2538:
2102:
3940:
5049:
2533:{\displaystyle {\begin{aligned}g\{\phi \}&=9.780327\,\,\mathrm {m} \cdot \mathrm {s} ^{-2}\,\,\left(1+0.0053024\,\sin ^{2}\phi -0.0000058\,\sin ^{2}2\phi \right),\\&=9.780327\,\,\mathrm {m} \cdot \mathrm {s} ^{-2}\,\,\left(1+0.0052792\,\sin ^{2}\phi +0.0000232\,\sin ^{4}\phi \right),\\&=9.780327\,\,\mathrm {m} \cdot \mathrm {s} ^{-2}\,\,\left(1.0053024-0.0053256\,\cos ^{2}\phi +0.0000232\,\cos ^{4}\phi \right),\\&=9.780327\,\,\mathrm {m} \cdot \mathrm {s} ^{-2}\,\,\left(1.0026454-0.0026512\,\cos 2\phi +0.0000058\,\cos ^{2}2\phi \right)\end{aligned}}}
512:(itself also caused by centrifugal force from rotation) causes objects at the Equator to be further from the planet's center than objects at the poles. The force due to gravitational attraction between two masses (a piece of the Earth and the object being weighed) varies inversely with the square of the distance between them. The distribution of mass is also different below someone on the equator and below someone at a pole. The net result is that an object at the Equator experiences a weaker gravitational pull than an object on one of the poles.
533:
1280:
5301:
3875:
489:
1384:(9.776 m/s). The effect of altitude can be seen in Mexico City (9.776 m/s; altitude 2,240 metres (7,350 ft)), and by comparing Denver (9.798 m/s; 1,616 metres (5,302 ft)) with Washington, D.C. (9.801 m/s; 30 metres (98 ft)), both of which are near 39° N. Measured values can be obtained from Physical and Mathematical Tables by T.M. Yarwood and F. Castle, Macmillan, revised edition 1970.
5940:
5313:
5061:
121:
757:
745:
24:
3758:
5325:
5073:
1340:
737:
3518:
525:
760:
Earth's gravity according to the
Preliminary Reference Earth Model (PREM). Two models for a spherically symmetric Earth are included for comparison. The dark green straight line is for a constant density equal to the Earth's average density. The light green curved line is for a density that decreases
557:
Gravity decreases with altitude as one rises above the Earth's surface because greater altitude means greater distance from the Earth's centre. All other things being equal, an increase in altitude from sea level to 9,000 metres (30,000 ft) causes a weight decrease of about 0.29%. (An additional
515:
In combination, the equatorial bulge and the effects of the surface centrifugal force due to rotation mean that sea-level gravity increases from about 9.780 m/s at the
Equator to about 9.832 m/s at the poles, so an object will weigh approximately 0.5% more at the poles than at the Equator.
1383:
Tools exist for calculating the strength of gravity at various cities around the world. The effect of latitude can be clearly seen with gravity in high-latitude cities: Anchorage (9.826 m/s), Helsinki (9.825 m/s), being about 0.5% greater than that in cities near the equator: Kuala Lumpur
4682:
Tapley, Byron D.; Watkins, Michael M.; Flechtner, Frank; Reigber, Christoph; Bettadpur, Srinivas; Rodell, Matthew; Sasgen, Ingo; Famiglietti, James S.; Landerer, Felix W.; Chambers, Don P.; Reager, John T.; Gardner, Alex S.; Save, Himanshu; Ivins, Erik R.; Swenson, Sean C.; Boening, Carmen; Dahle,
471:
near Paris in 1888, with a theoretical correction applied in order to convert to a latitude of 45° at sea level. This definition is thus not a value of any particular place or carefully worked out average, but an agreement for a value to use if a better actual local value is not known or not
4170:
Le nombre adopté dans le
Service international des Poids et Mesures pour la valeur de l'accĂ©lĂ©ration normale de la pesanteur est 980,665 cm/secÂČ, nombre sanctionnĂ© dĂ©jĂ par quelques lĂ©gislations. DĂ©claration relative Ă l'unitĂ© de masse et Ă la dĂ©finition du poids; valeur conventionnelle de
380:
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
3763:
This formula only works because of the mathematical fact that the gravity of a uniform spherical body, as measured on or above its surface, is the same as if all its mass were concentrated at a point at its centre. This is what allows us to use the Earth's radius for
577:
section). A person flying at 9,100 m (30,000 ft) above sea level over mountains will feel more gravity than someone at the same elevation but over the sea. However, a person standing on the Earth's surface feels less gravity when the elevation is higher.
3753:{\displaystyle g=G{\frac {M_{\oplus }}{r^{2}}}=6.674\cdot 10^{-11}\mathrm {{m}^{3}\,{kg}^{-1}{s}^{-2}} \times {\frac {6\times 10^{24}\mathrm {kg} }{(6.4\times 10^{6}\mathrm {m} )^{2}}}=9+{\frac {795}{2^{10}}}\approx 9.77637\,\mathrm {{m}\,{s}^{-2}} }
1192:
1288:
There is a strong correlation between the gravity derivation map of earth from NASA GRACE with positions of recent volcanic activity, ridge spreading and volcanos: these regions have a stronger gravitation than theoretical predictions.
3327:
673:
2920:
561:
It is a common misconception that astronauts in orbit are weightless because they have flown high enough to escape the Earth's gravity. In fact, at an altitude of 400 kilometres (250 mi), equivalent to a typical orbit of the
504:
produced by Earth's rotation is larger than at polar latitudes. This counteracts the Earth's gravity to a small degree â up to a maximum of 0.3% at the
Equator â and reduces the apparent downward acceleration of falling objects.
2984:
3115:
1283:
A map of recent volcanic activity and ridge spreading. The areas where NASA GRACE measured gravity to be stronger than the theoretical gravity have a strong correlation with the positions of the volcanic activity and ridge
3796:
only includes true gravity. It does not include the reduction of constraint force that we perceive as a reduction of gravity due to the rotation of Earth, and some of gravity being counteracted by centrifugal
1301:
force which reduces the apparent strength of gravity (as measured by an object's weight). The magnitude of the effect depends on the air density (and hence air pressure) or the water density respectively; see
558:
factor affecting apparent weight is the decrease in air density at altitude, which lessens an object's buoyancy. This would increase a person's apparent weight at an altitude of 9,000 metres by about 0.08%)
2836:
2689:
2107:
3476:
959:
3193:
230:
3906:
853:
761:
linearly from center to surface. The density at the center is the same as in the PREM, but the surface density is chosen so that the mass of the sphere equals the mass of the real Earth.
4140:§ 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."
3157:
1072:
2784:
4412:
783:
of gravitation. Another consequence is that the gravity is the same as if all the mass were concentrated at the center. Thus, the gravitational acceleration at this radius is
4242:
Hirt, Christian; Claessens, Sten; Fecher, Thomas; Kuhn, Michael; Pail, Roland; Rexer, Moritz (August 28, 2013). "New ultrahigh-resolution picture of Earth's gravity field".
775:
from the center of the Earth can be obtained by assuming that the Earth's density is spherically symmetric. The gravity depends only on the mass inside the sphere of radius
3923:(GRACE) consisted of two satellites that detected gravitational changes across the Earth. Also these changes could be presented as gravity anomaly temporal variations. The
3361:
2074:
4607:
2722:
2094:
3420:
740:
Gravity at different internal layers of Earth (1 = continental crust, 2 = oceanic crust, 3 = upper mantle, 4 = lower mantle, 5+6 = core, A = crust-mantle boundary)
3227:
587:
2843:
4150:
501:
728:
The formula treats the Earth as a perfect sphere with a radially symmetric distribution of mass; a more accurate mathematical treatment is discussed below.
