1535:
1512:
51:
566:
641:
1364:
705:
693:
2308:
684:
of 6,371 km (3,959 mi). Regardless of the model, any radius falls between the polar minimum of about 6,357 km (3,950 mi) and the equatorial maximum of about 6,378 km (3,963 mi). The difference 21 km (13 mi) correspond to the polar radius being approximately 0.3% shorter than the equatorial radius.
1466:
closely approximating the size and shape of the Earth in the area of the survey. The actual measurements made on the surface of the Earth with certain instruments are however referred to the geoid. The ellipsoid is a mathematically defined regular surface with specific dimensions. The geoid, on the
1028:, which is simply the radius of the sphere. More complex surfaces have radii of curvature that vary over the surface. The radius of curvature describes the radius of the sphere that best approximates the surface at that point. Oblate ellipsoids have a constant radius of curvature east to west along
1020:
are used. In practice, many reference ellipsoids have been developed over the centuries from different surveys. The flattening value varies slightly from one reference ellipsoid to another, reflecting local conditions and whether the reference ellipsoid is intended to model the entire Earth or only
683:
The Earth is only approximately spherical, so no single value serves as its natural radius. Distances from points on the surface to the center range from 6,353 km (3,948 mi) to 6,384 km (3,967 mi). Several different ways of modeling the Earth as a sphere each yield a mean radius
664:
from Earth's center to its surface, about 6,371 km (3,959 mi). While "radius" normally is a characteristic of perfect spheres, the Earth deviates from spherical by only a third of a percent, sufficiently close to treat it as a sphere in many contexts and justifying the term "the radius of
1252:
The possibility that the Earth's equator is better characterized as an ellipse rather than a circle and therefore that the ellipsoid is triaxial has been a matter of scientific inquiry for many years. Modern technological developments have furnished new and rapid methods for data collection and,
1486:
everywhere and to which the direction of gravity is always perpendicular. The latter is particularly important because optical instruments containing gravity-reference leveling devices are commonly used to make geodetic measurements. When properly adjusted, the vertical axis of the instrument
1344:
refined the estimate to a 45 m (148 ft) difference between north and south polar radii, owing to a 19 m (62 ft) "stem" rising in the North Pole and a 26 m (85 ft) depression in the South Pole. The polar asymmetry is about a thousand times smaller than the Earth's
1457:
It was stated earlier that measurements are made on the apparent or topographic surface of the Earth and it has just been explained that computations are performed on an ellipsoid. One other surface is involved in geodetic measurement: the geoid. In geodetic surveying, the computation of the
1257:, orbital data have been used to investigate the theory of ellipticity. More recent results indicate a 70 m difference between the two equatorial major and minor axes of inertia, with the larger semidiameter pointing to 15° W longitude (and also 180-degree away).
600:. This funding also drove the expansion of geoscientific disciplines, fostering the creation and growth of various geoscience departments at many universities. These developments benefited many civilian pursuits as well, such as weather and communication
2217:
585:. Improved maps and better measurement of distances and areas of national territories motivated these early attempts. Surveying instrumentation and techniques improved over the ensuing centuries. Models for the figure of the Earth improved in step.
