175:
554:, ran slower than their exact counterparts in Paris. Measurements of the acceleration due to gravity at the equator must also take into account the planet's rotation. Any object that is stationary with respect to the surface of the Earth is actually following a circular trajectory, circumnavigating the Earth's axis. Pulling an object into such a circular trajectory requires a force. The acceleration that is required to circumnavigate the Earth's axis along the equator at one revolution per
43:
217:
of the equatorial diameter. If Earth were scaled down to a globe with an equatorial diameter of 1 metre (3.3 ft), that difference would be only 3 mm (0.12 in). While too small to notice visually, that difference is still more than twice the largest deviations of the actual surface from
477:
As long as there is no equilibrium there can be violent convection, and as long as there is violent convection friction can convert kinetic energy to heat, draining rotational kinetic energy from the system. When the equilibrium state has been reached then large scale conversion of kinetic energy to
562:
At the poles, the gravitational acceleration is 9.8322 m/s. The difference of 0.0178 m/s between the gravitational acceleration at the poles and the true gravitational acceleration at the
Equator is because objects located on the Equator are about 21 km (13 mi) further away from
481:
The Earth's rotation rate is still slowing down, though gradually, by about two thousandths of a second per rotation every 100 years. Estimates of how fast the Earth was rotating in the past vary, because it is not known exactly how the moon was formed. Estimates of the Earth's rotation 500 million
570:
In summary, there are two contributions to the fact that the effective gravitational acceleration is less strong at the equator than at the poles. About 70% of the difference is contributed by the fact that objects circumnavigate the Earth's axis, and about 30% is due to the non-spherical shape of
473:
on contraction keeps driving the increase in rotational kinetic energy. As the contraction proceeds, the rotation rate keeps going up, hence the required force for further contraction keeps going up. There is a point where the increase of rotational kinetic energy on further contraction would be
1265:
807:
418:
Fixed to the vertical rod is a spring metal band. When stationary the spring metal band is circular in shape. The top of the metal band can slide along the vertical rod. When spun, the spring-metal band bulges at its equator and flattens at its poles in analogy with the
558:
is 0.0339 m/s. Providing this acceleration decreases the effective gravitational acceleration. At the
Equator, the effective gravitational acceleration is 9.7805 m/s. This means that the true gravitational acceleration at the Equator must be 9.8144 m/s
465:
Something analogous to this occurs in planet formation. Matter first coalesces into a slowly rotating disk-shaped distribution, and collisions and friction convert kinetic energy to heat, which allows the disk to self-gravitate into a very oblate spheroid.
667:
1145:
453:
A way for one to get a feel for the type of equilibrium involved is to imagine someone seated in a spinning swivel chair and holding a weight in each hand; if the individual pulls the weights inward towards them,
259:, therefore, is 21 km (13 mi) closer to Earth's center than if standing at sea level on the Equator. As a result, the highest point on Earth, measured from the center and outwards, is the peak of Mount
663:
for the equilibrium configuration of a self-gravitating spheroid, composed of uniform density incompressible fluid, rotating steadily about some fixed axis, for a small amount of flattening, is approximated by:
574:
The diagram illustrates that on all latitudes the effective gravitational acceleration is decreased by the requirement of providing a centripetal force; the decreasing effect is strongest on the
Equator.
1120:
981:
918:
504:
415:
1043:
625:
Such perturbations, which were earlier used to map the Earth's gravitational field from space, may play a relevant disturbing role when satellites are used to make tests of
1069:
1003:
858:
832:
661:
207:
has a rather slight equatorial bulge; its equatorial diameter is about 43 km (27 mi) greater than its polar diameter, with a difference of about
1724:
Renzetti, G. (2014). "Satellite orbital precessions caused by the first odd zonal J3 multipole of a non-spherical body arbitrarily oriented in space".
458:
is being done and their rotational kinetic energy increases. The increase in rotation rate is so strong that at the faster rotation rate the required
485:
The Earth's rate of rotation is slowing down mainly because of tidal interactions with the Moon and the Sun. Since the solid parts of the Earth are
1679:
Renzetti, G. (2013). "Satellite
Orbital Precessions Caused by the Octupolar Mass Moment of a Non-Spherical Body Arbitrarily Oriented in Space".