5910:
5111:
2929:
4084:
2992:
457:
4391:
1321:) have a very small effect on the apparent strength of Earth's gravity, depending on their relative positions; typical variations are 2 ÎŒm/s (0.2
1256:, the effect of topography and other known factors is subtracted, and from the resulting data conclusions are drawn. Such techniques are now used by
4837:
4026:
4376:
3920:
125:
4539:, revised edition, Macmillan and Co LTD, London and Basingstoke, Printed in Great Britain by The University Press, Glasgow, 1970, pp 22 & 23.
4570:
4319:
4133:
409:. The Earth is rotating and is also not spherically symmetric; rather, it is slightly flatter at the poles while bulging at the Equator: an
5915:
4551:
721:
4347:
4470:
3909:. These satellite missions aim at the recovery of a detailed gravity field model of the Earth, typically presented in the form of a
749:
107:
41:
4804:
1363:
is slightly flatter, there are consequently significant deviations in the direction of gravity: essentially the difference between
4809:
4631:
Meyer, Ulrich; Sosnica, Krzysztof; Arnold, Daniel; Dahle, Christoph; Thaller, Daniela; Dach, Rolf; JĂ€ggi, Adrian (22 April 2019).
566:, gravity is still nearly 90% as strong as at the Earth's surface. Weightlessness actually occurs because orbiting objects are in
4744:
SoĆnica, Krzysztof; JĂ€ggi, Adrian; Meyer, Ulrich; Thaller, Daniela; Beutler, Gerhard; Arnold, Daniel; Dach, Rolf (October 2015).
3882:
Currently, the static and time-variable Earth's gravity field parameters are determined using modern satellite missions, such as
136:. Red shows the areas where gravity is stronger than the smooth, standard value, and blue reveals areas where gravity is weaker (
5645:
5363:
5104:
2548:
275:
will increase by about 9.8 metres per second (32 ft/s) every second. This quantity is sometimes referred to informally as
88:
5964:
5474:
138:
60:
45:
1198:
2795:
2572:
2544:
236:
4830:
3218:
497:
67:
3927:(GRAIL) also consisted of two spacecraft orbiting the Moon, which orbited for three years before their deorbit in 2015.
5816:
5738:
563:
3431:
905:
3163:
197:
5743:
5175:
5097:
4520:
4002:
2787:
789:
377:
344:
74:
34:
5748:
5233:
5165:
323:(though this sometimes means the normal gravity at the equator, 9.7803267715 m/s (32.087686258 ft/s)),
5550:
4574:
Department of
Defense World Geodetic System 1984 â Its Definition and Relationships with Local Geodetic Systems
3905:
Large-scale gravity anomalies can be detected from space, as a by-product of satellite gravity missions, e.g.,
3898:. The lowest-degree parameters, including the Earth's oblateness and geocenter motion are best determined from
3127:
240:
5464:
5228:
4971:
4966:
4795:
4099:
3833:
are known then a reverse calculation will give an estimate of the mass of the Earth. This method was used by
56:
5185:
4823:
4388:
4311:
3997:
3899:
3784:
1356:
1187:{\displaystyle g(r)={\frac {4\pi }{3}}G\rho _{0}r-\pi G\left(\rho _{0}-\rho _{1}\right){\frac {r^{2}}{R}}.}
3814:
3482:
3371:
863:
283:
5329:
5517:
5139:
5134:
4153:(1901). "Déclaration relative à l'unité de masse et à la définition du poids; valeur conventionnelle de
3945:
2559:
532:
2729:
1279:
5678:
5630:
5411:
4886:
4757:
4700:
4644:
4583:
4495:
4427:
4251:
1359:. In a spherically symmetric Earth, gravity would point directly towards the sphere's centre. As the
1352:
468:
5821:
5778:
5612:
5555:
5406:
5398:
5356:
5317:
5243:
5077:
4032:
3968:
3910:
3198:
The difference between the WGS-84 formula and
Helmert's equation is less than 0.68 μm·s.
2042:
1372:
1368:
544:
417:
402:
260:
180:
129:
5690:
5160:
4903:
4865:
4860:
4684:
4277:
4215:
4198:
4163:
3980:
3960:
3913:
expansion of the Earth's gravitational potential, but alternative presentations, such as maps of
3895:
3891:
3339:
1334:
780:
508:
The second major reason for the difference in gravity at different latitudes is that the Earth's
398:
4294:
2050:
4548:
5920:
5902:
5806:
5773:
5305:
5300:
5253:
4726:
4466:
4443:
4315:
4129:
3887:
1364:
1360:
528:
The graph shows the variation in gravity relative to the height of an object above the surface
406:
176:
168:
81:
305:
is 9.80665 m/s (32.1740 ft/s) by definition. This quantity is denoted variously as
5979:
5969:
5833:
5685:
5562:
5542:
5484:
5388:
5383:
5258:
5065:
4991:
4898:
4765:
4716:
4708:
4662:
4652:
4503:
4435:
4267:
4259:
4207:
3874:
1735:
1273:
1265:
1210:
1197:
The actual depth dependence of density and gravity, inferred from seismic travel times (see
509:
301:
184:
120:
4355:
3336:
is the distance between the centre of the Earth and the body (see below), and here we take
2700:
2079:
488:
413:. There are consequently slight deviations in the magnitude of gravity across its surface.
5828:
5811:
5768:
5758:
5650:
5218:
5180:
4986:
4956:
4799:
4555:
4486:
Watts, A. B.; Daly, S. F. (May 1981). "Long wavelength gravity and topography anomalies".
4395:
4193:
4020:
4014:
3989:
3954:
3834:
3396:
3322:{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}=\left(G{\frac {M_{\oplus }}{r^{2}}}\right)m}
3202:
2563:
1348:
1303:
1234:
1230:
1216:
668:{\displaystyle g_{h}=g_{0}\left({\frac {R_{\mathrm {e} }}{R_{\mathrm {e} }+h}}\right)^{2}}
540:
410:
133:
2047:
If the terrain is at sea level, we can estimate, for the
Geodetic Reference System 1980,
1272:) cause higher than normal local gravitational fields on the Earth's surface. Less dense
4761:
4704:
4648:
4507:
4499:
4431:
4255:
2915:{\displaystyle k={\frac {b\,\mathbb {G} _{p}-a\,\mathbb {G} _{e}}{a\,\mathbb {G} _{e}}}}
299:
The precise strength of Earth's gravity varies with location. The agreed upon value for
5974:
5943:
5861:
5851:
5715:
5710:
5469:
5459:
5349:
5223:
5200:
5190:
5170:
5053:
4961:
4933:
4928:
4923:
4787:
4721:
4688:
3481:
So, to find the acceleration due to gravity at sea level, substitute the values of the
1908:
473:
397:
of uniform mass density, or whose density varies solely with distance from the centre (
264:
192:
4017: â Difference between ideal and observed gravitational acceleration at a location
5958:
5871:
5801:
5753:
5720:
5592:
5582:
5572:
5532:
5527:
5238:
4976:
4938:
4439:
4219:
1713:
766:
259:(N/kg or N·kg). Near Earth's surface, the acceleration due to gravity, accurate to 2
252:
4281:
4165:
Comptes Rendus des Séances de la TroisiÚme Conférence· Générale des Poids et
Mesures
4054:
2979:{\displaystyle \mathbb {G} _{p}=9.8321849378\,\,\mathrm {m} \cdot \mathrm {s} ^{-2}}
5925:
5876:
5866:
5856:
5796:
5577:
5431:
5421:
5263:
4524:
4308:
From
Artefacts to Atoms: The BIPM and the Search for Ultimate Measurement Standards
3974:
3789:
The Earth is not a perfect sphere, and an average value must be used for its radius
3110:{\displaystyle g\{\phi \}=9.7803253359\,\,\mathrm {m} \cdot \mathrm {s} ^{-2}\left}
1989:
1816:
706:
429:
421:
160:
1233:
cause local and regional differences in the Earth's gravitational field, known as
416:
Gravity on the Earth's surface varies by around 0.7%, from 9.7639 m/s on the
5673:
5479:
5416:
5155:
5027:
4891:
4881:
2011:
1884:
1851:
1597:
1257:
744:
581:
The following formula approximates the Earth's gravity variation with altitude:
477:
433:
343:
of an object on Earth's surface is the downwards force on that object, given by
164:
23:
756:
5763:
5730:
5705:
5507:
5426:
5195:
5120:
5022:
4918:
4770:
4745:
4712:
4295:"Wolfram|Alpha Gravity in Kuala Lumpur", Wolfram Alpha, accessed November 2020
4272:
4035: â Measure of the downward gravitational force's shift due to nearby mass
3935:
3867:
3853:
3846:
3775:. The difference may be attributed to several factors, mentioned above under "
1700:
1529:
1494:
1470:
1322:
1253:
1249:
1222:
4447:
5695:
5640:
5625:
5597:
5567:
5494:
5436:
5012:
4908:
3221:, the force on a body acted upon by Earth's gravitational force is given by
2000:
1943:
1862:
1770:
1608:
1562:
1505:
1483:
1437:
1238:
567:
551:
460:
defined a standard gravitational acceleration for the surface of the Earth:
437:
272:
188:
157:
4730:
4465:(4th ed.). New York: W.H. Freeman/Worth Publishers. pp. 336â337.