538:
to model the Earth as a close approximation. However, a more accurate figure is needed for measuring distances and areas on the scale beyond the purely local. Better approximations can be made by modeling the entire surface as an
1945:
Marchenko, A.N. (2009): Current estimation of the Earth’s mechanical and geometrical para meters. In
Sideris, M.G., ed. (2009): Observing our changing Earth. IAG Symp. Proceed. 133., pp. 473–481. DOI:10.1007/978-3-540-85426-5_57
966:
Eccentricity and flattening are different ways of expressing how squashed the ellipsoid is. When flattening appears as one of the defining quantities in geodesy, generally it is expressed by its reciprocal. For example, in the
822:
An ellipsoid of revolution is uniquely defined by two quantities. Several conventions for expressing the two quantities are used in geodesy, but they are all equivalent to and convertible with each other:
1601:, and others, a body having a uniform density of 5,515 kg/m that rotates like the Earth should have a flattening of 1:229. This can be concluded without any information about the composition of
1294:
in 1958. It was found to vary in its long periodic orbit, with the
Southern Hemisphere exhibiting higher gravitational attraction than the Northern Hemisphere. This indicated a flattening at the
1635:, which is the net effect of gravitation (due to mass attraction) and centrifugal force (due to rotation). It can be measured very accurately at the surface and remotely by satellites. True
1475:. As a result of the uneven distribution of the Earth's mass, the geoidal surface is irregular and, since the ellipsoid is a regular surface, the separations between the two, referred to as
592:
contributed to drastic improvements in the accuracy of the figure of the Earth. The primary utility of this improved accuracy was to provide geographical and gravitational data for the
1114:
1194:
1119:
because the pole is flattened: the flatter the surface, the larger the sphere must be to approximate it. Conversely, the ellipsoid's north–south radius of curvature at the equator
1425:
2414:
2383:
1491:
which is perpendicular to the geoid (sometimes called "the vertical") and the perpendicular to the ellipsoid (sometimes called "the ellipsoidal normal") is defined as the
616:
The models for the figure of the Earth vary in the way they are used, in their complexity, and in the accuracy with which they represent the size and shape of the Earth.
1467:
other hand, coincides with that surface to which the oceans would conform over the entire Earth if free to adjust to the combined effect of the Earth's mass attraction (
523:. While it is the surface on which Earth measurements are made, mathematically modeling it while taking the irregularities into account would be extremely complicated.
562:
surveys are made for relatively small areas without considering the size and shape of the entire Earth. A survey of a city, for example, might be conducted this way.
1452:
1144:
1061:
997:
1237:
1217:
960:
940:
918:
895:
869:
845:
2361:
31:
1012:
The difference between a sphere and a reference ellipsoid for Earth is small, only about one part in 300. Historically, flattening was computed from
410:
2427:
1998:
1310:
to be slightly flattened and the southern middle latitudes correspondingly bulged. Potential factors involved in this aberration include
232:
515:
surface is apparent with its variety of land forms and water areas. This topographic surface is generally the concern of topographers,
400:
368:
1763:
Cloud, John (2000). "Crossing the
Olentangy River: The Figure of the Earth and the Military-Industrial-Academic Complex, 1947–1972".
558:
For surveys of small areas, a planar (flat) model of Earth's surface suffices because the local topography overwhelms the curvature.
378:
1036:
is drawn on the surface, but varying curvature in any other direction. For an oblate ellipsoid, the polar radius of curvature
2046:
O’Keefe, J. A., Eckeis, A., and
Squires, R. K. (1959). "Vanguard Measurements Give Pear-Shaped Component of Earth’s Figure".
2008:
1967:
1817:
358:
534:
offers a simple surface that is easy to deal with mathematically. Many astronomical and navigational computations use a
338:
2141:
1025:
139:
577:
By the late 1600s, serious effort was devoted to modeling the Earth as an ellipsoid, beginning with French astronomer
438:
1271:
found that the length of a degree was apparently shorter north of Paris than to the south, implying the Earth to be
2391:
807:
shape that most nearly approximates the shape of the Earth. A spheroid describing the figure of the Earth or other
1325:
1562:
for the given point on the ellipsoid surface. This concept aids the interpretation of terrestrial and planetary
724:
1069:
652:
across the image, and the bases of the buildings on the far shore are below that horizon and hidden by the sea.
224:
1454:, respectively, corresponding to degree and order numbers 2.2 for the triaxiality and 3.0 for the pear shape.
1279:
dubiously suggested that the Earth was pear-shaped based on his disparate mobile readings of the angle of the
1152:
1487:
coincides with the direction of gravity and is, therefore, perpendicular to the geoid. The angle between the
1290:
The theory of a slightly pear-shaped Earth arose when data was received from the U.S.'s artificial satellite
240:
2156:
1708:
1033:
484:
1558:
direction. The center of the osculating sphere is offset from the center of the ellipsoid, but is at the
1315:
744:
680:
about 240 BC, with estimates of the accuracy of
Eratosthenes's measurement ranging from −1% to 15%.
1551:
608:
location-finding, which would be impossible without highly accurate models for the figure of the Earth.