1260:{\displaystyle J_{2}={\frac {2\varepsilon _{\mathrm {E} }}{3}}-{\frac {{R_{\mathrm {E} }}^{3}{\omega _{\mathrm {E} }}^{2}}{3GM_{\mathrm {E} }}}}
275:, Chimborazo is not as high above sea level as Everest is. Similarly the lowest point on Earth, measured from the center and outwards, is the
519:
The resultant force provides required centripetal force. Without this centripetal force frictionless objects would slide towards the equator.
591:
orbital precessions. They depend on the orientation of the Earth's symmetry axis in the inertial space, and, in the general case, affect
474:
larger than the release of gravitational potential energy. The contraction process can only proceed up to that point, so it halts there.
17:
244:. This surface coincides with the mean water surface level in oceans, and is extrapolated over land by taking into account the local
291:. But since the ocean also flattens, like Earth and its atmosphere, Litke Deep is not as low below sea level as Challenger Deep is.
1624:
Iorio, L. (2011). "Perturbed stellar motions around the rotating black hole in Sgr A* for a generic orientation of its spin axis".
802:{\displaystyle f={\frac {a_{e}-a_{p}}{a}}={\frac {5}{4}}{\frac {\omega ^{2}a^{3}}{GM}}={\frac {15\pi }{4}}{\frac {1}{GT^{2}\rho }}}
1929:
107:
583:
The fact that the Earth's gravitational field slightly deviates from being spherically symmetrical also affects the orbits of
1681:
79:
1074:
629:
because the much smaller relativistic effects are qualitatively indistinguishable from the oblateness-driven disturbances.
219:
923:
865:
86:
1855:
Renzetti, G. (2012). "Are higher degree even zonals really harmful for the LARES/LAGEOS frame-dragging experiment?".
126:
60:
409:
1597:
93:
1567:
1008:
608:
522:
In calculations, when a coordinate system is used that is co-rotating with the Earth, the vector of the notional
1726:
64:
75:
438:(sometimes called ellipticity or oblateness), which can depend on a variety of factors including the size,
160:
1857:
531:
489:, the Earth's equatorial bulge has been decreasing in step with the decrease in the rate of rotation.
478:
heat ceases. In that sense the equilibrium state is the lowest state of energy that can be reached.
1892:
53:
607:
axis of the coordinate system adopted is aligned along the Earth's symmetry axis, then only the
1562:
1380:
835:
612:
100:
311:
1739:
1866:
1827:
1784:
1735:
1690:
1645:
1577:
1054:
567:
of the Earth than at the poles, which corresponds to a smaller gravitational acceleration.
470:
447:
8:
1963:
1818:
1775:
1602:
498:
434:
causes a distortion from this spherical shape; a common measure of the distortion is the
272:
229:
198:
1870:
1831:
1788:
1694:
1649:
1406:
Real flattening is smaller due to mass concentration in the center of celestial bodies.
1840:
1813:
1797:
1771:"The Earth's Gravitational Potential, deduced from the Orbits of Artificial Satellites"
1770:
1751:
1706:
1661:
1635:
1572:
988:
843:
817:
646:
626:
1910:
526:
points outward, and is just as large as the vector representing the centripetal force.
1755:
1710:
1665:
1626:
588:
539:
523:
469:
As long as the proto-planet is still too oblate to be in equilibrium, the release of
459:
430:, the shape for which all the mass is as close to the center of gravity as possible.
256:
156:
507:
The forces at play in the case of a planet with an equatorial bulge due to rotation.
