184:
1036:
709:
161:
64:
25:
1737:
Le nombre adopté dans le
Service international des Poids et Mesures pour la valeur de l'accélération normale de la pesanteur est 980,665 cm/sec², nombre sanctionné déjà par quelques législations. Déclaration relative à l'unité de masse et à la définition du poids; valeur conventionnelle de
963:
contributes to the total gravity acceleration, but other factors, such as the rotation of Earth, also contribute, and, therefore, affect the weight of the object. Gravity does not normally include the gravitational pull of the Moon and Sun, which are accounted for in terms of
1096:
As mean sea level is physically realized by tide gauge bench marks on the coasts of different countries and continents, a number of slightly incompatible "near-geoids" will result, with differences of several decimetres to over one metre between them, due to the
1088:
The geoid, or mathematical mean sea surface, is defined not only on the seas, but also under land; it is the equilibrium water surface that would result, would sea water be allowed to move freely (e.g., through tunnels) under the land. Technically, an
679:
Potential is expressed as gravity times distance, m·s. Travelling one metre in the direction of a gravity vector of strength 1 m·s will increase your potential by 1 m·s. Again employing G as a multiplier, the units can be changed to
1268:
691:
change your potential by 1 GPU. Which again means that the difference in geopotential, in GPU, of a point with that of sea level can be used as a rough measure of height "above sea level" in metres.
1020:
of the geopotential, without the negation. In addition to the actual potential (the geopotential), a theoretical normal potential and their difference, the disturbing potential, can also be defined.
687:
A more convenient unit is the GPU, or geopotential unit: it equals 10 m·s. This means that travelling one metre in the vertical direction, i.e., the direction of the 9.8 m·s ambient gravity, will
1468:
814:
1707:§ 2.1: "The total force acting on a body at rest on the earth's surface is the resultant of gravitational force and the centrifugal force of the earth's rotation and is called gravity."
1392:
1314:
1212:
1508:
1055:, the geoid—mathematical mean sea level—sticks out as much as 100 m above the regular, rotationally symmetric reference ellipsoid of GRS80; in other places, like close to
1531:
1171:
1083:
1651:
164:
Ocean basins mapped gravitationally. Seafloor features larger than 10 km are detected by resulting gravitational distortion of sea surface. (1995,
635:
angles) are obtained with respect to this local vertical, and horizontal angles in the plane of the local horizon, perpendicular to the vertical.
543:
1717:
365:
533:
501:
1059:, it dives under the ellipsoid by nearly the same amount. The separation between the geoid and the reference ellipsoid is called the
645:
differences between points on the Earth's surface. These can then be expressed as "height" differences by conversion to metric units.
511:
1270:. (This is an oversimplification; in practice the location in space at which Îł is evaluated will differ slightly from that where
724:. Red shows the areas where gravity is stronger than the smooth, standard value, and blue reveals areas where gravity is weaker (
713:
1217:
859:
will increase by about 9.8 metres per second (32 ft/s) every second. This quantity is sometimes referred to informally as
128:
1700:
927:
491:
100:
1407:
471:
107:
272:
571:
147:
81:
781:
1816:
Springer-Verlag Wien, 2005. (This text is an updated edition of the 1967 classic by W.A. Heiskanen and H. Moritz).
114:
907:(though this sometimes means the normal gravity at the equator, 9.7803267715 m/s (32.087686258 ft/s)),
1098:
725:
357:
85:
43:
1666:
820:
373:
96:
1348:
1280:
1720:(1901). "Déclaration relative à l'unité de masse et à la définition du poids; valeur conventionnelle de
1553:
1047:
Due to the irregularity of the Earth's true gravity field, the equilibrium figure of sea water, or the
960:
1176:
336:
1563:
1480:
824:
303:
250:
1730:
1061:
441:
401:
74:
1130:
867:
662:
421:
1513:
1153:
121:
889:
is 9.80665 m/s (32.1740 ft/s) by definition. This quantity is denoted variously as
564:
481:
231:
381:
331:
257:
1760:
8:
1844:
1839:
1588:
844:
764:
717:
293:
241:
883:
The precise strength of Earth's gravity varies with location. The agreed upon value for
1782:
1765:
1598:
1541:
1118:
1068:
616:
588:
213:
183:
1786:
1696:
1603:
1398:
843:(N/kg or N·kg). Near Earth's surface, the acceleration due to gravity, accurate to 2
760:
752:
313:
298:
33:
1732:
Comptes Rendus des Séances de la Troisième Conférence· Générale des Poids et
Mesures
1624:
1834:
1829:
1774:
1573:
1320:
1005:
885:
768:
733:
701:
557:
308:
1622:
1474:
1142:
1110:
1035:
721:
926:
of an object on Earth's surface is the downwards force on that object, given by
1558:
1103:
1093:
of the true geopotential, chosen to coincide (on average) with mean sea level.