1605:. However, the measured flattening is 1:298.25, which is closer to a sphere and a strong argument that
1534:
898:
1268:
727:
as that of Earth. For comparison, the light blue circle within has a diameter equal to the ellipse's
203:
2174:
2031:
1805:
1723:
1390:
1329:
968:
635:
593:
170:
117:
2424:
2165:
800:
308:
268:
1593:
Determining the exact figure of the Earth is not only a geometric task of geodesy, but also has
1542:
The best local spherical approximation to the ellipsoid in the vicinity of a given point is the
2401:
2169:
1809:
1799:
1606:
288:
1613:
must be a function of the depth, ranging from 2,600 kg/m at the surface (rock density of
1713:
1664:
1578:
1328:
and co-authors are credited with the discovery that the Earth had a significant third degree
1306:
increased about 9 m (30 ft) at the latter. This theory implies the northern middle
431:
348:
98:
1511:
1430:
2271:
2077:
1955:
1903:
1868:
1772:
1733:
1640:
1459:
1276:
1122:
1039:
248:
198:
124:
8:
2461:
2346:
1994:
1632:
1602:
1588:
1559:
1523:
1515:
1492:
1472:
1463:
1380:
1029:
974:
812:
762:
716:
552:
160:
2275:
2081:
1907:
1872:
1776:
2237:
2202:
2123:
2101:
1919:
1728:
1636:
1584:
1346:
1333:
1222:
1219:
is the distance from the center of the ellipsoid to the equator (semi-major axis), and
1202:
945:
925:
903:
880:
854:
830:
772:
544:
80:
50:
2166:
International Loran
Association (ILA) – 32nd Annual Convention and Technical Symposium
1784:
2287:
2283:
2256:
2241:
2093:
2004:
1973:
1963:
1923:
1813:
1563:
1545:
1341:
1337:
1017:
1013:
597:
464:
180:
165:
2436:
565:
2456:
2357:
2279:
2229:
2198:
2105:
2085:
2051:
1911:
1876:
1780:
1743:
1738:
1652:
1631:
Also with implications for the physical exploration of the Earth's interior is the
1626:
1476:
796:
780:
424:
175:
2431:
2233:
2055:
1674:
1555:
1363:
1319:
756:
748:
697:
625:
540:
531:
480:
468:
20:
2318:
2127:
1845:
2451:
2336:
2027:
1703:
1655:
and mantle can be determined by geodetic-geophysical models of the subsurface.
1598:
1284:
808:
673:
669:
582:
570:
527:
388:
155:
129:
1977:
656:
The simplest model for the shape of the entire Earth is a sphere. The Earth's
2445:
2379:
2312:
2291:
2097:
1483:
589:
1894:
Burša, Milan (1993). "Parameters of the Earth's tri-axial level ellipsoid".
1880:
704:
640:
1689:
1684:
768:
677:
631:
113:
1680:
803:
obtained by rotating an ellipse about its shorter axis. It is the regular
676:. The first scientific estimation of the radius of the Earth was given by
2331:
2068:
King-Hele, D. G.; Cook, G. E. (1973). "Refining the Earth's Pear Shape".
1594:
1468:
732:
578:
559:
516:
479:
and many other purposes. Several models with greater accuracy (including
70:
467:
depends on application, including the precision needed for the model. A
1915:
1718:
1651:
disturb the gravitational field. Therefore, the gross structure of the
1644:
1566:
1488:
1299:
1295:
1291:
1280:
971:
spheroid used by today's GPS systems, the reciprocal of the flattening
776:
728:
709:
520:
512:
488:
24:
2189:
Razin, Sheldon (Fall 1967). "Explicit (Noniterative) Loran
Solution".
2089:
1307:
1303:
1254:
804:
736:
601:
492:
476:
472:
149:
75:
1387:
figure: they are represented by the spherical harmonic coefficients
719:, with north at the top. The outer edge of the dark blue line is an
569:
Topographic view of Earth relative to Earth's center (instead of to
2367:
1569:
measurements and in some navigation and surveillance applications.
1495:. It has two components: an east–west and a north–south component.
792:
661:
500:
496:
328:
145:
134:
1479:, geoid heights, or geoid separations, will be irregular as well.