1958:
1953:
1874:
1835:
1792:
1743:
1698:
1653:
1046:
596:
439:
397:
295:
255:
is thus about 21 km (13 mi). An observer standing at sea level on either
245:
31:
174:
315:
284:
237:
194:
164:
1657:
600:
564:
543:
455:
223:
1747:
1702:
1947:
551:
547:
393:
288:
268:
1414:
1410:
616:
555:
512:
323:
280:
503:
414:
307:
188:
1321:
641:
435:
389:
276:
260:
1878:
584:
303:
233:
294:
More precisely, Earth's surface is usually approximated by an ideal
42:
431:
299:
241:
148:
1640:
1530:
1455:
535:
486:
443:
423:
264:
144:
1814:"Geophysical researches with the orbits of the first satellites"
1505:
1480:
427:
252:
168:
152:
204:
1598:"Fact or Fiction: The Days (and Nights) Are Getting Longer"
403:
27:
Outward bulge around a planet's equator due to its rotation
319:
530:
Because of a planet's rotation around its own axis, the
163:
about the body's axis. A rotating body tends to form an
492:
1085:
1019:
954:
896:
542:. In the 17th century, following the invention of the
1148:
1115:{\displaystyle M\simeq {\tfrac {4}{3}}\pi \rho a^{3}}
1077:
1057:
1011:
991:
926:
868:
846:
820:
670:
649:
976:{\displaystyle a_{p}\approx a\,(1-{\tfrac {2f}{3}})}
913:{\displaystyle a_{e}\approx a\,(1+{\tfrac {f}{3}})}
396:is much closer to this standard ellipsoid than the
67:. Unsourced material may be challenged and removed.
1259:
1114:
1063:
1037:
997:
975:
912:
852:
826:
801:
655:
360: mi) to either pole, meaning a difference of
271:. But since the ocean also bulges, like Earth and
983:are respectively the equatorial and polar radius,
178:Comparison between an oblate spheroid and sphere.
1945:
559:(9.7805 + 0.0339 = 9.8144).
482:years ago are around 20 modern hours per "day".
462:is larger than with the starting rotation rate.
410:Hydrostatic equilibrium § Planetary geology
388: mi) between the diameters, and a relative
310:, as well as the "center of the Earth". In the
30:For the feature on some of Saturn's moons, see
546:, French scientists found that clocks sent to
578:
298:, for the purposes of defining precisely the
1912:UCSD David T.Sandwell – Gravity field (2002)
1038:{\displaystyle \omega ={\tfrac {2\pi }{T}}}
426:tends to contract a celestial body into a
1839:
1811:
1796:
1768:
1639:
943:
885:
127:Learn how and when to remove this message
1854:
1723:
1678:
502:
413:
404:The equilibrium as a balance of energies
173:
14:
1946:
1682:Journal of Astrophysics and Astronomy
1623:
1357:is the central body's rotation rate (
1335:is central body's equatorial radius (
318:, widely used for map-making and the
493:Effect on gravitational acceleration
65:adding citations to reliable sources
36:
1595:
24:
1841:10.1111/j.1365-246X.1983.tb01868.x
1798:10.1111/j.1365-246X.1961.tb06801.x
1248:
1221:
1200:
1174:
236:, the imaginary surface used as a
25:
1975:
1401:
1126:A related quantity is the body's
1931:IERS – Geopotential model (2010)
1563:Astronomical object § Shape
1379:is the product of the universal
41:
1922:
609:longitude of the ascending node
516:Blue arrow: the resultant force
374: mi) between the radii or
52:needs additional citations for
1903:
1885:
1848:
1805:
1762:
1727:Astrophysics and Space Science
1717:
1672:
1617:
1589:
970:
944:
907:
886:
635:
471:gravitational potential energy
13:
1:
1583:
1383:and the central body's mass (
622:undergo secular precessions.
340: mi) to the Equator and
218:the ellipsoid, including the
1568:Clairaut's theorem (gravity)
143:is a difference between the
7:
1858:Canadian Journal of Physics
1556:
1005:is the rotation period and
550:, on the northern coast of
248:and the centrifugal force.
182:
10:
1980:
1658:10.1103/PhysRevD.84.124001
1128:second dynamic form factor
599:with the exception of the
579:Effect on satellite orbits
532:gravitational acceleration
496:
407:
192:
186:
29:
18:Second dynamic form factor
1812:King-Hele, D. G. (1983).
1769:King-Hele, D. G. (1961).
1748:10.1007/s10509-014-1915-x
1703:10.1007/s12036-013-9186-4
1071:is the body density and
392:of 1/298.257223563. The
1893:"Rotational Flattening"
1740:2014Ap&SS.352..493R
1381:constant of gravitation
1122:is the total body mass.