736:
263:, is 9.8 m/s (32 ft/s). This means that, ignoring the effects of
4211:
1009:. If the density decreased linearly with increasing radius from a density
1781:
1621:
1551:
1516:
1448:
1298:
1242:
573:
The effect of ground elevation depends on the density of the ground (see
445:
256:
4667:
2547:
1967, the 1967 Geodetic
Reference System Formula, Helmert's equation or
1237:. Some of these anomalies can be very extensive, resulting in bulges in
779:. All the contributions from outside cancel out as a consequence of the
5788:
5665:
5635:
5451:
5441:
5284:
5032:
5017:
4846:
4657:
4632:
4008:
1976:
1954:
1930:
1838:
1678:
1632:
1575:
1226:
547:
4335:
4263:
1339:
5655:
5522:
5502:
3501:
1965:
1919:
1897:
1827:
1792:
1759:
1746:
1724:
1667:
1654:
1643:
1540:
394:
340:
248:
524:
4792:
3771:
The value obtained agrees approximately with the measured value of
467: = 9.80665 m/s. It was based on measurements at the
5843:
5620:
5602:
5587:
5372:
4633:"SLR, GRACE and Swarm Gravity Field Determination and Combination"
3924:
3914:
3873:
2022:
1873:
1805:
1586:
1338:
1278:
1006:
755:
743:
735:
536:
523:
492:
The differences of Earth's gravity around the Antarctic continent.
487:
268:
244:
172:
119:
3201:
Further reductions are applied to obtain gravity anomalies (see:
5892:
5512:
5268:
4996:
4683:
Christoph; Wiese, David N.; Dobslaw, Henryk; Tamisiea, Mark E.;
3883:
3490:
1689:
1459:
1318:
1310:
441:
382:
5345:
5093:
4819:
2838:
is the defined gravity at the equator and poles, respectively;
1314:
1269:
1261:
1248:
The study of these anomalies forms the basis of gravitational
17:
5089:
3983: â Theoretical description of Earth's gravimetric shape
997:
is acceleration due to gravity on the surface of the Earth,
1229:(such as the density of rocks in the vicinity), and deeper
4815:
3971: â Size and shape used to model the Earth for geodesy
3963: â Loss of planetary atmospheric gases to outer space
420:
mountain in Peru to 9.8337 m/s at the surface of the
163:
that is imparted to objects due to the combined effect of
4746:"Time variable Earth's gravity field from SLR satellites"
1375:, are caused by local mass anomalies, such as mountains.
5341:
4689:"Contributions of GRACE to understanding climate change"
4053:
NASA/JPL/University of Texas Center for Space Research.
3985:
Pages displaying short descriptions of redirect targets
4334:
Resolution of the 3rd CGPM (1901), page 70 (in cm/s).
4023: â Gravitational force exerted by the planet Mars
3179:
3143:
1252:. The fluctuations are measured with highly sensitive
3917:
undulations or gravity anomalies, are also produced.
3801:
There are significant uncertainties in the values of
3521:
3434:
3399:
3342:
3230:
3166:
3130:
2995:
2932:
2846:
2831:{\displaystyle \mathbb {G} _{e},\,\mathbb {G} _{p}\,}
2798:
2732:
2724:
are the equatorial and polar semi-axes, respectively;
2703:
2684:{\displaystyle g\{\phi \}=\mathbb {G} _{e}\left,\,\!}
2575:
2105:
2082:
2053:
1075:
908:
792:
748:
Earth's radial density distribution according to the
590:
200:
5901:
5885:
5842:
5787:
5729:
5664:
5611:
5541:
5493:
5450:
5397:
5277:
5209:
5148:
5127:
5005:
4947:
4874:
4853:
1343:
A plumb bob determines the local vertical direction
336:(which is also used for the variable local value).
48:. Unsourced material may be challenged and removed.
4230:Îłe = 9.780 326 7715 m/sÂČ normal gravity at equator
4168:(in French). Paris: Gauthier-Villars. p. 68.
3752:
3470:
3414:
3355:
3321:
3187:
3151:
3109:
2978:
2914:
2830:
2778:
2716:
2683:
2532:
2088:
2068:
1186:
953:
847:
667:
224:
4098:. Arlington, Texas: S.A.W.E., Inc. Archived from
2680:
1297:In air or water, objects experience a supporting
425:
4521:Gravitational Fields Widget as of Oct 25th, 2012
899:and the dependence of gravity on depth would be
4793:GRACE â Gravity Recovery and Climate Experiment
4377:"I feel 'lighter' when up a mountain but am I?"
4029: â Classical statement of gravity as force
3818:is also rather difficult to measure precisely.
3471:{\displaystyle g=G{\frac {M_{\oplus }}{r^{2}}}}
954:{\displaystyle g(r)={\frac {4\pi }{3}}G\rho r.}
771:An approximate value for gravity at a distance
500:. At latitudes nearer the Equator, the outward
496:The surface of the Earth is rotating, so it is
472:important. It is also used to define the units
3812:as used in this calculation, and the value of
3188:{\displaystyle b=6356752.314245\,\,{\mbox{m}}}
1388:Acceleration due to gravity in various cities
225:{\displaystyle g=\|{\mathit {\mathbf {g} }}\|}
5357:
5105:
4831:
4488:Annual Review of Earth and Planetary Sciences
3851:The measurement of Earth's gravity is called
848:{\displaystyle g(r)=-{\frac {GM(r)}{r^{2}}}.}
132:of an idealized, smooth Earth, the so-called
8:
4565:
4563:
4420:Physics of the Earth and Planetary Interiors
3425:Comparing the two formulas it is seen that:
3005:
2999:
2585:
2579:
2119:
2113:
2063:
2057:
690:is the gravitational acceleration at height
219:
207:
4577:,NIMA TR8350.2, 3rd ed., Tbl. 3.4, Eq. 4-1"
4005: â Change in speed due only to gravity
3776:
187:quantity, whose direction coincides with a
5364:
5350:
5342:
5112:
5098:
5090:
4838:
4824:
4816:
4124:Hofmann-Wellenhof, B.; Moritz, H. (2006).