471:
is a well-known historical approximation that is satisfactory for
2373:
2311:
This article incorporates text from this source, which is in the
1614:
1610:
788:
784:
720:
692:
649:
452:
208:
65:
42:
1379:
Modern geodesy tends to retain the ellipsoid of revolution as a
1859:
Heiskanen, W. A. (1962). "Is the Earth a triaxial ellipsoid?".
1239:
is the distance from the center to the pole. (semi-minor axis)
672:, but remained a matter of philosophical speculation until the
657:
535:
318:
278:
216:
1597:
considerations. According to theoretical arguments by Newton,
1669:
1384:
1372:
1368:
1358:
740:
645:
548:
460:
103:
2351:
1367:
Map of the undulation of the geoid in meters (based on the
1311:
713:
405:
298:
668:
The concept of a spherical Earth dates back to around the
1272:
605:
1960:
Admiral of the Ocean Sea: A Life of
Christopher Columbus
1247:
2419:
1639:
generally does not correspond to theoretical vertical (
1617:, etc.), up to 13,000 kg/m within the inner core.
2316:
1843:
1572:
1383:
and treat triaxiality and pear shape as a part of the
588:
In the mid- to late 20th century, research across the
1433:
1393:
1283:, which he incorrectly interpreted as having varying
1225:
1205:
1155:
1125:
1072:
1042:
977:
948:
928:
906:
883:
857:
833:
2158:
On Loran-C Time-Difference to Co-ordinate
Converters
2003:(1st ed.). New York: W. W. Norton. p. 61.
1936:
Torge & Müller (2012) Geodesy, De
Gruyter, p.100
1620:
1526:
is appropriate for analysis across small distances.
1765:
Studies in History and Philosophy of Modern Physics
32:
Empirical evidence for the spherical shape of Earth
19:For the historical development of the concept, see
2254:
2191:Navigation: Journal of the Institute of Navigation
1962:. Boston: Little, Brown and Company. p. 557.
1446:
1419:
1336:using Vanguard 1 satellite data. Based on further
1231:
1211:
1188:
1138:
1108:
1055:
991:
954:
934:
912:
889:
863:
839:
16:Size and shape used to model the Earth for geodesy
2228:(1). Mathematical Association of America: 25–29.
2155:Williams, Paul; Last, David (3–7 November 2003).
1848:(Report) (4th ed.). United States Air Force.
815:. The reference ellipsoid for Earth is called an
700:, highly exaggerated relative to the actual Earth
2443:
2345:Determination of the European geoid by means of
2118:King-Hele, D. (1967). "The Shape of the Earth".
2000:Death By Black Hole: And Other Cosmic Quandaries
791:represents the figure of the Earth as an oblate
1482:The geoid is a surface along which the gravity
648:. The curvature of the Earth is evident in the
644:A view across a 20-km-wide bay in the coast of
1554:, and its radial direction coincides with the
2425:Changes in Earth shape due to climate changes
2067:
432:
2372:. Geowissenschaftliche Mitteilungen Band 5,
2264:Physics of the Earth and Planetary Interiors
2154:
1242:
581:'s measurement of a degree of arc along the
2255:Dziewonski, A. M.; Anderson, D. L. (1981),
1503:Simpler local approximations are possible.
1267:Following work by Picard, Italian polymath
459:is the size and shape used to model planet
2036:. New York: Harper & Row. p. 242.
