:
6540:
6535:
6532:
6531:
6525:
6524:
6515:
6514:
6496:
6494:
6493:
6488:
6485:
6484:
6478:
6477:
6468:
6467:
6437:
6435:
6431:
6425:
6424:
6422:
6418:
6410:
6409:a = 6,378.137 km
6402:
6400:
6397:
6395:
6394:
6391:
6388:
6372:geodesic polygon
6347:of more general
6305:quarter meridian
6268:circle perimeter
6248:
6238:
6188:IUGG mean radius
6186:larger than the
6185:
6151:: the summit of
6095:
6093:
6092:
6087:
6081:
6076:
6065:
6060:
6059:
6058:
6038:
6031:
6029:
6028:
6023:
6017:
6016:
6008:
6006:
6002:
5997:
5996:
5995:
5987:
5978:
5977:
5969:
5962:
5952:
5951:
5950:
5924:
5922:
5921:
5916:
5889:
5881:
5879:
5870:
5862:
5857:
5856:
5855:
5835:
5828:
5826:
5825:
5820:
5807:
5799:
5798:
5789:
5788:
5787:
5768:
5767:
5758:
5757:
5756:
5746:
5743:
5735:
5733:
5724:
5716:
5711:
5710:
5709:
5670:Quarter meridian
5656:
5654:
5653:
5648:
5642:
5640:
5635:
5631:
5630:
5620:
5615:
5614:
5595:
5570:
5568:
5567:
5562:
5557:
5554:
5549:
5537:
5532:
5527:
5519:
5514:
5509:
5494:
5478:
5476:
5475:
5470:
5454:
5452:
5451:
5446:
5444:
5443:
5421:
5419:
5417:
5416:
5411:
5397:
5395:
5393:
5392:
5387:
5381:
5380:
5374:
5372:
5371:
5359:
5358:
5349:
5328:
5326:
5325:
5320:
5314:
5311:
5300:
5299:
5294:
5292:
5287:
5280:
5279:
5266:
5264:
5259:
5258:
5249:
5244:
5239:
5238:
5229:
5227:
5222:
5220:
5216:
5215:
5213:
5209:
5200:
5189:
5181:
5176:
5175:
5166:
5161:
5160:
5146:
5138:
5136:
5131:
5130:
5111:
5070:
5068:
5067:
5062:
5058:
5053:
5039:
5034:
5033:
5014:
4961:
4959:
4953:
4943:
4941:
4935:
4912:
4910:
4909:
4904:
4900:
4898:
4897:
4888:
4882:
4873:
4866:
4861:
4860:
4859:
4839:
4825:
4823:
4822:
4817:
4815:
4813:
4804:
4795:
4790:
4789:
4779:
4778:
4745:
4743:
4742:
4737:
4731:
4729:
4722:
4721:
4712:
4711:
4695:
4694:
4692:
4691:
4676:
4670:
4665:
4663:
4662:
4661:
4634:
4633:
4608:
4604:
4603:
4593:
4588:
4580:
4558:
4557:
4556:
4545:
4537:
4528:
4526:
4515:
4510:
4504:
4500:
4486:
4485:
4484:
4464:
4442:
4440:
4439:
4434:
4428:
4426:
4425:
4419:
4412:
4411:
4401:
4395:
4389:
4382:
4381:
4371:
4364:
4359:
4358:
4357:
4333:
4330:and at latitude
4329:
4295:
4293:
4292:
4287:
4275:
4273:
4272:
4267:
4240:
4238:
4237:
4232:
4227:
4225:
4224:
4212:
4207:
4206:
4190:
4188:
4187:
4182:
4180:
4178:
4177:
4165:
4160:
4159:
4137:
4135:
4134:
4129:
4123:
4115:
4110:
4109:
4093:
4091:
4090:
4085:
4083:
4075:
4070:
4069:
4050:
4048:
4047:
4042:
4015:
4013:
4012:
4007:
3992:
3990:
3989:
3984:
3982:
3980:
3972:
3964:
3959:
3957:
3949:
3941:
3923:
3921:
3920:
3915:
3913:
3911:
3903:
3895:
3886:
3884:
3883:
3878:
3876:
3874:
3866:
3858:
3849:
3847:
3846:
3841:
3829:
3827:
3826:
3821:
3819:
3817:
3816:
3808:
3799:
3782:
3780:
3779:
3774:
3769:
3765:
3730:
3728:
3727:
3726:
3714:
3713:
3700:
3699:
3698:
3689:
3688:
3678:
3676:
3675:
3665:
3653:
3652:
3621:
3619:
3618:
3613:
3608:
3607:
3565:
3564:
3545:
3544:
3532:
3531:
3519:
3518:
3505:
3468:
3466:
3465:
3460:
3449:
3448:
3432:
3430:
3429:
3424:
3416:
3415:
3399:
3397:
3396:
3391:
3389:
3388:
3358:
3357:
3348:
3347:
3335:
3334:
3322:
3321:
3294:
3292:
3291:
3286:
3281:
3277:
3242:
3240:
3239:
3238:
3225:
3224:
3223:
3210:
3208:
3206:
3205:
3204:
3191:
3190:
3189:
3176:
3173:
3161:
3160:
3125:
3123:
3122:
3117:
3112:
3111:
3069:
3068:
3049:
3048:
3036:
3035:
3023:
3022:
3009:
2994:
2993:
2964:
2962:
2961:
2956:
2917:
2916:
2852:
2851:
2838:
2837:
2800:Extended content
2796:
2785:
2781:
2778:
2777:
2775:
2774:
2769:
2766:
2732:
2711:
2707:
2704:
2703:
2701:
2700:
2695:
2692:
2656:
2654:
2653:
2648:
2601:
2599:
2598:
2593:
2587:
2578:
2577:
2568:
2567:
2552:
2548:
2543:
2540:
2539:
2512:
2511:
2487:
2486:
2485:
2476:
2449:
2445:
2418:
2416:
2415:
2410:
2372:
2370:
2369:
2364:
2350:
2349:
2332:
2330:
2329:
2324:
2284:measured in his
2275:
2273:
2272:
2267:
2252:
2250:
2249:
2244:
2238:
2237:
2219:
2217:
2216:
2207:
2206:
2205:
2189:
2184:
2182:
2181:
2180:
2172:
2160:
2159:
2150:
2149:
2130:
2126:
2125:
2103:
2098:
2096:
2095:
2094:
2086:
2084:
2083:
2076:
2075:
2048:
2047:
2023:
2022:
2015:
2014:
2013:
1994:
1967:
1913:
1909:
1902:
1900:
1899:
1894:
1889:
1886:
1885:
1884:
1857:
1856:
1831:
1830:
1829:
1811:
1810:
1795:
1794:
1776:
1775:
1762:
1761:
1734:
1707:
1703:
1699:
1678:
1654:
1576:
1573:
1513:
1511:
1509:
1508:
1503:
1500:
1489:
1487:
1485:
1484:
1479:
1476:
1468:
1460:
1452:
1445:
1443:
1442:
1437:
1431:
1429:
1421:
1420:
1419:
1410:
1409:
1399:
1381:
1374:
1370:
1363:
1341:oblate ellipsoid
1334:Equatorial bulge
1228:Earth's rotation
1132:
1130:
1129:
1124:
1121:
1120:
1114:
1113:
1107:
1106:
1009:oblate ellipsoid
968:
961:
954:
792:
771:
763:
755:
747:
739:
679:
638:
580:
566:
560:
557:
549:
542:
539:
531:
524:
522:
517:
509:
490:
488:
487:
482:
479:
478:
472:
471:
465:
464:
441:
439:
438:
433:
430:
429:
423:
422:
413:
412:
398:
396:
395:
390:
387:
386:
380:
379:
370:
369:
355:
353:
352:
347:
344:
343:
337:
336:
330:
329:
275:
263:
256:
254:
248:
239:
237:
231:
215:
213:
212:
207:
205:
204:
179:
161:
53:
41:
21:
8712:
8711:
8707:
8706:
8705:
8703:
8702:
8701:
8672:
8671:
8670:
8665:
8639:
8587:
8584:
8567:
8561:
8558:
8544:
8531:
8525:Units of length
8522:
8455:
8450:
8449:
8445:
8442:
8437:
8436:
8427:
8425:
8415:
8414:
8410:
8401:
8399:
8387:
8386:
8382:
8372:
8370:
8368:
8353:
8352:
8348:
8327:
8323:
8314:
8312:
8304:
8303:
8299:
8292:
8282:Early astronomy
8279:
8278:
8274:
8264:in Fragment 202
8261:
8257:
8249:
8245:
8232:
8231:
8227:
8198:
8197:
8193:
8179:
8178:
8174:
8164:
8162:
8151:
8150:
8146:
8139:
8126:
8125:
8121:
8113:
8111:
8100:
8099:
8095:
8085:
8083:
8082:on 30 July 2020
8079:
8048:
8043:
8042:
8035:
8026:
8024:
8015:
8014:
8005:
7967:
7966:
7957:
7950:
7935:
7934:
7925:
7918:
7897:
7896:
7887:
7877:
7875:
7871:
7864:
7863:
7859:
7844:
7843:
7839:
7817:
7816:
7812:
7802:
7800:
7796:
7789:
7788:
7781:
7774:
7759:
7758:
7754:
7745:
7743:
7730:
7729:
7725:
7714:
7703:
7694:
7692:
7688:
7677:
7673:
7672:
7668:
7659:
7657:
7653:
7652:
7633:
7621:
7617:
7605:
7601:
7596:Wayback Machine
7587:
7583:
7577:Wayback Machine
7565:
7542:
7526:
7525:
7510:
7505:
7500:
7499:
7492:
7491:
7487:
7481:
7477:
7453:
7449:
7444:
7440:
7434:
7430:
7421:
7417:
7400:
7396:
7391:
7386:
7342:
7302:Jacques Cassini
7298:oblate spheroid
7250:spherical Earth
7204:
7186:
7171:
7168:
7165:
7163:
7148:
7145:
7143:
7128:
7125:
7123:
7108:
7105:
7103:
7087:
7084:
7082:
7077:
7060:
7056:
7053:
7051:
7028:
7025:
7023:
7000:
6997:
6995:
6990:
6971:
6968:
6966:
6961:
6942:
6939:
6937:
6932:
6913:
6910:
6908:
6887:
6884:
6882:
6861:
6858:
6856:
6830:
6827:
6825:
6820:
6801:
6798:
6796:
6791:
6772:
6769:
6767:
6762:
6743:
6740:
6738:
6717:
6714:
6712:
6692:
6689:
6687:
6669:
6666:
6664:
6648:
6645:
6643:
6613:
6562:
6561:
6503:
6502:
6456:
6455:
6444:
6433:
6429:
6427:
6420:
6416:
6414:
6412:
6408:
6398:
6392:
6389:
6386:
6385:
6383:
6381:
6311:
6301:
6294:
6275:
6242:
6232:
6204:
6192:authalic radius
6183:
6176:
6163:
6149:
6141:
6133:
6111:
6105:
6066:
6049:
6044:
6043:
6036:
5982:
5964:
5963:
5957:
5956:
5941:
5936:
5935:
5846:
5841:
5840:
5833:
5790:
5779:
5759:
5748:
5700:
5695:
5694:
5676:
5666:
5622:
5621:
5606:
5601:
5600:
5594:
5588:
5577:
5520:
5495:
5488:
5487:
5461:
5460:
5435:
5430:
5429:
5402:
5401:
5399:
5363:
5350:
5336:
5335:
5333:
5304:
5268:
5267:
5250:
5230:
5201:
5190:
5167:
5152:
5151:
5147:
5122:
5117:
5116:
5110:
5104:
5086:
5080:
5078:Authalic radius
5040:
5025:
5020:
5019:
5013:
5007:
5002:arithmetic mean
4972:
4957:
4955:
4951:
4939:
4937:
4933:
4919:
4870:
4850:
4845:
4844:
4837:
4805:
4796:
4781:
4770:
4759:
4758:
4713:
4703:
4696:
4683:
4671:
4653:
4625:
4609:
4595:
4594:
4547:
4519:
4475:
4470:
4469:
4462:
4449:
4447:Non-directional
4403:
4402:
4373:
4372:
4368:
4348:
4343:
4342:
4331:
4327:
4312:
4307:
4302:
4278:
4277:
4249:
4248:
4216:
4198:
4193:
4192:
4169:
4151:
4146:
4145:
4101:
4096:
4095:
4061:
4056:
4055:
4021:
4020:
3998:
3997:
3973:
3965:
3950:
3942:
3929:
3928:
3904:
3896:
3889:
3888:
3867:
3859:
3852:
3851:
3832:
3831:
3803:
3787:
3786:
3763:
3762:
3757:
3751:
3750:
3745:
3734:
3718:
3705:
3701:
3690:
3680:
3679:
3667:
3641:
3630:
3629:
3599:
3556:
3536:
3523:
3507:
3480:
3479:
3440:
3435:
3434:
3407:
3402:
3401:
3380:
3349:
3339:
3326:
3313:
3299:
3298:
3275:
3274:
3269:
3263:
3262:
3257:
3246:
3230:
3226:
3215:
3211:
3196:
3192:
3181:
3177:
3149:
3138:
3137:
3103:
3060:
3040:
3027:
3011:
2985:
2977:
2976:
2908:
2843:
2829:
2812:
2811:
2801:
2793:
2783:
2779:
2770:
2767:
2762:
2761:
2759:
2757:
2750:
2744:
2727:
2721:
2709:
2705:
2696:
2693:
2688:
2687:
2685:
2683:
2677:
2663:
2618:
2617:
2610:normal distance
2569:
2559:
2531:
2503:
2477:
2455:
2454:
2447:
2443:
2375:
2374:
2341:
2335:
2334:
2306:
2305:
2294:
2286:arc measurement
2258:
2257:
2229:
2208:
2197:
2190:
2167:
2151:
2141:
2131:
2117:
2104:
2077:
2067:
2039:
2016:
2005:
1995:
1973:
1972:
1965:
1954:
1946:normal sections
1938:
1933:
1927:
1911:
1907:
1876:
1848:
1832:
1821:
1802:
1786:
1767:
1763:
1740:
1739:
1732:
1722:
1715:
1705:
1701:
1697:
1690:
1681:semi-minor axis
1676:
1657:semi-major axis
1652:
1622:
1574:
1561:
1504:
1501:
1498:
1497:
1495:
1494:
1480:
1477:
1474:
1473:
1471:
1470:
1466:
1458:
1450:
1422:
1411:
1401:
1400:
1387:
1386:
1379:
1372:
1368:
1361:
1336:
1330:
1276:of revolution,
1225:
1219:Earth ellipsoid
1213:Main articles:
1207:low Earth orbit
1160:
1095:
1094:
1066:
1055:
1047:authalic radius
1044:
1001:figure of Earth
994:
987:
972:
943:
942:
789:
781:
780:
769:
761:
753:
745:
737:
721:
713:
712:
671:
621:
613:
612:
588:
558:
555:
547:
540:
537:
529:
520:
518:
515:
507:
453:
452:
401:
400:
358:
357:
318:
317:
278:
252:
250:
246:
241:
235:
233:
229:
194:
193:
180:
175:
174:
173:Behaviour under
159:
142:
132:
122:
115:
100:
93:
85:
75:
68:
39:
36:
33:Arc measurement
29:Spherical Earth
23:
22:
15:
12:
11:
5:
8710:
8708:
8700:
8699:
8694:
8689:
8684:
8674:
8673:
8667:
8666:
8664:
8663:
8658:
8653:
8648:
8644:
8641:
8640:
8638:
8637:
8631:
8625:
8619:
8613:
8607:
8601:
8595:
8589:
8585:
8582:
8576:
8570:
8565:
8559:
8556:
8549:
8546:
8545:
8543:
8542:
8536:
8533:
8532:
8523:
8521:
8520:
8513:
8506:
8498:
8492:
8491:
8462:
8458:
8441:
8440:External links
8438:
8435:
8434:
8408:
8380:
8366:
8346:
8343:978-1468308501
8321:
8297:
8290:
8272:
8255:
8243:
8238:Britannica.com
8225:
8214:Chisholm, Hugh
8191:
8172:
8158:On the Heavens
8144:
8137:
8119:
8093:
8033:
8003:
7976:(1): 128–133.
7955:
7948:
7923:
7916:
7885:
7857:
7837:
7810:
7779:
7772:
7752:
7723:
7701:
7666:
7631:
7615:
7599:
7581:
7540:
7507:
7506:
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7501:
7498:
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7485:
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7447:
7438:
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7393:
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7390:
7387:
7385:
7384:
7379:
7374:
7369:
7364:
7359:
7354:
7349:
7343:
7341:
7338:
7217:On the Heavens
7185:
7182:
7179:
7178:
7176:
7161:
7158:
7155:
7154:
7152:
7141:
7138:
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7011:
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7005:
6993:
6988:
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6892:
6880:
6873:
6869:
6868:
6866:
6854:
6844:
6838:
6837:
6835:
6823:
6818:
6813:
6809:
6808:
6806:
6794:
6789:
6784:
6780:
6779:
6777:
6765:
6760:
6755:
6751:
6750:
6748:
6736:
6729:
6725:
6724:
6722:
6710:
6703:
6699:
6698:
6696:
6685:
6682:
6676:
6675:
6673:
6662:
6659:
6655:
6654:
6652:
6641:
6638:
6632:
6631:
6628:
6625:
6622:
6612:
6609:
6605:Jupiter radius
6589:
6582:
6578:
6572:
6550:unit of length
6530:
6523:
6519:
6513:
6483:
6476:
6472:
6466:
6443:
6440:
6378:Earth's volume
6368:map projection
6349:surface curves
6309:
6299:
6292:
6273:
6266:is simply the
6251:
6250:
6240:
6222:polar diameter
6203:
6200:
6175:
6172:
6171:
6170:
6161:
6156:
6147:
6140:
6137:
6131:
6123:topographical
6104:
6101:
6097:
6096:
6085:
6079:
6075:
6072:
6069:
6063:
6057:
6052:
6033:
6032:
6021:
6014:
6011:
6005:
6000:
5993:
5990:
5985:
5981:
5975:
5972:
5967:
5960:
5955:
5949:
5944:
5926:
5925:
5914:
5910:
5907:
5903:
5900:
5897:
5894:
5887:
5884:
5878:
5874:
5868:
5865:
5860:
5854:
5849:
5830:
5829:
5818:
5814:
5811:
5805:
5802:
5797:
5793:
5786:
5782:
5777:
5774:
5771:
5766:
5762:
5755:
5751:
5741:
5738:
5732:
5728:
5722:
5719:
5714:
5708:
5703:
5665:
5662:
5658:
5657:
5646:
5639:
5634:
5629:
5625:
5618:
5613:
5609:
5592:
5576:
5573:
5572:
5571:
5560:
5553:
5548:
5544:
5540:
5535:
5530:
5526:
5523:
5517:
5512:
5508:
5505:
5501:
5498:
5468:
5442:
5438:
5409:
5384:
5379:
5370:
5366:
5362:
5357:
5353:
5347:
5344:
5330:
5329:
5318:
5310:
5307:
5303:
5297:
5290:
5286:
5283:
5278:
5275:
5271:
5262:
5257:
5253:
5247:
5242:
5237:
5233:
5225:
5219:
5212:
5208:
5204:
5199:
5196:
5193:
5187:
5184:
5179:
5174:
5170:
5164:
5159:
5155:
5150:
5144:
5141:
5134:
5129:
5125:
5108:
5079:
5076:
5072:
5071:
5056:
5052:
5049:
5046:
5043:
5037:
5032:
5028:
5011:
4971:
4968:
4964:
4963:
4945:
4918:
4915:
4914:
4913:
4894:
4891:
4885:
4879:
4876:
4869:
4864:
4858:
4853:
4812:
4808:
4803:
4799:
4793:
4788:
4784:
4777:
4773:
4769:
4766:
4747:
4746:
4735:
4728:
4725:
4720:
4716:
4710:
4706:
4702:
4699:
4690:
4686:
4682:
4679:
4674:
4668:
4660:
4656:
4652:
4649:
4646:
4643:
4640:
4637:
4632:
4628:
4624:
4621:
4618:
4615:
4612:
4607:
4602:
4598:
4591:
4586:
4583:
4578:
4574:
4571:
4567:
4564:
4561:
4555:
4550:
4544:
4541:
4536:
4532:
4525:
4522:
4518:
4513:
4507:
4503:
4498:
4495:
4492:
4489:
4483:
4478:
4448:
4445:
4444:
4443:
4432:
4422:
4418:
4415:
4410:
4406:
4398:
4392:
4388:
4385:
4380:
4376:
4367:
4362:
4356:
4351:
4311:
4308:
4306:
4303:
4299:
4298:
4285:
4265:
4262:
4259:
4256:
4242:
4241:
4230:
4223:
4219:
4215:
4210:
4205:
4201:
4176:
4172:
4168:
4163:
4158:
4154:
4139:
4138:
4127:
4121:
4118:
4113:
4108:
4104:
4081:
4078:
4073:
4068:
4064:
4040:
4037:
4034:
4031:
4028:
4005:
3994:
3993:
3979:
3976:
3971:
3968:
3962:
3956:
3953:
3948:
3945:
3939:
3936:
3910:
3907:
3902:
3899:
3873:
3870:
3865:
3862:
3850:, and because
3839:
3815:
3811:
3807:
3802:
3797:
3794:
3784:
3783:
3772:
3768:
3761:
3758:
3756:
3753:
3752:
3749:
3746:
3744:
3741:
3740:
3737:
3733:
3725:
3721:
3717:
3712:
3708:
3704:
3697:
3693:
3687:
3683:
3674:
3670:
3664:
3660:
3656:
3651:
3648:
3644:
3640:
3637:
3623:
3622:
3611:
3606:
3602:
3598:
3594:
3591:
3588:
3585:
3581:
3578:
3574:
3571:
3568:
3563:
3559:
3555:
3551:
3548:
3543:
3539:
3535:
3530:
3526:
3522:
3517:
3514:
3510:
3504:
3501:
3497:
3493:
3490:
3487:
3458:
3455:
3452:
3447:
3443:
3422:
3419:
3414:
3410:
3387:
3383:
3379:
3376:
3373:
3370:
3367:
3364:
3361:
3356:
3352:
3346:
3342:
3338:
3333:
3329:
3325:
3320:
3316:
3312:
3309:
3306:
3296:
3295:
3284:
3280:
3273:
3270:
3268:
3265:
3264:
3261:
3258:
3256:
3253:
3252:
3249:
3245:
3237:
3233:
3229:
3222:
3218:
3214:
3203:
3199:
3195:
3188:
3184:
3180:
3172:
3168:
3164:
3159:
3156:
3152:
3148:
3145:
3127:
3126:
3115:
3110:
3106:
3102:
3098:
3095:
3092:
3089:
3085:
3082:
3078:
3075:
3072:
3067:
3063:
3059:
3055:
3052:
3047:
3043:
3039:
3034:
3030:
3026:
3021:
3018:
3014:
3008:
3005:
3001:
2997:
2992:
2988:
2984:
2966:
2965:
2954:
2951:
2948:
2944:
2941:
2938:
2935:
2932:
2929:
2926:
2923:
2920:
2915:
2911:
2907:
2904:
2901:
2898:
2895:
2892:
2888:
2885:
2882:
2879:
2876:
2873:
2870:
2867:
2864:
2861:
2858:
2855:
2850:
2846:
2841:
2836:
2832:
2828:
2825:
2822:
2819:
2803:
2802:
2799:
2794:
2792:
2789:
2788:
2787:
2755:
2748:
2725:
2714:
2713:
2681:
2662:
2659:
2646:
2643:
2640:
2637:
2634:
2631:
2628:
2625:
2603:
2602:
2591:
2584:
2581:
2576:
2572:
2566:
2562:
2558:
2555:
2551:
2546:
2538:
2534:
2530:
2527:
2524:
2521:
2518:
2515:
2510:
2506:
2502:
2499:
2496:
2493:
2490:
2484:
2480:
2474:
2471:
2468:
2465:
2462:
2430:prime-vertical
2408:
2405:
2401:
2398:
2394:
2391:
2388:
2385:
2382:
2362:
2359:
2356:
2353:
2348:
2344:
2322:
2319:
2316:
2313:
2293:
2292:Prime vertical
2290:
2265:
2254:
2253:
2242:
2236:
2232:
2228:
2225:
2222:
2215:
2211:
2204:
2200:
2196:
2193:
2187:
2178:
2175:
2170:
2166:
2163:
2158:
2154:
2148:
2144:
2140:
2137:
2134:
2129:
2124:
2120:
2116:
2113:
2110:
2107:
2101:
2092:
2089:
2082:
2074:
2070:
2066:
2063:
2060:
2057:
2054:
2051:
2046:
2042:
2038:
2035:
2032:
2029:
2026:
2021:
2012:
2008:
2004:
2001:
1998:
1992:
1989:
1986:
1983:
1980:
1953:
1950:
1940:There are two
1937:
1934:
1926:
1923:
1904:
1903:
1892:
1883:
1879:
1875:
1872:
1869:
1866:
1863:
1860:
1855:
1851:
1847:
1844:
1841:
1838:
1835:
1828:
1824:
1820:
1817:
1814:
1809:
1805:
1801:
1798:
1793:
1789:
1785:
1782:
1779:
1774:
1770:
1766:
1759:
1756:
1753:
1750:
1747:
1714:
1711:
1689:
1686:
1685:
1684:
1669:
1668:
1621:
1618:
1610:remote sensing
1560:
1557:
1447:
1446:
1435:
1428:
1425:
1418:
1414:
1408:
1404:
1397:
1394:
1357:, so that the
1329:
1326:
1292:
1291:
1285:
1266:
1263:mean sea level
1255:
1181:with the same
1159:
1156:
1119:
1112:
1105:
1074:or the actual
1064:
1053:
1042:
1005:Earth spheroid
992:
985:
974:
973:
971:
970:
963:
956:
948:
945:
944:
941:
940:
935:
930:
922:
921:
918:
912:
911:
908:
902:
901:
898:
892:
891:
888:
882:
881:
878:
872:
871:
868:
862:
861:
858:
852:
851:
848:
842:
841:
838:
832:
831:
828:
822:
821:
818:
812:
811:
808:
802:
801:
798:
790:
787:
786:
783:
782:
779:
778:
773:
765:
757:
749:
741:
733:
728:
722:
719:
718:
715:
714:
711:
710:
705:
700:
695:
690:
685:
683:Map projection
680:
669:
664:
659:
657:Geodetic datum
654:
649:
633:
628:
622:
619:
618:
615:
614:
611:
610:
605:
600:
595:
589:
586:
585:
582:
581:
573:
572:
562:
561:
553:
544:
543:
535:
526:
525:
513:
504:
503:
500:
499:
494:
477:
470:
463:
448:
447:
443:
442:
428:
421:
417:
411:
385:
378:
374:
368:
342:
335:
328:
315:
311:
310:
305:
301:
300:
291:
285:
284:
280:
279:
276:
268:
267:
259:
258:
223:
217:
216:
203:
191:
185:
184:
181:
172:
169:
168:
163:
154:
153:
150:
144:
143:
137:
127:
120:
113:
98:
91:
86:
84:Common symbols
83:
80:
79:
76:
73:
70:
69:
54:
46:
45:
37:
24:
14:
13:
10:
9:
6:
4:
3:
2:
8709:
8698:
8695:
8693:
8690:
8688:
8685:
8683:
8680:
8679:
8677:
8662:
8659:
8657:
8654:
8652:
8649:
8646:
8645:
8642:
8635:
8632:
8629:
8626:
8623:
8620:
8617:
8614:
8611:
8608:
8605:
8602:
8599:
8596:
8593:
8590:
8580:
8577:
8574:
8571:
8568:
8554:
8551:
8550:
8547:
8541:
8538:
8537:
8534:
8530:
8526:
8519:
8514:
8512:
8507:
8505:
8500:
8499:
8496:
8488:
8484:
8480:
8479:Sixty Symbols
8476:
8460:
8456:
8444:
8443:
8439:
8423:
8419:
8412:
8409:
8398:on 2018-01-27
8397:
8393:
8392:
8384:
8381:
8369:
8363:
8359:
8358:
8350:
8347:
8344:
8340:
8336:
8335:
8330:
8325:
8322:
8311:
8307:
8301:
8298:
8293:
8291:0-387-94107-X
8287:
8283:
8276:
8273:
8269:
8265:
8259:
8256:
8253:
8247:
8244:
8239:
8235:
8229:
8226:
8221:
8220:
8215:
8210:
8205:
8201:
8195:
8192:
8187:
8183:
8176:
8173:
8160:
8159:
8154:
8148:
8145:
8140:
8134:
8130:
8123:
8120:
8110:
8106:
8105:
8097:
8094:
8078:
8074:
8070:
8066:
8062:
8058:
8054:
8047:
8040:
8038:
8034:
8023:on 2012-09-10
8022:
8018:
8012:
8010:
8008:
8004:
7999:
7995:
7991:
7987:
7983:
7979:
7975:
7971:
7964:
7962:
7960:
7956:
7951:
7949:9783110170726
7945:
7941:
7940:
7932:
7930:
7928:
7924:
7919:
7917:9780070365209
7913:
7909:
7904:
7903:
7894:
7892:
7890:
7886:
7870:
7869:
7861:
7858:
7853:
7852:
7847:
7841:
7838:
7833:
7829:
7825:
7821:
7820:Survey Review
7814:
7811:
7795:
7794:
7786:
7784:
7780:
7775:
7769:
7765:
7764:
7756:
7753:
7742:on 2016-08-26
7741:
7737:
7733:
7727:
7724:
7720:
7719:
7712:
7710:
7708:
7706:
7702:
7691:on 2020-08-04
7687:
7683:
7676:
7670:
7667:
7656:
7650:
7648:
7646:
7644:
7642:
7640:
7638:
7636:
7632:
7628:
7624:
7619:
7616:
7612:
7608:
7603:
7600:
7597:
7593:
7590:
7585:
7582:
7578:
7574:
7571:
7570:
7563:
7561:
7559:
7557:
7555:
7553:
7551:
7549:
7547:
7545:
7541:
7535:
7530:
7523:
7521:
7519:
7517:
7515:
7513:
7509:
7502:
7489:
7486:
7479:
7476:
7472:
7468:
7464:
7460:
7457:
7451:
7448:
7442:
7439:
7432:
7429:
7425:
7419:
7416:
7412:
7408:
7404:
7398:
7395:
7388:
7383:
7380:
7378:
7375:
7373:
7370:
7368:
7365:
7363:
7360:
7358:
7355:
7353:
7350:
7348:
7345:
7344:
7339:
7337:
7335:
7331:
7327:
7323:
7322:Arctic Circle
7319:
7315:
7311:
7307:
7304:argued for a
7303:
7299:
7295:
7291:
7288:Around 1690,
7286:
7284:
7280:
7276:
7272:
7268:
7264:
7259:
7257:
7256:
7251:
7247:
7243:
7239:
7235:
7230:
7227:
7223:
7219:
7218:
7213:
7209:
7203:
7199:
7195:
7191:
7183:
7177:
7162:
7159:
7157:
7156:
7153:
7142:
7139:
7137:
7136:
7133:
7122:
7119:
7117:
7116:
7113:
7102:
7099:
7097:
7096:
7093:
7081:
7078:
7071:
7069:
7068:
7065:
7050:
7047:
7043:
7040:
7038:
7037:
7034:
7022:
7019:
7015:
7012:
7010:
7009:
7006:
6994:
6991:
6984:
6981:
6980:
6977:
6965:
6962:
6955:
6952:
6951:
6948:
6936:
6933:
6926:
6923:
6922:
6919:
6907:
6904:
6900:
6897:
6896:
6893:
6881:
6878:
6874:
6871:
6870:
6867:
6855:
6852:
6848:
6845:
6843:
6840:
6839:
6836:
6824:
6821:
6814:
6811:
6810:
6807:
6795:
6792:
6785:
6782:
6781:
6778:
6766:
6763:
6757:mean radius (
6756:
6753:
6752:
6749:
6737:
6734:
6730:
6727:
6726:
6723:
6711:
6708:
6704:
6701:
6700:
6697:
6686:
6683:
6681:
6678:
6677:
6674:
6663:
6660:
6657:
6656:
6653:
6642:
6639:
6637:
6634:
6633:
6629:
6626:
6623:
6620:
6619:
6616:
6610:
6608:
6606:
6576:
6559:
6555:
6551:
6547:
6517:
6500:
6470:
6453:
6449:
6442:Nominal radii
6441:
6439:
6406:
6379:
6375:
6373:
6369:
6365:
6362:Likewise for
6360:
6358:
6354:
6353:meridian arcs
6350:
6346:
6342:
6341:for details.