246:gravitational potential
1320:is the central body's
1261:
1116:
1065:
1039:
999:
977:
914:
854:
836:gravitational constant
828:
803:
657:
613:argument of pericenter
527:
420:
251:The difference of the
240:from which to measure
179:
1262:
1117:
1066:
1064:{\displaystyle \rho }
1040:
1000:
978:
915:
855:
829:
804:
658:
506:
417:
408:Further information:
193:Further information:
177:
1578:Planetary flattening
1146:
1075:
1055:
1009:
989:
924:
866:
844:
818:
668:
647:
61:improve this article
1871:2012CaJPh..90..883R
1832:1983GeoJ...74....7K
1819:Geophysical Journal
1789:1961GeoJ....4....3K
1776:Geophysical Journal
1695:2013JApA...34..341R
1650:2011PhRvD..84l4001I
1603:Scientific American
1417:
860:is the mean radius,
603:. If the reference
499:Theoretical gravity
199:Figure of the Earth
1409:
1257:
1112:
1094:
1061:
1035:
1033:
995:
973:
968:
910:
905:
850:
824:
799:
653:
627:general relativity
528:
509:Red arrow: gravity
421:
180:
76:"Equatorial bulge"
1879:10.1139/p2012-081
1627:Physical Review D
1554:
1553:
1255:
1184:
1093:
1032:
998:{\displaystyle T}
967:
904:
853:{\displaystyle a}
834:is the universal
827:{\displaystyle G}
797:
772:
754:
720:
707:
656:{\displaystyle f}
524:centrifugal force
511:Green arrow: the
460:centripetal force
326:is assumed to be
232:also affects the
220:tallest mountains
157:centrifugal force
137:
136:
129:
111:
16:(Redirected from
1971:
1939:
1938:
1936:
1926:
1920:
1919:
1917:
1907:
1901:
1900:
1889:
1883:
1882:
1852:
1846:
1845:
1843:
1809:
1803:
1802:
1800:
1766:
1760:
1759:
1721:
1715:
1714:
1676:
1670:
1669:
1643:
1621:
1615:
1614:
1612:
1610:
1593:
1418:
1408:
1396:
1394:
1391:
1388:
1378:
1367:
1365:
1362:
1356:
1345:
1343:
1340:
1334:
1319:
1307:
1305:
1303:
1300:
1297:
1285:
1284:
1266:
1264:
1263:
1258:
1256:
1254:
1253:
1252:
1251:
1234:
1233:
1232:
1227:
1226:
1225:
1224:
1212:
1211:
1206:
1205:
1204:
1203:
1190:
1185:
1180:
1179:
1178:
1177:
1163:
1158:
1157:
1138:
1121:
1119:
1118:
1113:
1111:
1110:
1095:
1086:
1070:
1068:
1067:
1062:
1047:angular velocity
1044:
1042:
1041:
1036:
1034:
1028:
1020:
1004:
1002:
1001:
996:
982:
980:
979:
974:
969:
963:
955:
936:
935:
919:
917:
916:
911:
906:
897:
878:
877:
859:
857:
856:
851:
833:
831:
830:
825:
808:
806:
805:
800:
798:
796:
792:
791:
775:
773:
768:
760:
755:
753:
745:
744:
743:
734:
733:
723:
721:
713:
708:
703:
702:
701:
689:
688:
678:
662:
660:
659:
654:
597:orbital elements
440:angular velocity
387:
386:
380:
379:
373:
372:
366:
365:
359:
358:
355:
349:
348:
345:
339:
338:
332:
331:
296:oblate ellipsoid
230:Earth's rotation
224:oceanic trenches
216:
215:
211:
141:equatorial bulge
132:
125:
121:
118:
112:
110:
69:
45:
37:
32:equatorial ridge
21:
1979:
1978:
1974:
1973:
1972:
1970:
1969:
1968:
1944:
1943:
1942:
1934:
1928:
1927:
1923:
1915:
1909:
1908:
1904:
1891:
1890:
1886:
1853:
1849:
1810:
1806:
1767:
1763:
1722:
1718:
1677:
1673:
1622:
1618:
1608:
1606:
1596:Hadhazy, Adam.