1013:
848:
776:
521:
288:
262:
1823:
1593:
1335:
997:
836:
708:
669:
611:
rely on the gravity field for orienting their vertical axis along the local
985:
979:
847:, is 9.8 m/s (32 ft/s). This means that, ignoring the effects of
744:
642:
620:
592:
246:
1778:
1716:
1540:
the local terrain height value but apply a further correction called the
748:
203:
1173:. These are computed as the differences between true (observed) gravity
1578:
1568:
1327:
1122:
612:
608:
1330:, these anomalies are often further reduced by removing from them the
1536:
In case the terrain is not a flat plate (the usual case!) we use for
1056:
989:
856:
772:
741:
638:
632:
282:
208:
160:
63:
1017:
840:
673:
461:
278:
267:
1052:
596:
341:
198:
175:
38:
1583:
1051:, will also be of irregular form. In some places, like west of
923:
832:
658:
628:
451:
411:
349:
1048:
1040:
1030:
993:
852:
828:
756:
681:
654:
624:
236:
16:
Study of the physical properties of the Earth's gravity field
1323:, and are the ones to be used in the above Stokes equation.
1117:
For every point on Earth, the local direction of gravity or
1039:
Map of the undulation of the geoid in meters (based on the
1009:
965:
538:
431:
165:
747:
that is imparted to objects due to the combined effect of
1263:{\displaystyle \gamma =\|{\vec {\gamma }}\|=\|\nabla U\|}
661:
squared). This also can be expressed (multiplying by the
1623:
NASA/JPL/University of Texas Center for Space
Research.
1690:
1643:
1516:
1483:
1410:
1351:
1283:
1220:
1179:
1156:
1071:
784:
1463:{\displaystyle \Delta g_{B}=\Delta g_{FA}-a_{B},\,}
920:(which is also used for the variable local value).
88:. Unsourced material may be challenged and removed.
1797:γe = 9.780 326 7715 m/s² normal gravity at equator
1735:(in French). Paris: Gauthier-Villars. p. 68.
1525:
1502:
1462:
1386:
1308:
1262:
1206:
1165:
1077:
808:
1665:. Arlington, Texas: S.A.W.E., Inc. Archived from
1821:
809:{\displaystyle g=\|{\mathit {\mathbf {g} }}\|}
653:Gravity is commonly measured in units of m·s (
1000:. For convenience it is often defined as the
720:of an idealized, smooth Earth, the so-called
565:
1257:
1248:
1242:
1227:
1201:
1186:
803:
791:
771:quantity, whose direction coincides with a
587:is the study of the physical properties of
32:It has been suggested that this article be
1691:Hofmann-Wellenhof, B.; Moritz, H. (2006).
1625:"PIA12146: GRACE Global Gravity Animation"
775:and strength or magnitude is given by the
572:
558:
539:Spatial Reference System Identifier (SRID)
534:International Terrestrial Reference System
1718:Bureau International des Poids et Mesures
1459:
1383:
1305:
607:Traditional geodetic instruments such as
148:Learn how and when to remove this message
1034:
707:
602:
159:
1649:
595:), with a view to their application in
1822:
1758:
1334:, which for a flat, horizontal plate (
1387:{\displaystyle a_{B}=2\pi G\rho H,\,}
1309:{\displaystyle \Delta g=g-\gamma .\,}
716:mission, showing deviations from the
641:instruments again are used to obtain
1812:B. Hofmann-Wellenhof and H. Moritz,
1136:
823:, this acceleration is expressed in
86:adding citations to reliable sources
57:
18:
972:
544:Universal Transverse Mercator (UTM)
506:European Terrestrial Ref. Sys. 1989
13:
1806:
1517:
1484:
1427:
1411:
1284:
1251:
1214:, and calculated (normal) gravity
1157:
416:Ordnance Survey Great Britain 1936
382:Discrete Global Grid and Geocoding
273:Horizontal position representation
14:
1856:
712:Earth's gravity measured by NASA
1761:"Geodetic Reference System 1980"
1631:. NASA Jet Propulsion Laboratory
1274:has been measured.) We thus get
1207:{\displaystyle g=\|{\vec {g}}\|}
978:This section is an excerpt from
797:
700:This section is an excerpt from
684:per kilogram of attracted mass.