687:
439:
425:
406:Spatial Reference System Identifier (SRID)
401:International Terrestrial Reference System
2173:
1858:
1109:{\displaystyle r_{p}={\frac {a^{2}}{b}},}
2148:
1533:
1510:
1362:
1189:{\displaystyle r_{e}={\frac {b^{2}}{a}}}
703:
691:
639:
564:
2218:"Euler and the Flattening of the Earth"
2026:
1954:
1498:
551:, or modeling a region with a best-fit
2444:
1506:
1298:and a bulge of the same degree at the
1248:Triaxiality (equatorial eccentricity)
2215:
2188:
2182:
2022:
2020:
1993:
1893:
1839:
1837:
1835:
1833:
1831:
1829:
1797:
1762:
1609:is extremely compact. Therefore, the
1462:of points is commonly performed on a
1345:flattening and even smaller than its
30:For effects of and evidence for, see
2437:Jos Leys "The shape of Planet Earth"
2415:Reference Ellipsoids (PCI Geomatics)
2370:/ Das isostatische Geoid 31. Ordnung
2248:
1989:
1987:
1552:Earth's Gaussian radius of curvature
1529:
1262:
739:, while the yellow band denotes the
2257:"Preliminary reference Earth model"
1573:Earth rotation and Earth's interior
1471:) and the centrifugal force of the
411:Universal Transverse Mercator (UTM)
373:European Terrestrial Ref. Sys. 1989
13:
2325:
2321:(Report). United States Air Force.
2203:10.1002/j.2161-4296.1967.tb02208.x
2017:
1826:
1801:Early Greek Astronomy to Aristotle
1016:. Nowadays, geodetic networks and
283:Ordnance Survey Great Britain 1936
249:Discrete Global Grid and Geocoding
140:Horizontal position representation
14:
2473:
2408:
1984:
1621:Global and regional gravity field
2306:
2076:(5428). Springer Nature: 86–88.
573:, as in common topographic maps)
199:Global Nav. Sat. Systems (GNSSs)
49:
2317:Defense Mapping Agency (1983).
2209:
2133:
2112:
2061:
2040:
1896:Studia Geophysica et Geodaetica
1861:Journal of Geophysical Research
1844:Defense Mapping Agency (1983).
1538:Ellipsoid and osculating sphere
735:100 km (62 mi) above
731:. The red curve represents the
487:can serve the precise needs of
363:N. American Vertical Datum 1988
1948:
1939:
1930:
1887:
1852:
1791:
1756:
1063:is larger than the equatorial
503:, and various other concerns.
483:) have been developed so that
393:Internet link to a point 2010
323:Geodetic Reference System 1980
241:Quasi-Zenith Sat. Sys. (QZSS)
1:
2420:Reference Ellipsoids (ScanEx)
1785:10.1016/S1355-2198(00)00017-4
1749:
1709:Earth's circumference#History
1420:{\displaystyle C_{22},S_{22}}
506:
383:Chinese obfuscated datum 2002
2284:10.1016/0031-9201(81)90046-7
2234:10.4169/mathhorizons.21.1.25
2056:10.1126/science.129.3348.565
333:Geographic point coord. 1983
7:
2394:, Wien & New York 2005.
1658:
293:Systema Koordinat 1942 goda
10:
2478:
2354:10th Gen. Ass., Rome 1954.
1643:ranges up to 50") because
1624:
1582:
1576:
1493:deflection of the vertical
1356:
1146:is smaller than the polar
795:. The oblate spheroid, or
760:
754:
629:
623:
353:World Geodetic System 1984
29:
18:
1269:Giovanni Domenico Cassini
1243:Non-spheroidal deviations
619:
611:
594:inertial guidance systems
343:North American Datum 1983
313:South American Datum 1969
1806:Cornell University Press
1724:Friedrich Robert Helmert
1352:
1330:zonal spherical harmonic
204:Global Pos. System (GPS)
171:Spatial reference system
2430:22 January 2009 at the
2340:, Oxford 1952 and 1980.
1881:10.1029/JZ067i001p00321
801:ellipsoid of revolution
708:A scale diagram of the
688:Ellipsoid of revolution
2402:Defense Mapping Agency
2398:Geodesy for the Layman
2319:Geodesy for the Layman
2216:Heine, George (2013).
2139:Günter Seeber (2008),
2050:, 129(3348), 565–566.
1846:Geodesy for the Layman
1714:Earth's radius#History
1539:
1519:
1448:
1447:{\displaystyle C_{30}}
1421:
1376:
1371:gravity model and the
1233:
1213:
1190:
1140:
1110:
1057:
1024:A sphere has a single
993:
956:
936:
914:
891:
865:
841:
752:
701:
653:
574:
2168:. Boulder, Colorado.
1956:Morison, Samuel Eliot
1583:Further information:
1537:
1514:
1449:
1422:
1375:reference ellipsoid).