1594:
1590:
1586:
1573:Earth's gravity
1559:
1450:
1438:
1432:
1426:
1404:
1392:
1389:
1386:
1384:
1377:
1371:
1363:
1360:
1358:
1355:
1349:
1341:
1338:
1336:
1333:
1327:
1318:
1312:
1301:
1298:
1295:
1293:
1291:
1282:
1280:
1278:
1276:
1247:
1246:
1242:
1235:
1228:
1220:
1219:
1215:
1214:
1213:
1207:
1199:
1198:
1194:
1193:
1192:
1191:
1189:
1173:
1172:
1168:
1164:
1162:
1153:
1149:
1147:
1144:
1143:
1137:
1131:
1106:
1102:
1084:
1076:
1073:
1072:
1056:
1053:
1052:
1021:
1018:
1010:
1007:
1006:
990:
987:
986:
956:
953:
931:
927:
925:
922:
921:
895:
873:
869:
867:
864:
863:
845:
842:
841:
819:
816:
815:
787:
783:
779:
774:
761:
759:
746:
739:
735:
729:
725:
724:
722:
712:
697:
693:
684:
680:
679:
677:
669:
666:
665:
648:
645:
644:
638:
632:
581:
534:is less at the
521:
520:
518:
517:
515:
510:
508:
501:
495:
412:
406:
384:
382:
377:
375:
370:
368:
363:
361:
356:
353:
351:
346:
343:
341:
336:
334:
329:
327:
316:Earth ellipsoid
285:Challenger Deep
238:reference frame
213:
209:
208:
201:
195:Earth ellipsoid
191:
185:
165:oblate spheroid
159:exerted by the
133:
122:
116:
113:
70:
68:
58:
46:
35:
28:
23:
22:
15:
12:
11:
5:
1977:
1967:
1966:
1961:
1956:
1941:
1940:
1921:
1902:
1884:
1865:(9): 883–888.
1847:
1804:
1761:
1734:(2): 493–496.
1716:
1689:(4): 341–348.
1671:
1634:(12): 124001.
1616:
1587:
1585:
1582:
1581:
1580:
1575:
1570:
1565:
1558:
1555:
1552:
1551:
1548:
1545:
1542:
1539:
1536:
1533:
1527:
1526:
1523:
1520:
1517:
1514:
1511:
1508:
1502:
1501:
1498:
1495:
1492:
1489:
1486:
1483:
1477:
1476:
1473:
1470:
1467:
1464:
1461:
1458:
1452:
1451:
1448:
1445:
1442:
1439:
1436:
1433:
1430:
1427:
1424:
1421:
1403:
1402:Typical values
1400:
1399:
1398:
1375:
1369:
1353:
1347:
1331:
1325:
1316:
1289:
1274:
1268:
1267:
1250:
1245:
1241:
1238:
1231:
1223:
1218:
1210:
1202:
1197:
1188:
1183:
1176:
1171:
1167:
1161:
1156:
1152:
1135:
1124:
1123:
1109:
1105:
1101:
1098:
1092:
1089:
1083:
1080:
1060:
1050:
1031:
1027:
1024:
1017:
1014:
994:
984:
972:
966:
962:
959:
952:
949:
946:
942:
939:
934:
930:
909:
903:
900:
894:
891:
888:
884:
881:
876:
872:
861:
849:
839:
823:
795:
790:
786:
782:
778:
771:
767:
764:
758:
752:
749:
742:
738:
732:
728:
719:
716:
711:
706:
700:
696:
692:
687:
683:
676:
673:
652:
637:
634:
601:semimajor axis
595:the Keplerian
580:
577:
565:center of mass
544:pendulum clock
497:Main article:
494:
491:
405:
402:
324:Earth's radius
273:its atmosphere
187:Main article:
184:
181:
167:rather than a
135:
134:
49:
47:
40:
26:
9:
6:
4:
3:
2:
1976:
1965:
1962:
1960:
1957:
1955:
1952:
1951:
1949:
1933:
1932:
1925:
1914:
1913:
1906:
1898:
1894:
1888:
1880:
1876:
1872:
1868:
1864:
1860:
1859:
1851:
1842:
1837:
1833:
1829:
1825:
1821:
1820:
1815:
1808:
1799:
1794:
1790:
1786:
1782:
1778:
1777:
1772:
1765:
1757:
1753:
1749:
1745:
1741:
1737:
1733:
1729:
1728:
1720:
1712:
1708:
1704:
1700:
1696:
1692:
1688:
1684:
1683:
1675:
1667:
1663:
1659:
1655:
1651:
1647:
1642:
1637:
1633:
1629:
1628:
1620:
1605:
1604:
1599:
1592:
1588:
1579:
1576:
1574:
1571:
1569:
1566:
1564:
1561:
1560:
1549:
1546:
1543:
1540:
1537:
1534:
1532:
1529:
1528:
1524:
1521:
1518:
1515:
1512:
1509:
1507:
1504:
1503:
1499:
1496:
1493:
1490:
1487:
1484:
1482:
1479:
1478:
1474:
1471:
1468:
1465:
1462:
1459:
1457:
1454:
1453:
1446:
1443:
1440:
1434:
1428:
1422:
1420:
1419:
1416:
1412:
1411:Giant planets
1407:
1382:
1374:
1370:
1366:10 rad/s
1352:
1348:
1330:
1326:
1323:
1315:
1311:
1310:
1309:
1288:
1273:
1243:
1239:
1236:
1229:
1216:
1208:
1195:
1186:
1181:
1169:
1165:
1159:
1154:
1150:
1142:
1141:
1140:
1134:
1129:
1107:
1103:
1099:
1096:
1090:
1087:
1081:
1078:
1058:
1051:
1048:
1029:
1025:
1022:
1015:
1012:
992:
985:
964:
960:
957:
950:
947:
940:
937:
932:
928:
901:
898:
892:
889:
882:
879:
874:
870:
862:
847:
840:
837:
821:
814:
813:
812:
809:
793:
788:
784:
780:
776:
769:
765:
762:
756:
750:
747:
740:
736:
730:
726:
717:
714:
709:
704:
698:
694:
690:
685:
681:
674:
671:
650:
643:
633:
630:
628:
623:
621:
618:
614:
610:
606:
602:
598:
594:
590:
586:
576:
572:
568:
566:
560:
557:
553:
552:South America
549:
548:French Guiana
545:
541:
537:
533:
525:
514:
505:
500:
490:
488:
483:
479:
475:
472:
467:
463:
461:
457:
451:
449:
445:
441:
437:
433:
429:
425:
416:
411:
401:
400:of Earth is.
399:
398:solid surface
395:
394:ocean surface
391:
325:
321:
317:
313:
309:
305:
301:
297:
292:
290:
289:Pacific Ocean
286:
282:
278:
274:
270:
269:Mount Everest
266:
262:
258:
254:
249:
247:
243:
239:
235:
231:
227:
225:
221:
206:
200:
196:
190:
176:
172:
170:
166:
162:
158:
155:, due to the
154:
150:
146:
142:
131:
128:
120:
109:
106:
102:
99:
95:
92:
88:
85:
81:
78: –
77:
73:
72:Find sources:
66:
62:
56:
55:
50:This article
48:
44:
39:
38:
33:
19:
1930:
1924:
1911:
1905:
1896:
1887:
1862:
1856:
1850:
1823:
1817:
1807:
1780:
1774:
1764:
1731:
1725:
1719:
1686:
1680:
1674:
1631:
1625:
1619:
1607:. Retrieved
1601:
1591:
1415:Solar System
1405:
1372:
1350:
1328:
1313:
1286:
1271:
1269:
1132:
1127:
1125:
810:
639:
631:
624:
619:
617:mean anomaly
604:
592:
582:
573:
569:
561:
556:sidereal day
538:than at the
529:
513:normal force
484:
480:
476:
468:
464:
452:
422:
293:
283:rather than
281:Arctic Ocean
267:rather than
250:
228:
222:and deepest
202:
140:
138:
123:
114:
104:
97:
90:
83:
71:
59:Please help
54:verification
51:
1826:(1): 7–23.
1783:(1): 3–16.
1397:for Earth).
1395:10 m/s
1368:for Earth),
1346:for Earth),
636:Formulation
571:the Earth.