332:Global Nav. Sat. Systems (GNSSs)
182:
62:
23:
496:N. American Vertical Datum 1988
73:needs additional citations for
1752:
1710:
1684:
1616:
1236:
1195:
1099:dynamic sea surface topography
526:Internet link to a point 2010
456:Geodetic Reference System 1980
374:Quasi-Zenith Sat. Sys. (QZSS)
1:
1609:
1503:{\displaystyle \Delta g_{FA}}
1147:Above we already made use of
928:Newton's second law of motion
668:in order to change units) as
591:and its potential field (the
516:Chinese obfuscated datum 2002
1332:attraction of the topography
466:Geographic point coord. 1983
7:
1654:Precise Measurement of Mass
1547:
1319:These anomalies are called
1101:. These are referred to as
835:or m·s) or equivalently in
426:Systema Koordinat 1942 goda
10:
1861:
1695:(2nd ed.). Springer.
1554:Deflection of the vertical
1401:to be applied as follows:
1140:
1028:
977:
961:Gravitational acceleration
699:
694:
631:angles or, alternatively,
486:World Geodetic System 1984
49:Proposed since March 2024.
1650:Boynton, Richard (2001).
825:metres per second squared
476:North American Datum 1983
446:South American Datum 1969
1564:Friedrich Robert Helmert
1533:, the free-air anomaly.
1526:{\displaystyle \Delta g}
1166:{\displaystyle \Delta g}
1121:, materialized with the
1024:
648:
337:Global Pos. System (GPS)
304:Spatial reference system
1759:Moritz, Helmut (2000).
1062:undulation of the geoid
623:. After that, vertical
1527:
1504:
1464:
1388:
1310:
1264:
1208:
1167:
1131:astrogeodetic leveling
1079:
1044:
868:gravitational constant
810:
729:
663:gravitational constant
169:
1779:10.1007/s001900050278
1528:
1505:
1465:
1389:
1311:
1265:
1209:
1168:
1091:equipotential surface
1080:
1038:
811:
711:
603:Measurement procedure
232:Geographical distance
163:
1514:
1481:
1408:
1349:
1281:
1218:
1177:
1154:
1069:
782:
406:Sea Level Datum 1929
258:Geodetic coordinates
82:improve this article
1672:on 27 February 2007
1663:Sawe Paper No. 3147
1589:Mikhail Molodenskii
1016:is obtained as the
845:significant figures
718:theoretical gravity
676:of attracted mass.
436:European Datum 1950
394:Standards (history)
294:Reference ellipsoid
242:Figure of the Earth
1766:Journal of Geodesy
1599:Orthometric height
1542:terrain correction
1523:
1500:
1460:
1384:
1321:free-air anomalies
1306:
1260:
1204:
1163:
1129:to the geoid (see
1119:vertical direction
1075:
1045:
873:is referred to as
866:(in contrast, the
806:
730:
619:with the aid of a
617:vertical direction
314:Vertical positions
170:
97:"Physical geodesy"
1814:Physical Geodesy,
1702:978-3-211-33544-4
1604:Satellite geodesy
1475:Bouguer anomalies
1399:Bouguer reduction
1239:
1198:
1149:gravity anomalies
1137:Gravity anomalies
1078:{\displaystyle N}
761:centrifugal force
753:mass distribution
582:
581:
530:
529:
309:Spatial relations
299:Satellite geodesy
254:
158:
157:
150:
132:
56:
55:
51:
1852:
1800:
1799:
1794:
1793:
1756:
1750:
1749:
1746:
1728:
1714:
1708:
1706:
1693:Physical Geodesy
1688:
1682:
1681:
1679:
1677:
1671:
1660:
1647:
1641:
1640:
1638:
1636:
1620:
1574:Gravity of Earth
1532:
1530:
1529:
1524:
1509:
1507:
1506:
1501:
1499:
1498:
1469:
1467:
1466:
1461:
1455:
1454:
1442:
1441:
1423:
1422:
1393:
1391:
1390:
1385:
1361:
1360:
1315:
1313:
1312:
1307:
1269:
1267:
1266:
1261:
1241:
1240:
1232:
1213:
1211:
1210:
1205:
1200:
1199:
1191:
1172:
1170:
1169:
1164:
1084:
1082:
1081:
1076:
1006:potential energy
973:Potential fields
958:
944:
943:
919:
915:
906:
897:
888:
886:standard gravity
878:
872:
864:
815:
813:
812:
807:
802:
801:
800:
765:Earth's rotation
739:
734:gravity of Earth
726:Animated version
702:Gravity of Earth
585:Physical geodesy
574:
567:
560:
398:
397:
377:
369:
361:
353:
345:
285:
244:
186:
172:
171:
153:
146:
142:
139:
133:
131:
90:
66:
58:
47:
27:
26:
19:
1860:
1859:
1855:
1854:
1853:
1851:
1850:
1849:
1820:
1819:
1809:
1807:Further reading
1804:
1803:
1791:
1789:
1757:
1753:
1745:
1739:
1727:
1721:
1715:
1711:
1703:
1689:
1685:
1675:
1673:
1669:
1658:
1648:
1644:
1634:
1632:
1621:
1617:
1612:
1550:
1515:
1512:
1511:
1510:is our earlier
1491:
1487:
1482:
1479:
1478:
1450:
1446:
1434:
1430:
1418:
1414:
1409:
1406:
1405:
1356:
1352:
1350:
1347:
1346:
1338:) of thickness
1282:
1279:
1278:
1231:
1230:
1219:
1216:
1215:
1190:
1189:
1178:
1175:
1174:
1155:
1152:
1151:
1145:
1143:Gravity anomaly
1139:
1104:vertical datums
1070:
1067:
1066:
1033:
1027:
1022:
1021:
983:
975:
970:
969:
946:
932:
931:
917:
914:
908:
905:
899:
896:
890:
884:
876:
870:
862:
796:
795:
794:
783:
780:
779:
737:
722:Earth ellipsoid
705:
697:
651:
605:
589:Earth's gravity
578:
549:
548:
395:
387:
386:
375:
367:
359:
351:
343:
327:
319:
318:
277:
227:
219:
218:
194:
154:
143:
137:
134:
91:
89:
79:
67:
52:
28:
24:
17:
12:
11:
5:
1858:
1848:
1847:
1842:
1837:
1832:
1818:
1817:
1808:
1805:
1802:
1801:
1773:(1): 128–133.
1751:
1743:
1725:
1709:
1701:
1683:
1642:
1614:
1613:
1611:
1608:
1607:
1606:
1601:
1596:
1591:
1586:
1581:
1576:
1571:
1566:
1561:
1559:Dynamic height
1556:
1549:
1546:
1522:
1519:
1497:
1494:
1490:
1486:
1471:
1470:
1458:
1453:
1449:
1445:
1440:
1437:
1433:
1429:
1426:
1421:
1417:
1413:
1395:
1394:
1382:
1379:
1376:
1373:
1370:
1367:
1364:
1359:
1355:
1317:
1316:
1304:
1301:
1298:
1295:
1292:
1289:
1286:
1259:
1256:
1253:
1250:
1247:
1244:
1238:
1235:
1229:
1226:
1223:
1203:
1197:
1194:
1188:
1185:
1182:
1162:
1159:
1141:Main article:
1138:
1135:
1074:
1029:Main article:
1026:
1023:
1014:gravity vector
1012:, so that the
984:
976:
974:
971:
912:
903:
894:
857:falling freely
849:air resistance
805:
799:
793:
790:
787:
706:
698:
696:
693:
650:
647:
604:
601:
580:
579:
577:
576:
569:
562:
554:
551:
550:
547:
546:
541:
536:
528:
527:
524:
518:
517:
514:
508:
507:
504:
498:
497:
494:
488:
487:
484:
478:
477:
474:
468:
467:
464:
458:
457:
454:
448:
447:
444:
438:
437:
434:
428:
427:
424:
418:
417:
414:
408:
407:
404:
396:
393:
392:
389:
388:
385:
384:
379:
371:
363:
355:
347:
339:
334:
328:
325:
324:
321:
320:
317:
316:
311:
306:
301:
296:
291:
289:Map projection
286:
275:
270:
265:
263:Geodetic datum
260:
255:
239:
234:
228:
225:
224:
221:
220:
217:
216:
211:
206:
201:
195:
192:
191:
188:
187:
179:
178:
156:
155:
70:
68:
61:
54:
53:
31:
29:
22:
15:
9:
6:
4:
3:
2:
1857:
1846:
1843:
1841:
1838:
1836:
1833:
1831:
1828:
1827:
1825:
1815:
1811:
1810:
1798:
1788:
1784:
1780:
1776:
1772:
1768:
1767:
1762:
1755:
1748:
1742:
1734:
1733:
1724:
1719:
1713:
1704:
1698:
1694:
1687:
1668:
1664:
1657:
1655:
1646:
1630:
1626:
1619:
1615:
1605:
1602:
1600:
1597:
1595:
1594:Normal height
1592:
1590:
1587:
1585:
1582:
1580:
1577:
1575:
1572:
1570:
1567:
1565:
1562:
1560:
1557:
1555:
1552:
1551:
1545:
1543:
1539:
1534:
1520:
1495:
1492:
1488:
1476:
1456:
1451:
1447:
1443:
1438:
1435:
1431:
1424:
1419:
1415:
1404:
1403:
1402:
1400:
1380:
1377:
1374:
1371:
1368:
1365:
1362:
1357:
1353:
1345:
1344:
1343:
1341:
1337:
1336:Bouguer plate
1333:
1329:
1324:
1322:
1302:
1299:
1296:
1293:
1290:
1287:
1277:
1276:
1275:
1273:
1254:
1245:
1233:
1224:
1221:
1192:
1183:
1180:
1160:
1150:
1144:
1134:
1132:
1128:
1127:perpendicular
1124:
1120:
1115:
1113:
1112:
1106:
1105:
1100:
1094:
1092:
1086:
1072:
1064:
1063:
1058:
1054:
1050:
1042:
1037:
1032:
1019:
1015:
1011:
1007:
1003:
999:
998:gravity field
995:
991:
987:
981:
967:
966:tidal effects
962:
957:
953:
949:
942:
939:
935:
929:
925:
921:
911:
902:
893:
887:
881:
879:
869:
865:
858:
855:of an object
854:
850:
846:
842:
838:
834:
830:
827:(in symbols,
826:
822:
817:
788:
785:
778:
774:
770:
766:
762:
758:
754:
750:
746:
743:
736:, denoted by
735:
727:
723:
719:
715:
710:
703:
692:
690:
689:approximately
685:
683:
677:
675:
671:
667:
664:
660:
656:
646:
644:
640:
636:
634:
630:
626:
622:
618:
614:
610:
600:
598:
594:
590:
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1674:. Retrieved
1667:the original
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1629:Photojournal
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326:Technologies
281: /
193:Fundamentals
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138:October 2021
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80:Please help
75:verification
72:
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1676:22 December
1635:30 December
767:). It is a
749:gravitation
609:theodolites
204:Geodynamics
1845:Gravimetry
1840:Geophysics
1824:Categories
1792:2023-07-26
1610:References
1579:Gravimetry
1569:Geophysics
1473:so-called
1328:geophysics
1123:plumb line
763:(from the
759:) and the
613:plumb line
108:newspapers
1787:195290884
1518:Δ
1485:Δ
1444:−
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1300:γ
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1258:‖
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1065:, symbol
1057:Sri Lanka
1008:per unit
990:potential
804:‖
792:‖
773:plumb bob
740:, is the
639:Levelling
633:elevation
615:or local
283:Longitude
209:Geomatics
1548:See also
1477:. Here,
1018:gradient
1002:negative
841:kilogram
821:SI units
674:kilogram
462:ISO 6709
360:(Europe)
358:Galileo
344:(Russia)
342:GLONASS
279:Latitude
268:Geodesic
226:Concepts
1835:Gravity
1830:Geodesy
1109:height
1053:Ireland
1004:of the
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988:is the
861:little
837:newtons
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695:Gravity
670:newtons
597:geodesy
522:Geo URI
492:NAVD 88
402:NGVD 29
376:(Japan)
368:(India)
352:(China)
214:History
199:Geodesy
176:Geodesy
122:scholar
44:Discuss
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1584:LAGEOS
1111:datums
924:weight
851:, the
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751:(from
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659:second
655:metres
629:zenith
625:angles
512:GCJ-02
502:ETRS89
482:WGS 84
472:NAD 83
452:GRS 80
412:OSGB36
366:NAVIC
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1783:S2CID
1670:(PDF)
1659:(PDF)
1125:, is
1049:geoid
1041:EGM96
1031:Geoid
1025:Geoid
994:Earth
948:force
930:, or
853:speed
757:Earth
714:GRACE
649:Units
442:SAD69
422:SK-42
237:Geoid
129:JSTOR
115:books
36:into
1697:ISBN
1678:2023
1637:2013
1397:The
1010:mass
952:mass
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875:big
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777:norm
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1775:doi
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