1366:
1234:
1214:
1191:
1141:
1139:{\displaystyle r_{e}}
1111:
1058:
1056:{\displaystyle r_{p}}
999:is set to be exactly
994:
957:
937:
915:
892:
866:
842:
761:Further information:
707:
695:
643:
636:Earth's circumference
630:Further information:
568:
99:Geographical distance
2347:vertical deflections
2145:, Walter de Gruyter.
1995:Tyson, Neil deGrasse
1798:Dicks, D.R. (1970).
1739:Meridian arc#History
1734:History of the metre
1550:. Its radius equals
1499:Local approximations
1460:geodetic coordinates
1431:
1391:
1277:Christopher Columbus
1253:since the launch of
1223:
1203:
1153:
1123:
1070:
1040:
1021:some portion of it.
975:
946:
926:
904:
881:
855:
851:), and polar radius
831:
273:Sea Level Datum 1929
125:Geodetic coordinates
2362:Gottfried Gerstbach
2350:. Rpt of Comm. 14,
2276:1981PEPI...25..297D
2120:Scientific American
2082:1973Natur.246...86K
2033:Splendor in the Sky
1908:1993StGG...37....1B
1873:1962JGR....67..321H
1777:2000SHPMP..31..371C
1633:gravitational field
1589:Theoretical gravity
1560:center of curvature
1524:local tangent plane
1516:Local tangent plane
1507:Local tangent plane
1464:reference ellipsoid
1381:reference ellipsoid
1334:gravitational field
1026:radius of curvature
992:{\displaystyle 1/f}
813:reference ellipsoid
763:Reference ellipsoid
717:reference ellipsoid
553:reference ellipsoid
547:to approximate the
545:spherical harmonics
457:figure of the Earth
303:European Datum 1950
261:Standards (history)
161:Reference ellipsoid
109:Figure of the Earth
2404:, St. Louis, 1983.
2028:Hawkins, Gerald S.
1916:10.1007/BF01613918
1729:History of geodesy
1665:Clairaut's theorem
1585:Structure of Earth
1579:Clairaut's theorem
1540:
1520:
1484:potential is equal
1444:
1417:
1377:
1347:geoidal undulation
1275:-shaped. In 1498,
1229:
1209:
1186:
1136:
1106:
1053:
1014:grade measurements
989:
952:
932:
910:
887:
861:
837:
827:Equatorial radius
773:Christiaan Huygens
753:
702:
654:
598:ballistic missiles
575:
485:coordinate systems
181:Vertical positions
2142:Satellite Geodesy
2122:, 217(4), 67-80.
2010:978-0-393-11378-5
1969:978-0-316-58478-4
1819:978-0-8014-0561-7
1649:geological masses
1564:radio occultation
1530:Osculating sphere
1477:geoid undulations
1349:in some regions.
1342:Desmond King-Hele
1338:satellite geodesy
1263:Egg or pear shape
1232:{\displaystyle b}
1212:{\displaystyle a}
1184:
1101:
1018:satellite geodesy
955:{\displaystyle f}
935:{\displaystyle a}
913:{\displaystyle e}
890:{\displaystyle a}
864:{\displaystyle b}
840:{\displaystyle a}
779:at the poles and
449:
448:
397:
396:
176:Spatial relations
166:Satellite geodesy
121:
2469:
2388:Physical Geodesy
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723:with the same
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899:eccentricity
872:
848:
821:
816:
811:is called a
769:Isaac Newton
766:
725:eccentricity
712:of the 2003
682:
678:Eratosthenes
667:
665:the Earth".
655:
632:Earth radius
615:
604:control and
587:
576:
557:
525:
510:
456:
450:
193:Technologies
148: /
108:
60:Fundamentals
36:
2332:Guy Bomford
2302:Attribution
1902:(1): 1–13.
1808:. pp.