6340:
6336:
6332:
6328:
6324:
6320:
6316:
6312:
6306:
6302:
6295:
6288:
6284:
6280:
6276:
6269:
6265:
6261:
6257:
6256:
6246:
6241:
6236:
6231:
6230:
6229:
6227:
6223:
6219:
6215:
6211:
6210:
6201:
6199:
6197:
6193:
6189:
6181:
6173:
6168:
6164:
6157:
6154:
6150:
6143:
6142:
6138:
6136:
6134:
6127:
6126:
6120:
6116:
6110:
6102:
6100:
6083:
6077:
6073:
6070:
6067:
6061:
6050:
6042:
6041:
6040:
6019:
6012:
6009:
6003:
5998:
5991:
5988:
5983:
5979:
5973:
5970:
5965:
5958:
5953:
5942:
5934:
5933:
5932:
5929:
5912:
5908:
5905:
5898:
5892:
5885:
5882:
5876:
5872:
5866:
5863:
5858:
5847:
5839:
5838:
5837:
5816:
5812:
5809:
5803:
5800:
5795:
5791:
5784:
5780:
5775:
5772:
5769:
5764:
5760:
5753:
5749:
5739:
5736:
5730:
5726:
5720:
5717:
5712:
5701:
5693:
5692:
5691:
5689:
5685:
5681:
5675:
5671:
5663:
5661:
5644:
5637:
5632:
5627:
5623:
5616:
5611:
5607:
5599:
5598:
5597:
5591:
5586:
5582:
5574:
5558:
5551:
5546:
5542:
5538:
5533:
5528:
5524:
5521:
5515:
5510:
5506:
5503:
5499:
5496:
5486:
5485:
5484:
5483:, this gives
5482:
5466:
5458:
5440:
5436:
5426:
5423:
5407:
5382:
5368:
5364:
5360:
5355:
5351:
5345:
5342:
5316:
5308:
5305:
5301:
5295:
5288:
5284:
5281:
5276:
5273:
5269:
5260:
5255:
5251:
5245:
5240:
5235:
5231:
5223:
5217:
5210:
5206:
5202:
5197:
5194:
5191:
5185:
5182:
5177:
5172:
5168:
5162:
5157:
5153:
5148:
5142:
5139:
5132:
5127:
5123:
5115:
5114:
5113:
5107:
5102:
5098:
5094:
5090:
5085:
5077:
5075:
5054:
5050:
5047:
5044:
5041:
5035:
5030:
5026:
5018:
5017:
5016:
5010:
5005:
5003:
4997:
4989:
4985:
4981:
4976:
4969:
4967:
4960:.7523 km
4949:
4946:
4942:.1370 km
4931:
4928:
4927:
4926:
4924:
4916:
4892:
4889:
4883:
4877:
4874:
4867:
4862:
4851:
4843:
4842:
4841:
4835:
4834:
4827:
4810:
4801:
4791:
4786:
4782:
4775:
4771:
4767:
4764:
4756:
4752:
4733:
4726:
4723:
4718:
4714:
4708:
4704:
4700:
4697:
4688:
4684:
4680:
4677:
4672:
4666:
4658:
4650:
4647:
4644:
4641:
4635:
4630:
4622:
4619:
4616:
4613:
4605:
4600:
4596:
4589:
4584:
4581:
4576:
4572:
4569:
4562:
4548:
4542:
4539:
4534:
4530:
4523:
4520:
4516:
4511:
4505:
4501:
4496:
4490:
4476:
4468:
4467:
4466:
4460:
4459:
4452:
4446:
4430:
4420:
4416:
4413:
4408:
4404:
4396:
4390:
4386:
4383:
4378:
4374:
4365:
4360:
4349:
4341:
4340:
4339:
4337:
4325:
4321:
4317:
4309:
4304:
4297:
4283:
4263:
4260:
4257:
4254:
4245:
4228:
4221:
4217:
4213:
4208:
4203:
4199:
4174:
4170:
4166:
4161:
4156:
4152:
4144:
4143:
4142:
4125:
4119:
4116:
4111:
4106:
4102:
4079:
4076:
4071:
4066:
4062:
4054:
4053:
4052:
4038:
4035:
4032:
4029:
4026:
4017:
4003:
3977:
3969:
3960:
3954:
3946:
3937:
3934:
3927:
3926:
3925:
3908:
3900:
3871:
3863:
3837:
3809:
3800:
3795:
3792:
3770:
3766:
3759:
3754:
3747:
3742:
3735:
3731:
3723:
3719:
3710:
3706:
3695:
3691:
3685:
3672:
3668:
3662:
3658:
3654:
3649:
3646:
3642:
3638:
3635:
3628:
3627:
3626:
3609:
3604:
3600:
3596:
3592:
3589:
3586:
3583:
3579:
3576:
3572:
3569:
3566:
3561:
3557:
3553:
3549:
3546:
3541:
3537:
3533:
3528:
3524:
3520:
3515:
3512:
3508:
3502:
3499:
3495:
3491:
3488:
3485:
3478:
3477:
3476:
3474:
3469:
3456:
3453:
3450:
3445:
3441:
3420:
3417:
3412:
3408:
3385:
3377:
3374:
3371:
3368:
3365:
3359:
3354:
3344:
3340:
3336:
3331:
3327:
3323:
3318:
3314:
3307:
3304:
3282:
3278:
3271:
3266:
3259:
3254:
3247:
3243:
3235:
3231:
3220:
3216:
3201:
3197:
3186:
3182:
3170:
3166:
3162:
3157:
3154:
3150:
3146:
3143:
3136:
3135:
3134:
3132:
3131:metric tensor
3113:
3108:
3104:
3100:
3096:
3093:
3090:
3087:
3083:
3080:
3076:
3073:
3070:
3065:
3061:
3057:
3053:
3050:
3045:
3041:
3037:
3032:
3028:
3024:
3019:
3016:
3012:
3006:
3003:
2999:
2995:
2990:
2986:
2982:
2975:
2974:
2973:
2971:
2968:where in the
2952:
2946:
2942:
2939:
2936:
2927:
2924:
2921:
2913:
2909:
2905:
2902:
2899:
2893:
2890:
2883:
2880:
2877:
2874:
2871:
2868:
2865:
2862:
2859:
2853:
2848:
2844:
2834:
2830:
2826:
2823:
2820:
2810:
2809:
2808:
2805:
2804:
2797:
2790:
2773:
2765:
2754:
2747:
2743:
2742:
2741:
2739:
2734:
2731:
2724:
2719:
2699:
2691:
2680:
2676:
2675:
2674:
2672:
2668:
2660:
2658:
2641:
2635:
2632:
2629:
2626:
2623:
2615:
2611:
2607:
2589:
2582:
2579:
2574:
2570:
2564:
2560:
2556:
2553:
2549:
2544:
2536:
2528:
2525:
2522:
2519:
2513:
2508:
2500:
2497:
2494:
2491:
2482:
2478:
2472:
2466:
2460:
2453:
2452:
2451:
2441:
2437:
2433:
2431:
2424:
2403:
2399:
2396:
2392:
2389:
2383:
2380:
2357:
2351:
2346:
2342:
2317:
2311:
2303:
2298:
2291:
2289:
2287:
2283:
2279:
2263:
2240:
2234:
2226:
2220:
2213:
2209:
2202:
2198:
2194:
2191:
2185:
2176:
2173:
2164:
2161:
2156:
2152:
2146:
2142:
2138:
2135:
2122:
2118:
2114:
2111:
2105:
2099:
2090:
2087:
2072:
2064:
2061:
2058:
2055:
2049:
2044:
2036:
2033:
2030:
2027:
2010:
2002:
1999:
1990:
1984:
1978:
1971:
1970:
1969:
1963:
1961:
1951:
1949:
1947:
1943:
1935:
1932:
1924:
1922:
1920:
1915:
1890:
1881:
1873:
1870:
1867:
1864:
1858:
1853:
1845:
1842:
1839:
1836:
1826:
1818:
1815:
1812:
1807:
1803:
1796:
1791:
1783:
1780:
1777:
1772:
1768:
1757:
1751:
1745:
1738:
1737:
1736:
1731:
1727:
1720:
1712:
1694:
1687:
1682:
1675:
1671:
1670:
1666:
1662:
1658:
1651:
1647:
1646:
1645:
1641:
1639:
1635:
1631:
1627:
1619:
1617:
1615:
1611:
1607:
1603:
1598:
1596:
1592:
1588:
1583:
1569:
1565:
1558:
1556:
1554:
1548:
1546:
1542:
1538:
1536:
1531:
1527:
1519:
1515:
1507:
1493:
1483:
1464:
1456:
1433:
1426:
1423:
1416:
1412:
1406:
1402:
1395:
1392:
1385:
1384:
1383:
1378:
1367:
1360:
1356:
1352:
1348:
1344:
1342:
1335:
1325:
1323:
1318:
1313:
1311:
1307:
1306:
1301:
1297:
1290:
1286:
1283:
1279:
1275:
1271:
1267:
1264:
1261:, defined by
1260:
1256:
1253:
1252:
1251:
1249:
1245:
1240:
1237:
1233:
1229:
1224:
1220:
1216:
1208:
1204:
1201:range of the
1200:
1196:
1192:
1188:
1184:
1180:
1176:
1173:
1169:
1164:
1157:
1155:
1153:
1148:
1144:
1140:
1136:
1092:
1087:
1085:
1081:
1077:
1073:
1068:
1063:
1059:
1052:
1048:
1041:
1037:
1033:
1028:
1026:
1022:
1018:
1014:
1010:
1006:
1002:
998:
991:
984:
980:
969:
964:
962:
957:
955:
950:
949:
947:
946:
939:
936:
934:
931:
929:
926:
925:
919:
917:
914:
913:
909:
907:
904:
903:
899:
897:
894:
893:
889:
887:
884:
883:
879:
877:
874:
873:
869:
867:
864:
863:
859:
857:
854:
853:
849:
847:
844:
843:
839:
837:
834:
833:
829:
827:
824:
823:
819:
817:
814:
813:
809:
807:
804:
803:
799:
797:
794:
793:
785:
784:
777:
774:
772:
766:
764:
758:
756:
750:
748:
744:BeiDou (BDS)
742:
740:
734:
732:
729:
727:
724:
723:
717:
716:
709:
706:
704:
701:
699:
696:
694:
691:
689:
686:
684:
681:
678:
674:
670:
668:
665:
663:
660:
658:
655:
653:
650:
646:
645:circumference
642:
637:
634:
632:
629:
627:
624:
623:
617:
616:
609:
606:
604:
601:
599:
596:
594:
591:
590:
584:
583:
579:
575:
574:
571:
567:
554:
552:
551:English units
545:
536:
534:
533:Metric system
527:
514:
512:
505:
501:
498:
495:
493:
450:
444:
415:
372:
316:
312:
309:
306:
302:
299:
295:
292:
290:
286:
281:
274:
269:
264:
255:.7523 km
244:
238:.1370 km
227:
224:
222:
218:
192:
190:
186:
182:
178:
170:
167:
164:
162:
155:
151:
149:
145:
140:
136:
130:
126:
119:
112:
108:
104:
97:
90:
87:
81:
77:
71:
66:
62:
58:
52:
47:
42:
34:
30:
19:
8579:Solar radius
8573:Light-second
8563:
8553:Earth radius
8478:
8426:. Retrieved
8421:
8411:
8400:. Retrieved
8396:the original
8390:
8383:
8371:. Retrieved
8356:
8349:
8333:
8324:
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7290:Isaac Newton
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6624:Description
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6364:surface area
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4965:
4948:Polar radius
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4917:Global radii
4836:at latitude
4830:
4828:
4754:
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4461:at latitude
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4338:as follows:
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4314:The Earth's
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2282:Eratosthenes
2278:eccentricity
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1674:polar radius
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1672:The Earth's
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1648:The Earth's
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1602:Eratosthenes
1599:
1595:true horizon
1584:
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1376:
1366:polar radius
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1358:
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1309:
1303:
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1295:
1293:
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1241:
1232:tidal forces
1226:
1187:eccentricity
1170:of the 2003
1158:Introduction
1090:
1088:
1069:
1061:
1057:
1050:
1046:
1039:
1035:
1029:
1024:
1021:polar radius
1020:
1016:
1012:
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982:
981:(denoted as
979:Earth radius
978:
977:
720:Technologies
675: /
640:
587:Fundamentals
511:SI base unit
496:
491:
304:Unit of
243:Polar radius
242:
225:
148:SI unit
138:
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128:
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117:
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106:
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44:Earth radius
8483:Brady Haran
8329:John Freely
8262:Cleomedes (
8086:18 November
7846:Bomford, G.
7483:discussion.
7426:conditions.
6428:V = 1.08321
6258:equals the
4318:, along an
1575: 1050
1355:South Poles
1305:mean radius
1191:Karman line
1082:radius and
1056:); and the
1036:mean radius
598:Geodynamics
289:Unit system
74:Other names
8676:Categories
8634:gigaparsec
8628:megaparsec
8622:kiloparsec
8610:light-year
8428:2019-05-22
8402:2023-02-09
8315:2022-11-05
8165:5 November
8138:0471334588
8114:2007-03-17
8027:2013-09-16
7746:2016-08-10
7695:2008-12-31
7660:2018-10-17
7534:1510.07674
7503:References
7459:definition
7411:Earth tide
7352:Earth mass
7188:See also:
6546:Earth tide
6351:, such as
6345:Arc length
6184:230 m
6153:Chimborazo
6115:topography
6107:See also:
5668:See also:
5082:See also:
4982:), polar (
2791:Derivation
2440:orthogonal
1960:meridional
1952:Meridional
1929:See also:
1570:'s (973 –
1553:Earth tide
1492:flattening
1317:geocentric
1278:geocentric
1236:topography
1183:minor axis
1168:oblateness
1143:geophysics
1084:equatorial
1076:topography
1023:, denoted
1015:, denoted
298:geophysics
59:), polar (
8604:terametre
8592:gigametre
8529:Astronomy
8461:⊕
8153:Aristotle
7998:195290884
7261:By 1490,
7212:Aristotle
6554:astronomy
6357:geodesics
6260:perimeter
6194:, or the
6062:≈
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3000:∑
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1568:Al-Biruni
1545:Greenland
1512:≈ 298.257
1413:ω
1343:/spheroid
1274:ellipsoid
1195:sea level
1139:astronomy
1093:(denoted
677:Longitude
603:Geomatics
523:10 m
294:astronomy
189:Dimension
8647:See also
8586:☉
8527:used in
8485:for the
8337:(2013),
8206:(1911).
7848:(1952).
7592:Archived
7573:Archived
7424:geodetic
7340:See also
7318:latitude
7255:Almagest
6560:; e.g.,
6423: km
6209:diameter
6207:Earth's
6158:Minimum
6144:Maximum
5015:) to be
5000:Earth's
4831:Earth's
4456:Earth's
2450:and is:
2428:Earth's
1958:Earth's
1919:vertices
1644:needed.
1638:accuracy
1282:geodetic
1270:spheroid
1199:altitude
856:ISO 6709
754:(Europe)
752:Galileo
738:(Russia)
736:GLONASS
673:Latitude
662:Geodesic
620:Concepts
356:,
308:distance
8422:Gallica
8373:31 July
8240:. 2016.
8216:(ed.).
8061:Bibcode
7978:Bibcode
7939:Geodesy
7851:Geodesy
7467:gravity
7362:Geodesy
7326:equator
7210:, when
7184:History
6621:Agency
6558:planets
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6289:equals
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1453:is the
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1179:ellipse
1154:(IAU).