308:cartography
203:The planet
189:Earth radii
1964:Topography
1948:Categories
1897:utexas.edu
1609:5 December
1584:References
1322:oblateness
1306:for Earth,
642:flattening
615:ω and the
585:satellites
448:elasticity
436:flattening
390:flattening
381: km (
367: km (
350: km (
333: km (
277:Litke Deep
261:Chimborazo
147:and polar
145:equatorial
117:April 2023
87:newspapers
1756:119537102
1711:120030309
1666:118305813
1641:1107.2916
1217:ω
1187:−
1170:ε
1100:ρ
1097:π
1082:≃
1059:ρ
1026:π
1013:ω
951:−
938:≈
880:≈
794:ρ
766:π
727:ω
691:−
314:standard
306:grid for
304:longitude
242:altitudes
234:sea level
149:diameters
1557:See also
589:secular
587:through
432:Rotation
322:system,
300:latitude
183:On Earth
161:rotation
1959:Geodesy
1954:Planets
1867:Bibcode
1828:Bibcode
1785:Bibcode
1736:Bibcode
1691:Bibcode
1646:Bibcode
1531:Neptune
1456:Jupiter
1449:formula
1413:of the
1344: m
1308:where
1281:√
1045:is the
811:where
611:Ω, the
536:equator
487:ductile
444:density
424:Gravity
354:949.902
344:356.752
337:963.191
330:378.137
287:in the
279:in the
265:Ecuador
212:⁄
101:scholar
1754:
1709:
1664:
1550:0.032
1538:24,341
1535:24,764
1525:0.036
1513:24,973
1510:25,559
1506:Uranus
1500:0.178
1488:54,364
1485:60,268
1481:Saturn
1475:0.104
1463:66,854
1460:71,492
446:, and
428:sphere
419:Earth.
383:26.575
376:42.769
369:13.287
362:21.384
312:WGS-84
169:sphere
153:planet
103:
96:
89:
82:
74:
1935:(PDF)
1916:(PDF)
1752:S2CID
1707:S2CID
1662:S2CID
1636:arXiv
1541:0.017
1516:0.023
1491:0.108
1472:18.98
1466:0.066
1385:3.986
1359:7.292
1294:1.082
1270:with
540:poles
253:radii
205:Earth
151:of a
108:JSTOR
94:books
1611:2011
1547:1.02
1544:16.1
1522:0.87
1519:17.2
1497:5.68
1494:10.6
1437:real
920:and
640:The
563:the
456:work
385:6554
378:3716
371:8277
364:6858
357:7642
347:3142
302:and
257:pole
197:and
80:news
1875:doi
1836:doi
1793:doi
1744:doi
1732:352
1699:doi
1654:doi
1469:9.9
1390:418
1387:004
1361:115
1342:137
1339:378
1296:626
593:all
320:GPS
263:in
214:298
139:An
63:by
1950::
1895:.
1873:.
1863:90
1861:.
1834:.
1824:74
1822:.
1816:.
1791:.
1779:.
1773:.
1750:.
1742:.
1730:.
1705:.
1697:.
1687:34
1685:.
1660:.
1652:.
1644:.
1632:84
1630:.
1600:.
1444:M
1441:T
1373:GM
1304:10
1299:68
1290:20
1139::
1130:,
763:15
450:.
442:,
226:.
171:.
1937:.
1918:.
1899:.
1881:.
1877::
1869::
1844:.
1838::
1830::
1801:.
1795::
1787::
1781:4
1758:.
1746::
1738::
1713:.
1701::
1693::
1668:.
1656::
1648::
1638::
1613:.
1447:f
1435:f
1431:p
1429:a
1425:e
1423:a
1393:×
1376:E
1364:×
1354:E
1351:ω
1337:6
1332:E
1329:R
1324:,
1317:E
1314:ε
1302:×
1292:=
1287:C
1283:5
1279:−
1277:=
1275:2
1272:J
1249:E
1244:M
1240:G
1237:3
1230:2
1222:E
1209:3
1201:E
1196:R
1182:3
1175:E
1166:2
1160:=
1155:2
1151:J
1136:2
1133:J
1108:3
1104:a
1091:3
1088:4
1079:M
1049:,
1030:T
1023:2
1016:=
993:T
971:)
965:3
961:f
958:2
948:1
945:(
941:a
933:p
929:a
908:)
902:3
899:f
893:+
890:1
887:(
883:a
875:e
871:a
848:a
838:,
822:G
789:2
785:T
781:G
777:1
770:4
757:=
751:M
748:G
741:3
737:a
731:2
718:4
715:5
710:=
705:a
699:p
695:a
686:e
682:a
675:=
672:f
651:f
620:M
605:z
352:3
342:6
335:3
328:6
210:1
130:)
124:(
119:)
115:(
105:·
98:·
91:·
84:·
57:.
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