4055:"PIA12146: GRACE Global Gravity Animation"
3977: â Energy related to Earth's gravity
1386:
458:General Conference on Weights and Measures
405:of uniform magnitude at all points on its
191:and strength or magnitude is given by the
4769:
4720:
4666:
4656:
4411:A. M. Dziewonski, D. L. Anderson (1981).
4271:
4151:Bureau International des Poids et Mesures
4078:
4076:
3740:
3735:
3733:
3728:
3727:
3726:
3712:
3703:
3685:
3676:
3670:
3647:
3641:
3628:
3615:
3610:
3600:
3592:
3590:
3584:
3579:
3577:
3568:
3547:
3537:
3531:
3520:
3460:
3450:
3444:
3433:
3398:
3347:
3341:
3303:
3293:
3287:
3268:
3257:
3247:
3240:
3229:
3178:
3177:
3176:
3165:
3152:{\displaystyle a=6378137.0\,\,{\mbox{m}}}
3142:
3141:
3140:
3129:
3088:
3083:
3060:
3055:
3043:
3030:
3025:
3016:
3015:
3014:
2994:
2967:
2962:
2953:
2952:
2951:
2939:
2935:
2934:
2931:
2903:
2899:
2898:
2896:
2885:
2881:
2880:
2878:
2866:
2862:
2861:
2859:
2853:
2845:
2827:
2821:
2817:
2816:
2814:
2805:
2801:
2800:
2797:
2770:
2758:
2737:
2731:
2710:
2702:
2679:
2657:
2647:
2623:
2607:
2597:
2593:
2592:
2574:
2506:
2501:
2482:
2467:
2466:
2457:
2452:
2443:
2442:
2441:
2408:
2403:
2385:
2380:
2365:
2364:
2355:
2350:
2341:
2340:
2339:
2306:
2301:
2283:
2278:
2263:
2262:
2253:
2248:
2239:
2238:
2237:
2201:
2196:
2178:
2173:
2158:
2157:
2148:
2143:
2134:
2133:
2132:
2106:
2104:
2081:
2052:
1268:. Denser rocks (often containing mineral
1170:
1164:
1153:
1140:
1113:
1091:
1074:
924:
907:
877:is the total mass enclosed within radius
834:
811:
791:
659:
639:
638:
626:
625:
619:
608:
595:
589:
212:
211:
210:
199:
108:Learn how and when to remove this message
3925:Gravity Recovery and Interior Laboratory
531:
4406:
4404:
4045:
4011: â Attraction of masses and energy
3957: â Concept in celestial mechanics
3921:Gravity Recovery and Climate Experiment
3121:where the semi-axes of the earth are:
2558:as a function of latitude is the WGS (
1387:
881:. If the Earth had a constant density
4027:Newton's law of universal gravitation
3213:from the law of universal gravitation
1225:(such as the presence of mountains),
128:mission, showing deviations from the
7:
5916:Geology of solar terrestrial planets
5324:
5072:
4463:Physics for scientists and engineers
3390:is acceleration, here tells us that
574:
239:, this acceleration is expressed in
46:adding citations to reliable sources
4805:GGMplus high resolution data (2013)
4508:10.1146/annurev.ea.09.050181.002215
4413:"Preliminary reference Earth model"
722:standard gravitational acceleration
4379:, National Physical Laboratory FAQ
3736:
3729:
3677:
3651:
3648:
3611:
3596:
3593:
3580:
3026:
3017:
2963:
2954:
2453:
2444:
2351:
2342:
2249:
2240:
2144:
2135:
1217:Gravity anomaly § Computation
640:
627:
498:not an inertial frame of reference
14:
4336:BIPM â Resolution of the 3rd CGPM
3868:Gravimetry § Satellite gravimetry
2779:{\displaystyle e^{2}=1-(b/a)^{2}}
1309:The gravitational effects of the
1201:), is shown in the graphs below.
750:Preliminary Reference Earth Model
124:Earth's gravity measured by NASA
5939:
5938:
5323:
5312:
5311:
5299:
5071:
5060:
5059:
5047:
4537:Physical and Mathematical Tables
4194:"Geodetic Reference System 1980"
4061:. NASA Jet Propulsion Laboratory
3938:
3866:This section is an excerpt from
3363:to be the mass of the Earth and
213:
22:
5646:Human impact on the environment
3992: â Type of gravity anomaly
2076:, the acceleration at latitude
1245:clocks out of synchronisation.
33:needs additional citations for
5475:Climate variability and change
4398:, NASA, see "Editor's note #2"
3878:Gravity anomaly map from GRACE
3682:
3657:
2767:
2752:
1085:
1079:
1066:, and the dependence would be
918:
912:
826:
820:
802:
796:
1:
5911:Evolution of the Solar System
4549:International Gravity formula
2545:International Gravity Formula
1371:. Smaller deviations, called
345:Newton's second law of motion
5651:Evolutionary history of life
4535:T.M. Yarwood and F. Castle,
4440:10.1016/0031-9201(81)90046-7
4244:Geophysical Research Letters
3367:to be the mass of the body.
3219:law of universal gravitation
1379:Comparative values worldwide
1325:) over the course of a day.
1205:Local topography and geology
5259:Precession of the equinoxes
4992:Precession of the equinoxes
4788:Altitude gravity calculator
4087:Precise Measurement of Mass
3356:{\displaystyle M_{\oplus }}
3203:Gravity anomaly#Computation
2554:An alternative formula for
251:or m·s) or equivalently in
5996:
5176:Geophysical fluid dynamics
4348:"Curious About Astronomy?"
4128:(2nd ed.). Springer.
4003:Gravitational acceleration
3865:
3844:
2069:{\displaystyle g\{\phi \}}
2040:
1423:
1412:
1401:
1347:Gravity acceleration is a
1332:
1214:
1208:
764:
426:In large cities, it ranges
378:Gravitational acceleration
5934:
5379:
5293:
5041:
4771:10.1007/s00190-015-0825-1
4713:10.1038/s41558-019-0456-2
4083:Boynton, Richard (2001).
3792:This calculated value of
3508:, to obtain the value of
1199:AdamsâWilliamson equation
241:metres per second squared
5921:Location in the Universe
5852:Antarctic/Southern Ocean
5551:List of sovereign states
4461:Tipler, Paul A. (1999).
4389:"The G's in the Machine"
428:from 9.7806 m/s in
5186:Near-surface geophysics
4312:Oxford University Press
4192:Moritz, Helmut (2000).
3998:Gravitation of the Moon
3900:satellite laser ranging
1317:(also the cause of the
1235:gravitational anomalies
393:A non-rotating perfect
5234:Earth's magnetic field
4812:Potsdam Gravity Potato
3879:
3861:Satellite measurements
3777:Variation in magnitude
3754:
3483:gravitational constant
3472:
3416:
3357:
3323:
3189:
3153:
3111:
2980:
2916:
2832:
2780:
2718:
2685:
2534:
2090:
2070:
1344:
1285:
1188:
955:
864:gravitational constant
849:
762:
753:
741:
669:
554:
529:
493:
389:Variation in magnitude
284:gravitational constant
226:
143:
5965:Gravimetry of objects
5631:Biogeochemical cycles
5556:dependent territories
5306:Geophysics portal
5229:Earth's energy budget
4972:Earth's gravity field
4967:Earth's energy budget
4693:Nature Climate Change
4212:10.1007/s001900050278
3946:Earth sciences portal
3877:
3755:
3473:
3417:
3358:
3324:
3190:
3154:
3112:
2981:
2917:
2833:
2781:
2719:
2717:{\displaystyle a,\,b}
2686:
2560:World Geodetic System
2535:
2091:
2089:{\displaystyle \phi }
2071:
1342:
1282:
1221:Local differences in
1215:Further information:
1189:
1027:at the surface, then
1005:is the radius of the
956:
850:
759:
747:
739:
670:
535:
527:
491:
440:to 9.825 m/s in
227:
123:
5679:Computer cartography
5412:Prebiotic atmosphere
4887:Computer cartography
4306:Terry Quinn (2011).