916:Geo URI
886:NAVD 88
796:NGVD 29
770:(Japan)
762:(India)
746:(China)
608:History
593:Geodesy
570:Geodesy
451:1
8616:parsec
8364:
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7878:13 May
7803:13 May
7770:
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1465:, and
1449:where
1375:. The
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1289:sphere
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1244:radius
1221:, and
1003:by an
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876:WGS 84
866:NAD 83
846:GRS 80
806:OSGB36
760:NAVIC
641:radius
519:6.3781
492:in ...
314:Symbol
183:scalar
152:meters
8697:Radii
8682:Earth
8636:(Gpc)
8630:(Mpc)
8624:(kpc)
8212:. In
8080:(PDF)
8049:(PDF)
7994:S2CID
7910:–77.
7872:(PDF)
7797:(PDF)
7689:(PDF)
7678:(PDF)
7529:arXiv
7407:geoid
7389:Notes
7330:poles
7090:.0195
7003:.7900
6974:.1809
6945:.7714
6916:.6258
6890:.3142
6833:.7900
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6370:or a
4019:With
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2304:, is
1679:, or
1655:, or
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1535:geoid
1488:≈ 289
1351:North
1259:geoid
1080:polar
997:Earth
836:SAD69
816:SK-42
631:Geoid
221:Value
8618:(pc)
8612:(ly)
8606:(Tm)
8600:(au)
8594:(Gm)
8575:(ls)
8375:2010
8362:ISBN
8339:ISBN
8286:ISBN
8167:2017
8133:ISBN
8109:NASA
8088:2017
7944:ISBN
7912:ISBN
7880:2023
7805:2023
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7469:and
7292:and
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1145:, a
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4421:N
4409:2
4397:+
4391:M
4379:2
4366:1
4361:=
4355:c
4350:R
4332:φ
4328:α
4284:r
4264:r
4261:d
4258:+
4255:r
4229:.
4222:2
4214:1
4209:=
4204:2
4200:R
4175:1
4167:1
4162:=
4157:1
4153:R
4126:,
4120:E
4117:e
4112:=
4107:2
4080:G
4077:g
4072:=
4067:1
4039:0
4036:=
4033:f
4030:=
4027:F
4004:r
3970:r
3947:r
3938:=
3935:N
3901:r
3864:r
3838:r
3814:|
3810:N
3806:|
3801:N
3796:=
3793:n
3771:,
3767:]
3760:g
3755:f
3748:f
3743:e
3736:[
3732:=
3724:j
3720:w
3711:i
3707:w
3692:r
3686:2
3669:n
3655:=
3650:j
3647:i
3643:b
3639:=
3636:B
3610:,
3605:2
3597:d
3593:g
3590:+
3584:d
3577:d
3573:f
3570:2
3567:+
3562:2
3554:d
3550:e
3547:=
3542:j
3538:w
3534:d
3529:i
3525:w
3521:d
3516:j
3513:i
3509:b
3503:j
3500:i
3492:=
3489:D
3486:2
3457:,
3451:=
3446:2
3442:w
3418:=
3413:1
3409:w
3386:T
3382:]
3378:z
3375:,
3372:y
3369:,
3366:x
3363:[
3360:=
3355:T
3351:]
3345:3
3341:r
3337:,
3332:2
3328:r
3324:,
3319:1
3315:r
3311:[
3308:=
3305:r
3283:,
3279:]
3272:G
3267:F
3260:F
3255:E
3248:[
3244:=
3236:j
3232:w
3217:r
3202:i
3198:w
3183:r
3163:=
3158:j
3155:i
3151:a
3147:=
3144:A
3114:,
3109:2
3101:d
3097:G
3094:+
3088:d
3081:d
3077:F
3074:2
3071:+
3066:2
3058:d
3054:E
3051:=
3046:j
3042:w
3038:d
3033:i
3029:w
3025:d
3020:j
3017:i
3013:a
3007:j
3004:i
2996:=
2991:2
2987:s
2983:d
2953:,
2950:)
2947:B
2937:A
2934:(
2928:=
2925:0
2922:=
2919:)
2914:2
2910:f
2903:g
2900:e
2897:(
2894:+
2887:)
2884:F
2881:f
2878:2
2872:E
2869:g
2866:+
2863:G
2860:e
2857:(
2849:2
2840:)
2835:2
2831:F
2824:G
2821:E
2818:(
2782:=
2772:b
2768:/
2764:a
2758:=
2756:p
2753:N
2751:=
2749:p
2746:M
2730:a
2726:e
2723:N
2708:=
2698:a
2694:/
2690:b
2684:=
2682:e
2679:M
2645:)
2639:(
2630:N
2627:=
2624:p
2606:N
2590:.
2575:2
2565:2
2561:e
2554:1
2550:a
2545:=
2537:2
2533:)
2520:b
2517:(
2514:+
2509:2
2505:)
2492:a
2489:(
2483:2
2479:a
2473:=
2470:)
2464:(
2461:N
2448:φ
2444:M
2419:.
2407:)
2404:Z
2400:,
2397:Y
2393:,
2390:X
2387:(
2384:=
2381:R
2361:)
2355:(
2352:N
2347:2
2343:e
2321:)
2315:(
2312:N
2264:e
2241:.
2235:3
2231:)
2224:(
2221:N
2214:2
2210:a
2203:2
2199:e
2192:1
2186:=
2177:2
2174:3
2169:)
2157:2
2147:2
2143:e
2136:1
2133:(
2128:)
2123:2
2119:e
2112:1
2109:(
2106:a
2100:=
2091:2
2088:3
2081:)
2073:2
2069:)
2056:b
2053:(
2050:+
2045:2
2041:)
2028:a
2025:(
2020:(
2011:2
2007:)
2003:b
2000:a
1997:(
1991:=
1988:)
1982:(
1979:M
1966:φ
1912:b
1908:a
1891:,
1882:2
1878:)
1865:b
1862:(
1859:+
1854:2
1850:)
1837:a
1834:(
1827:2
1823:)
1808:2
1804:b
1800:(
1797:+
1792:2
1788:)
1773:2
1769:a
1765:(
1758:=
1755:)
1749:(
1746:R
1733:φ
1721:.
1706:N
1702:M
1698:R
1677:b
1667:.
1653:a
1506:f
1502:/
1499:1
1482:q
1478:/
1475:1
1467:M
1459:G
1451:ω
1434:,
1427:M
1424:G
1417:2
1407:3
1403:a
1396:=
1393:q
1380:q
1369:b
1362:a
1209:.
1118:N
1111:E
1104:R
1065:3
1062:R
1054:2
1051:R
1043:1
1040:R
1038:(
1025:b
1017:a
993:E
990:R
983:R
967:e
960:t
953:v
647:)
639:(
521:×
476:N
469:E
462:R
427:N
420:E
416:p
410:R
384:N
377:E
373:e
367:R
341:N
334:E
327:R
257:)
251:6
247:b
234:6
230:a
202:L
166:m
141:E
139:p
135:R
131:E
129:e
125:R
121:E
118:b
114:E
111:a
107:b
103:a
99:E
96:R
89:R
61:b
57:a
35:.
20:)
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