1595:geophysical
1469:gravitation
1302:, with the
733:Karman line
590:geosciences
579:Jean Picard
560:Plane-table
528:Pythagorean
513:topographic
71:Geodynamics
2462:Geophysics
2446:Categories
1978:1154365097
1750:References
1719:Flat Earth
1645:topography
1641:deflection
1567:refraction
1546:osculating
1489:plumb line
1316:subcrustal
1300:North Pole
1296:South Pole
1281:North Star
729:minor axis
710:oblateness
507:Motivation
489:navigation
25:Flat Earth
2368:Isostasie
2292:0031-9201
2242:126412032
2170:CiteSeerX
2098:0028-0836
2030:(1969) .
1958:(1991) .
1924:128674427
1685:Curvature
1308:latitudes
1304:sea level
1255:Sputnik 1
1034:graticule
1030:parallels
805:geometric
777:flattened
737:sea level
602:satellite
493:surveying
481:ellipsoid
477:astronomy
473:geography
150:Longitude
76:Geomatics
2428:Archived
2392:Springer
1997:(2007).
1681:Distance
1659:See also
1647:and all
1637:vertical
1544:Earth's
871:(called
847:(called
799:, is an
793:spheroid
787:. Thus,
741:altitude
662:distance
543:, using
511:Earth's
501:land use
497:cadastre
329:ISO 6709
227:(Europe)
225:Galileo
211:(Russia)
209:GLONASS
146:Latitude
135:Geodesic
93:Concepts
2457:Geodesy
2374:TU Wien
2337:Geodesy
2272:Bibcode
2106:4260099
2078:Bibcode
2048:Science
1904:Bibcode
1869:Bibcode
1773:Bibcode
1696:History
1615:granite
1611:density
1332:in its
1032:, if a
1001:298.257
789:geodesy
785:equator
783:at the
721:ellipse
660:is the
650:horizon
453:geodesy
389:Geo URI
359:NAVD 88
269:NGVD 29
243:(Japan)
235:(India)
219:(China)
81:History
66:Geodesy
43:Geodesy
2315::
2290:
2240:
2172:
2126:
2104:
2096:
2070:Nature
2007:
1976:
1966:
1922:
1816:
1810:72–198
1548:sphere
1340:data,
1199:where
969:WGS 84
781:bulged
658:radius
620:Sphere
612:Models
536:sphere
519:, and
465:figure
455:, the
379:GCJ-02
369:ETRS89
349:WGS 84
339:NAD 83
319:GRS 80
279:OSGB36
233:NAVIC
114:radius
2452:Earth
2376:1975.
2260:(PDF)
2238:S2CID
2162:(PDF)
2124:JSTOR
2102:S2CID
1920:S2CID
1670:EGM96
1385:geoid
1373:WGS84
1369:EGM96
1359:Geoid
1353:Geoid
1312:tides
646:Spain
549:geoid
461:Earth
309:SAD69
289:SK-42
104:Geoid
2382:and
2360:and
2352:IUGG
2288:ISSN
2094:ISSN
2005:ISBN
1974:OCLC
1964:ISBN
1814:ISBN
1587:and
1522:The
1427:and
1314:and
897:and
771:and
714:IERS
634:and
526:The
299:ED50
116:and
23:and
2280:doi
2230:doi
2199:doi
2086:doi
2074:246
2052:doi
1912:doi
1877:doi
1781:doi
1322:).
1273:egg
1006:563
1003:223
747:in
745:ISS
696:An
606:GPS
596:of
451:In
2448::
2400:,
2390:.
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2364:,
2334:,
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2224:.
2220:.
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2193:.
2164:.
2100:.
2092:.
2084:.
2072:.
2019:^
1986:^
1972:.
1918:.
1910:.
1900:37
1898:.
1875:.
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1863:.
1828:^
1812:.
1779:.
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1767:.
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1009:.
875:);
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2088::
2080::
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2054::
2013:.
1980:.
1926:.
1914::
1906::
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1879::
1871::
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1787:.
1783::
1775::
1518:.
1436:C
1409:S
1405:,
1396:C
1227:b
1207:a
1182:a
1177:2
1173:b
1167:=
1162:e
1158:r
1132:e
1128:r
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1099:b
1094:2
1090:a
1084:=
1079:p
1075:r
1049:p
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962:.
950:f
930:a
920:;
908:e
885:a
859:b
835:a
751:.
440:e
433:t
426:v
120:)
112:(
34:.
27:.
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