3519:
3432:
3415:{\displaystyle F=mg}
3397:
3340:
3228:
3164:
3128:
2993:
2930:
2844:
2796:
2730:
2701:
2573:
2103:
2080:
2051:
1276:cause the opposite.
1073:
906:
885:, the mass would be
790:
588:
469:Pavillon de Breteuil
198:
42:improve this article
5822:Geologic time scale
5543:Culture and society
5407:Atmosphere of Earth
5278:Related disciplines
5244:Geothermal gradient
5006:Related disciplines
4762:2015JGeod..89..945S
4705:2019NatCC...9..358T
4685:Velicogna, Isabella
4649:2019RemS...11..956M
4500:1981AREPS...9..415W
4432:1981PEPI...25..297D
4256:2013GeoRL..40.4279H
4105:on 27 February 2007
4096:Sawe Paper No. 3147
4033:Vertical deflection
3969:Figure of the Earth
3372:Newton's second law
2922:(formula constant);
2043:Theoretical gravity
2037:Mathematical models
1389:
1373:vertical deflection
1369:geocentric latitude
707:Earth's mean radius
456:In 1901, the third
403:gravitational field
401:), would produce a
261:significant figures
130:theoretical gravity
5817:Geological history
5691:Geodetic astronomy
5161:Geophysical survey
5054:Geodesy portal
4904:Geodetic astronomy
4798:2009-12-01 at the
4750:Journal of Geodesy
4658:10.3390/rs11080956
4554:2008-08-20 at the
4394:2020-09-21 at the
4352:Cornell University
4273:20.500.11937/46786
4199:Journal of Geodesy
3981:Geopotential model
3961:Atmospheric escape
3911:spherical-harmonic
3896:GRACE and GRACE-FO
3880:
3750:
3500:, and the Earth's
3468:
3412:
3353:
3319:
3185:
3183:
3149:
3147:
3107:
2976:
2912:
2828:
2786:is the spheroid's
2776:
2714:
2681:
2549:Clairaut's formula
2530:
2528:
2086:
2066:
1345:
1335:Vertical direction
1286:
1231:tectonic structure
1184:
951:
845:
781:inverse-square law
763:
754:
742:
665:
555:
530:
494:
452:Conventional value
399:spherical symmetry
289:is referred to as
282:(in contrast, the
222:
144:
57:"Gravity of Earth"
5952:
5951:
5903:Planetary science
5886:Natural satellite
5807:Extremes on Earth
5774:Signal processing
5339:
5338:
5254:Mantle convection
5087:
5086:
4321:978-0-19-530786-3
4264:10.1002/grl.50838
4250:(16): 4279â4283.
4135:978-3-211-33544-4
3783:The Earth is not
3718:
3692:
3553:
3466:
3309:
3274:
3182:
3146:
3101:
3100:
2910:
2670:
2669:
2562:) 84 Ellipsoidal
2034:
2033:
1365:geodetic latitude
1274:sedimentary rocks
1179:
1104:
1018:at the center to
937:
840:
653:
502:centrifugal force
177:centrifugal force
169:mass distribution
118:
117:
110:
92:
5987:
5942:
5941:
5834:History of Earth
5485:Paleoclimatology
5366:
5359:
5352:
5343:
5327:
5326:
5315:
5314:
5304:
5303:
5249:Gravity of Earth
5114:
5107:
5100:
5091:
5075:
5074:
5063:
5062:
5052:
5051:
5050:
4982:Gravity of Earth
4914:Gravity of Earth
4840:
4833:
4826:
4817:
4810:Geoid 2011 model
4776:
4775:
4773:
4741:
4735:
4734:
4724:
4679:
4673:
4672:
4670:
4660:
4628:
4622:
4621:
4619:
4618:
4604:
4598:
4597:
4595:
4594:
4588:
4582:. Archived from
4581:
4567:
4558:
4546:
4540:
4533:
4527:
4518:
4512:
4511:
4483:
4477:
4476:
4458:
4452:
4451:
4417:
4408:
4399:
4386:
4380:
4374:
4368:
4367:
4365:
4363:
4354:. Archived from
4344:
4338:
4332:
4326:
4325:
4303:
4297:
4292:
4286:
4285:
4275:
4239:
4233:
4232:
4227:
4226:
4189:
4183:
4182:
4179:
4161:
4147:
4141:
4139:
4126:Physical Geodesy
4121:
4115:
4114:
4112:
4110:
4104:
4093:
4080:
4071:
4070:
4068:
4066:
4050:
3986:
3948:
3943:
3942:
3941:
3759:
3757:
3756:
3751:
3749:
3748:
3747:
3739:
3732:
3719:
3717:
3716:
3704:
3693:
3691:
3690:
3689:
3680:
3675:
3674:
3655:
3654:
3646:
3645:
3629:
3624:
3623:
3622:
3614:
3608:
3607:
3599:
3589:
3588:
3583:
3576:
3575:
3554:
3552:
3551:
3542:
3541:
3532:
3493:(in kilograms),
3477:
3475:
3474:
3469:
3467:
3465:
3464:
3455:
3454:
3445:
3421:
3419:
3418:
3413:
3362:
3360:
3359:
3354:
3352:
3351:
3328:
3326:
3325:
3320:
3315:
3311:
3310:
3308:
3307:
3298:
3297:
3288:
3275:
3273:
3272:
3263:
3262:
3261:
3252:
3251:
3241:
3194:
3192:
3191:
3186:
3184:
3180:
3158:
3156:
3155:
3150:
3148:
3144:
3116:
3114:
3113:
3108:
3106:
3102:
3093:
3092:
3073:
3072:
3065:
3064:
3044:
3038:
3037:
3029:
3020:
2985:
2983:
2982:
2977:
2975:
2974:
2966:
2957:
2944:
2943:
2938:
2921:
2919:
2918:
2913:
2911:
2909:
2908:
2907:
2902:
2891:
2890:
2889:
2884:
2871:
2870:
2865:
2854:
2837:
2835:
2834:
2829:
2826:
2825:
2820:
2810:
2809:
2804:
2785:
2783:
2782:
2777:
2775:
2774:
2762:
2742:
2741:
2723:
2721:
2720:
2715:
2690:
2688:
2687:
2682:
2675:
2671:
2662:
2661:
2652:
2651:
2636:
2635:
2628:
2627:
2608:
2602:
2601:
2596:
2539:
2537:
2536:
2531:
2529:
2525:
2521:
2511:
2510:
2465:
2464:
2456:
2447:
2431:
2424:
2420:
2413:
2412:
2390:
2389:
2363:
2362:
2354:
2345:
2329:
2322:
2318:
2311:
2310:
2288:
2287:
2261:
2260:
2252:
2243:
2227:
2220:
2216:
2206:
2205:
2183:
2182:
2156:
2155:
2147:
2138:
2095:
2093:
2092:
2087:
2075:
2073:
2072:
2067:
1736:Washington, D.C.
1390:
1266:mineral deposits
1211:Physical geodesy
1193:
1191:
1190:
1185:
1180:
1175:
1174:
1165:
1163:
1159:
1158:
1157:
1145:
1144:
1118:
1117:
1105:
1100:
1092:
1065:
1026:
1017:
1004:
1000:
996:
992:
973:
969:
960:
958:
957:
952:
938:
933:
925:
898:
884:
880:
876:
861:
854:
852:
851:
846:
841:
839:
838:
829:
812:
778:
774:
719:
704:
694:above sea level.
693:
689:
674:
672:
671:
666:
664:
663:
658:
654:
652:
645:
644:
643:
632:
631:
630:
620:
613:
612:
600:
599:
510:equatorial bulge
418:Nevado HuascarĂĄn
375:
361:
360:
335:
331:
322:
313:
304:
302:standard gravity
294:
288:
280:
231:
229:
228:
223:
218:
217:
216:
181:Earth's rotation
154:
148:gravity of Earth
139:Animated version
113:
106:
102:
99:
93:
91:
50:
26:
18:
5995:
5994:
5990:
5989:
5988:
5986:
5985:
5984:
5955:
5954:
5953:
5948:
5930:
5897:
5881:
5838:
5829:Geologic record
5783:
5769:Plate tectonics
5759:Mineral physics
5739:Earth structure
5725:
5660:
5607:
5537:
5489:
5446:
5393:
5375:
5370:
5340:
5335:
5298:
5289:
5273:
5224:Coriolis effect
5219:Chandler wobble
5211:
5205:
5181:Mineral physics
5144:
5123:
5118:
5088:
5083:
5048:
5046:
5037:
5001:
4987:Plate tectonics
4962:Coriolis effect
4957:Chandler wobble
4949:
4943:
4870:
4849:
4844:
4800:Wayback Machine
4784:
4779:
4756:(10): 945â960.
4743:
4742:
4738:
4681:
4680:
4676:
4630:
4629:
4625:
4616:
4614:
4606:
4605:
4601:
4592:
4590:
4586:
4579:
4569:
4568:
4561:
4556:Wayback Machine
4547:
4543:
4534:
4530:
4519:
4515:
4485:
4484:
4480:
4473:
4460:
4459:
4455:
4415:
4410:
4409:
4402:
4396:Wayback Machine
4387:
4383:
4375:
4371:
4361:
4359:
4358:on 28 July 2013
4346:
4345:
4341:
4333:
4329:
4322:
4314:. p. 127.
4305:
4304:
4300:
4293:
4289:
4241:
4240:
4236:
4224:
4222:
4191:
4190:
4186:
4178:
4172:
4160:
4154:
4149:
4148:
4144:
4136:
4123:
4122:
4118:
4108:
4106:
4102:
4091:
4082:
4081:
4074:
4064:
4062:
4052:
4051:
4047:
4043:
4038:
4021:Gravity of Mars
4015:Gravity anomaly
3990:Bouguer anomaly
3984:
3955:Escape velocity
3944:
3939:
3937:
3934:
3929:
3928:
3871:
3863:
3849:
3843:
3835:Henry Cavendish
3811:
3734:
3708:
3681:
3666:
3656:
3637:
3630:
3609:
3591:
3578:
3564:
3543:
3533:
3517:
3516:
3499:
3456:
3446:
3430:
3429:
3395:
3394:
3343:
3338:
3337:
3299:
3289:
3283:
3279:
3264:
3253:
3243:
3242:
3226:
3225:
3215:
3162:
3161:
3126:
3125:
3084:
3081:0.0066943799901
3056:
3045:
3039:
3024:
2991:
2990:
2961:
2933:
2928:
2927:
2897:
2892:
2879:
2860:
2855:
2842:
2841:
2815:
2799:
2794:
2793:
2766:
2733:
2728:
2727:
2699:
2698:
2653:
2643:
2619:
2609:
2603:
2591:
2571:
2570:
2564:Gravity Formula
2527:
2526:
2502:
2472:
2468:
2451:
2429:
2428:
2404:
2381:
2370:
2366:
2349:
2327:
2326:
2302:
2279:
2268:
2264:
2247:
2225:
2224:
2197:
2174:
2163:
2159:
2142:
2122:
2101:
2100:
2078:
2077:
2049:
2048:
2045:
2039:
1381:
1355:in addition to
1349:vector quantity
1337:
1331:
1304:Apparent weight
1295:
1241:, and throwing
1219:
1213:
1207:
1166:
1149:
1136:
1135:
1131:
1109:
1093:
1071:
1070:
1056:
1049:
1042:
1028:
1025:
1019:
1016:
1010:
1002:
998:
994:
975:
971:
965:
926:
904:
903:
886:
882:
878:
867:
859:
830:
813:
788:
787:
776:
772:
769:
734:
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4608:"Gravitation"
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4589:on 2014-04-11
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4185:
4181:
4175:
4167:
4166:
4157:
4152:
4146:
4143:
4137:
4131:
4127:
4120:
4117:
4101:
4097:
4090:
4088:
4079:
4077:
4073:
4060:
4056:
4049:
4046:
4040:
4034:
4031:
4028:
4025:
4022:
4019:
4016:
4013:
4010:
4007:
4004:
4001:
3999:
3996:
3991:
3988:
3982:
3979:
3978:
3976:
3973:
3970:
3967:
3962:
3959:
3958:
3956:
3953:
3952:
3947:
3936:
3931:
3926:
3922:
3918:
3916:
3912:
3908:
3903:
3901:
3897:
3893:
3889:
3885:
3876:
3869:
3860:
3858:
3856:
3855:
3848:
3840:
3838:
3836:
3832:
3828:
3824:
3819:
3817:
3816:
3808:
3804:
3795:
3791:
3788:
3786:
3782:
3781:
3780:
3778:
3774:
3769:
3767:
3744:
3741:
3723:
3720:
3713:
3709:
3705:
3700:
3697:
3694:
3686:
3671:
3667:
3663:
3660:
3642:
3638:
3634:
3631:
3625:
3619:
3616:
3604:
3601:
3585:
3572:
3569:
3565:
3561:
3558:
3555:
3548:
3544:
3538:
3534:
3528:
3525:
3522:
3515:
3514:
3513:
3511:
3507:
3504:(in metres),
3503:
3496:
3492:
3488:
3484:
3461:
3457:
3451:
3447:
3441:
3438:
3435:
3428:
3427:
3426:
3409:
3406:
3403:
3400:
3393:
3392:
3391:
3389:
3385:
3381:
3377:
3373:
3368:
3366:
3348:
3344:
3335:
3316:
3312:
3304:
3300:
3294:
3290:
3284:
3280:
3276:
3269:
3265:
3258:
3254:
3248:
3244:
3237:
3234:
3231:
3224:
3223:
3222:
3220:
3212:
3208:
3206:
3204:
3199:
3173:
3170:
3167:
3160:
3137:
3134:
3131:
3124:
3123:
3122:
3103:
3097:
3094:
3089:
3085:
3080:
3077:
3074:
3069:
3066:
3061:
3057:
3052:
3049:
3046:
3040:
3034:
3031:
3021:
3011:
3008:
3002:
2996:
2989:
2988:
2987:
2971:
2968:
2958:
2948:
2945:
2940:
2904:
2893:
2886:
2875:
2872:
2867:
2856:
2850:
2847:
2840:
2822:
2811:
2806:
2792:
2789:
2771:
2763:
2759:
2755:
2749:
2746:
2743:
2738:
2734:
2726:
2711:
2707:
2704:
2697:
2696:
2695:
2676:
2672:
2666:
2663:
2658:
2654:
2648:
2644:
2640:
2637:
2632:
2629:
2624:
2620:
2616:
2613:
2610:
2604:
2598:
2588:
2582:
2576:
2569:
2568:
2567:
2565:
2561:
2557:
2552:
2550:
2546:
2522:
2518:
2515:
2512:
2507:
2503:
2498:
2495:
2492:
2489:
2486:
2483:
2479:
2476:
2473:
2469:
2461:
2458:
2448:
2438:
2435:
2433:
2425:
2421:
2417:
2414:
2409:
2405:
2400:
2397:
2394:
2391:
2386:
2382:
2377:
2374:
2371:
2367:
2359:
2356:
2346:
2336:
2333:
2331:
2323:
2319:
2315:
2312:
2307:
2303:
2298:
2295:
2292:
2289:
2284:
2280:
2275:
2272:
2269:
2265:
2257:
2254:
2244:
2234:
2231:
2229:
2221:
2217:
2213:
2210:
2207:
2202:
2198:
2193:
2190:
2187:
2184:
2179:
2175:
2170:
2167:
2164:
2160:
2152:
2149:
2139:
2129:
2126:
2124:
2116:
2110:
2099:
2098:
2097:
2083:
2060:
2054:
2044:
2036:
2029:
2026:
2024:
2021:
2018:
2015:
2013:
2010:
2007:
2004:
2002:
1999:
1996:
1993:
1991:
1988:
1987:
1983:
1980:
1978:
1975:
1972:
1969:
1967:
1964:
1961:
1958:
1956:
1953:
1950:
1947:
1945:
1942:
1941:
1937:
1934:
1932:
1929:
1926:
1923:
1921:
1918:
1915:
1912:
1910:
1907:
1904:
1901:
1899:
1896:
1895:
1891:
1888:
1886:
1883:
1880:
1877:
1875:
1872:
1869:
1866:
1864:
1861:
1858:
1855:
1853:
1850:
1849:
1845:
1842:
1840:
1837:
1834:
1831:
1829:
1826:
1823:
1820:
1818:
1815:
1812:
1809:
1807:
1804:
1803:
1799:
1796:
1794:
1791:
1788:
1785:
1783:
1780:
1777:
1774:
1772:
1769:
1766:
1763:
1761:
1758:
1757:
1753:
1750:
1748:
1745:
1742:
1739:
1737:
1734:
1731:
1728:
1726:
1723:
1720:
1717:
1715:
1714:New York City
1712:
1711:
1707:
1704:
1702:
1699:
1696:
1693:
1691:
1688:
1685:
1682:
1680:
1677:
1674:
1671:
1669:
1666:
1665:
1661:
1658:
1656:
1653:
1650:
1647:
1645:
1642:
1639:
1636:
1634:
1631:
1628:
1625:
1623:
1620:
1619:
1615:
1612:
1610:
1607:
1604:
1601:
1599:
1596:
1593:
1590:
1588:
1585:
1582:
1579:
1577:
1574:
1573:
1569:
1566:
1564:
1561:
1558:
1555:
1553:
1550:
1547:
1544:
1542:
1539:
1536:
1533:
1531:
1528:
1527:
1523:
1520:
1518:
1515:
1512:
1509:
1507:
1504:
1501:
1498:
1496:
1493:
1490:
1487:
1485:
1482:
1481:
1477:
1474:
1472:
1469:
1466:
1463:
1461:
1458:
1455:
1452:
1450:
1447:
1444:
1441:
1439:
1436:
1435:
1431:
1428:
1425:
1420:
1417:
1414:
1409:
1406:
1403:
1398:
1395:
1392:
1391:
1385:
1378:
1376:
1374:
1370:
1366:
1362:
1358:
1354:
1350:
1341:
1336:
1328:
1326:
1324:
1320:
1316:
1312:
1307:
1306:for details.
1305:
1300:
1293:Other factors
1292:
1290:
1281:
1277:
1275:
1271:
1267:
1263:
1259:
1255:
1251:
1246:
1244:
1240:
1236:
1232:
1228:
1224:
1218:
1212:
1204:
1202:
1200:
1181:
1176:
1171:
1167:
1160:
1154:
1150:
1146:
1141:
1137:
1132:
1128:
1125:
1122:
1119:
1114:
1110:
1106:
1101:
1097:
1094:
1088:
1082:
1076:
1069:
1068:
1067:
1064:
1060:
1053:
1046:
1039:
1035:
1031:
1022:
1013:
1008:
1001:is depth and
990:
986:
982:
978:
968:
948:
945:
942:
939:
934:
930:
927:
921:
915:
909:
902:
901:
900:
897:
893:
889:
874:
870:
865:
842:
835:
831:
823:
817:
814:
808:
805:
799:
793:
786:
785:
784:
782:
768:
767:Shell theorem
758:
751:
746:
738:
731:
729:
723:
715:
711:
708:
700:
696:
688:
681:
680:
679:
660:
655:
649:
646:
635:
622:
616:
609:
605:
601:
596:
592:
584:
583:
582:
579:
576:
571:
569:
565:
559:
553:
549:
546:
542:
538:
534:
526:
519:
517:
513:
511:
506:
503:
499:
490:
483:
481:
479:
475:
470:
463:
459:
451:
449:
447:
443:
439:
435:
431:
427:
423:
419:
414:
412:
408:
404:
400:
396:
388:
386:
384:
383:tidal effects
379:
374:
370:
366:
359:
356:
352:
346:
342:
337:
327:
318:
309:
303:
297:
295:
285:
281:
274:
271:of an object
270:
266:
262:
258:
254:
250:
246:
243:(in symbols,
242:
238:
233:
204:
201:
194:
190:
186:
182:
178:
174:
170:
166:
162:
159:
155:
150:, denoted by
149:
141:
140:
135:
131:
127:
122:
112:
109:
101:
90:
87:
83:
80:
76:
73:
69:
66:
62:
59: â
58:
54:
53:Find sources:
47:
43:
37:
36:
31:This article
29:
25:
20:
19:
16:
5926:Solar System
5877:Oceanography
5867:Indian Ocean
5857:Arctic Ocean
5797:Age of Earth
5749:Geomagnetism
5700:
5432:Thermosphere
5422:Stratosphere
5328:
5316:
5297:
5264:Seismic wave
5248:
5166:Geomagnetism
5076:
5064:
5045:
4981:
4913:
4753:
4749:
4739:
4696:
4692:
4687:(May 2019).
4677:
4668:10281/240694
4640:
4636:
4626:
4615:. Retrieved
4611:
4602:
4591:. Retrieved
4584:the original
4573:
4572:
4544:
4536:
4531:
4525:WolframAlpha
4516:
4491:
4487:
4481:
4462:
4456:
4423:
4419:
4384:
4372:
4360:. Retrieved
4356:the original
4351:
4342:
4330:
4307:
4301:
4290:
4247:
4243:
4237:
4229:
4223:. Retrieved
4203:
4197:
4187:
4173:
4169:
4164:
4155:
4145:
4125:
4119:
4107:. Retrieved
4100:the original
4095:
4086:
4063:. Retrieved
4059:Photojournal
4058:
4048:
3975:Geopotential
3904:
3881:
3852:
3850:
3830:
3826:
3822:
3820:
3813:
3806:
3802:
3800:
3793:
3772:
3770:
3765:
3762:
3509:
3505:
3494:
3486:
3480:
3424:
3387:
3386:is mass and
3383:
3379:
3375:
3369:
3364:
3333:
3331:
3216:
3210:
3200:
3197:
3120:
3012:9.7803253359
2949:9.8321849378
2926:then, where
2925:
2788:eccentricity
2693:
2555:
2553:
2543:This is the
2542:
2046:
1990:Kuala Lumpur
1817:Buenos Aires
1382:
1346:
1308:
1296:
1287:
1247:
1220:
1196:
1062:
1058:
1051:
1044:
1037:
1033:
1029:
1020:
1011:
988:
984:
980:
976:
974:is given by
966:
964:The gravity
963:
895:
891:
887:
872:
868:
857:
770:
727:
713:
698:
683:
677:
580:
572:
560:
556:
514:
507:
495:
461:
455:
430:Kuala Lumpur
422:Arctic Ocean
415:
392:
373:acceleration
372:
368:
364:
357:
354:
350:
338:
332:, or simply
325:
316:
307:
298:
290:
276:
234:
161:acceleration
151:
147:
145:
137:
104:
95:
85:
78:
71:
64:
52:
40:Please help
35:verification
32:
15:
5674:Cartography
5613:Environment
5480:Climatology
5417:Troposphere
5156:Geodynamics
5028:Mathematics
4892:Web mapping
4882:Cartography
4494:: 415â418.
4362:22 December
4109:22 December
4065:30 December
3841:Measurement
3785:homogeneous
3209:Estimating
2012:Mexico City
1885:Kuwait City
1852:Los Angeles
1258:prospectors
1254:gravimeters
478:pound force
434:Mexico City
183:). It is a
165:gravitation
5959:Categories
5779:Tomography
5764:Seismology
5731:Geophysics
5706:Navigation
5598:Time zones
5563:In culture
5508:Antarctica
5495:Continents
5427:Mesosphere
5399:Atmosphere
5196:Seismology
5121:Geophysics
5023:Geophysics
4919:Navigation
4866:Geodesists
4643:(8): 956.
4617:2022-01-25
4593:2015-10-15
4225:2023-07-26
4041:References
3854:gravimetry
3847:Gravimetry
2790:, squared;
1701:Wellington
1530:Birmingham
1495:Manchester
1471:Copenhagen
1284:spreading.
1250:geophysics
1223:topography
1209:See also:
765:See also:
179:(from the
175:) and the
68:newspapers
5696:Geomatics
5641:Ecosystem
5626:Biosphere
5588:Etymology
5568:Earth Day
5518:Australia
5437:Exosphere
5239:Geodynamo
5212:phenomena
5210:Physical
5149:Subfields
5013:Astronomy
4977:Geodynamo
4950:phenomena
4948:Physical
4909:Geomatics
4875:Subfields
4448:0031-9201
4220:195290884
3742:−
3721:≈
3664:×
3635:×
3626:×
3617:−
3602:−
3570:−
3562:⋅
3539:⊕
3452:⊕
3349:⊕
3295:⊕
3217:From the
3138:6378137.0
3098:ϕ
3095:
3078:−
3070:ϕ
3067:
3032:−
3022:⋅
3003:ϕ
2969:−
2959:⋅
2873:−
2750:−
2667:ϕ
2664:
2641:−
2633:ϕ
2630:
2583:ϕ
2519:ϕ
2513:
2499:0.0000058
2493:ϕ
2487:
2480:0.0026512
2477:−
2474:1.0026454
2459:−
2449:⋅
2418:ϕ
2415:
2401:0.0000232
2395:ϕ
2392:
2378:0.0053256
2375:−
2372:1.0053024
2357:−
2347:⋅
2316:ϕ
2313:
2299:0.0000232
2293:ϕ
2290:
2276:0.0052792
2255:−
2245:⋅
2214:ϕ
2208:
2194:0.0000058
2191:−
2188:ϕ
2185:
2171:0.0053024
2150:−
2140:⋅
2117:ϕ
2084:ϕ
2061:ϕ
2001:Singapore
1944:Hong Kong
1863:Cape Town
1771:Melbourne
1609:Vancouver
1563:Frankfurt
1506:Amsterdam
1484:Stockholm
1438:Anchorage
1357:magnitude
1353:direction
1329:Direction
1239:sea level
1151:ρ
1147:−
1138:ρ
1126:π
1123:−
1111:ρ
1098:π
970:at depth
943:ρ
931:π
894:) = (4/3)
809:−
568:free-fall
552:elevation
438:Singapore
220:‖
208:‖
189:plumb bob
156:, is the
5944:Category
5318:Category
5128:Overview
5066:Category
4854:Overview
4796:Archived
4731:31534490
4552:Archived
4392:Archived
4282:54867946
3932:See also
3382:, where
2439:9.780327
2337:9.780327
2235:9.780327
2130:9.780327
1782:Auckland
1622:Istanbul
1598:Montréal
1552:Brussels
1517:Kotagiri
1449:Helsinki
1426:Location
1415:Location
1404:Location
1393:Location
1313:and the
1299:buoyancy
1260:to find
1243:pendulum
520:Altitude
484:Latitude
446:Helsinki
257:kilogram
237:SI units
5980:Geodesy
5970:Gravity
5789:Geology
5701:Gravity
5666:Geodesy
5636:Ecology
5452:Climate
5442:Weather
5389:History
5384:Outline
5330:Commons
5285:Geodesy
5135:Outline
5078:Commons
5033:Physics
5018:Geology
4861:History
4847:Geodesy
4758:Bibcode
4722:6750016
4701:Bibcode
4645:Bibcode
4496:Bibcode
4428:Bibcode
4252:Bibcode
4009:Gravity
3724:9.77637
2694:where,
1977:Jakarta
1955:Bangkok
1931:Kolkata
1839:Nicosia
1679:Chicago
1633:Toronto
1576:Seattle
1351:, with
1227:geology
862:is the
752:(PREM).
720:is the
705:is the
548:gravity
407:surface
277:little
253:newtons
171:within
82:scholar
5844:Oceans
5812:Future
5656:Nature
5578:Symbol
5523:Europe
5503:Africa
4729:
4719:
4469:
4446:
4318:
4280:
4218:
4132:
3797:force.
3502:radius
3332:where
2030:32.07
2027:9.775
2019:32.07
2016:9.776
2008:32.07
2005:9.776
1997:32.07
1994:9.776
1984:32.08
1981:9.777
1973:32.09
1970:9.780
1966:Manila
1962:32.09
1959:9.780
1951:32.10
1948:9.785
1938:32.10
1935:9.785
1927:32.11
1924:9.786
1920:Havana
1916:32.11
1913:9.788
1905:32.12
1902:9.790
1898:Taipei
1892:32.13
1889:9.792
1881:32.13
1878:9.794
1870:32.14
1867:9.796
1859:32.14
1856:9.796
1846:32.14
1843:9.797
1835:32.14
1832:9.797
1828:Sydney
1824:32.14
1821:9.797
1813:32.15
1810:9.798
1800:32.15
1797:9.798
1793:Denver
1789:32.15
1786:9.799
1778:32.15
1775:9.800
1767:32.15
1764:9.800
1760:Madrid
1754:32.15
1751:9.800
1747:Athens
1743:32.16
1740:9.801
1732:32.16
1729:9.801
1725:Lisbon
1721:32.16
1718:9.802
1708:32.16
1705:9.803
1697:32.16
1694:9.803
1686:32.17
1683:9.804
1675:32.17
1672:9.804
1668:Skopje
1662:32.17
1659:9.806
1655:Ottawa
1651:32.18
1648:9.807
1644:Zurich
1640:32.18
1637:9.807
1629:32.18
1626:9.808
1616:32.18
1613:9.809
1605:32.18
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