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| {{double image|right|GRACE globe 1.png|150|GRACE globe 2.png|150|Earth's gravity measured by NASA's [[Gravity Recovery and Climate Experiment|GRACE]] mission, showing deviations from the [[theoretical gravity]] of an idealized smooth Earth, the so-called [[earth ellipsoid]]. Red shows the areas where gravity is stronger than the smooth, standard value, and blue reveals areas where gravity is weaker. ('''[[:Image:GRACE globe animation.gif|Animated version]].''')<ref>{{cite web|last=NASA/JPL/University of Texas Center for Space Research|title=PIA12146: GRACE Global Gravity Animation|url=http://photojournal.jpl.nasa.gov/catalog/PIA12146|work=Photojournal|publisher=NASA Jet Propulsion Laboratory|accessdate=30 December 2013}}</ref>}}
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| The '''gravity of Earth''', denoted '''''g''''', refers to the [[acceleration]] that the [[Earth]] imparts to objects on or near its [[elevation|surface]]. In [[International System of Units|SI units]] this acceleration is measured in [[meters per second squared]] (in symbols, [[Metre|m]]/[[Second|s]]<sup>2</sup> or m·s<sup>−2</sup>) or equivalently in [[Newton (unit)|newtons]] per [[kilogram]] (N/kg or N·kg<sup>−1</sup>). It has an approximate value of 9.81 m/s<sup>2</sup>, which means that, ignoring the effects of [[air resistance]], the [[speed]] of an object [[free fall|falling freely]] near the Earth's surface will increase by about {{convert|9.81|m|ft}} per second every second. This quantity is sometimes referred to informally as ''little g'' (in contrast, the [[gravitational constant]] ''G'' is referred to as ''big G''). | |
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| There is a direct relationship between [[gravitational acceleration]] and the downwards [[weight]] force experienced by objects on Earth, given by the equation {{nowrap|[[Newton's laws of motion|''F'' {{=}} ''ma'']]}} ({{nowrap|''force'' {{=}} ''mass'' × ''acceleration''}}). However, other factors such as the rotation of the Earth also contribute to the net acceleration.
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| The precise strength of Earth's gravity varies depending on location. The nominal "average" value at the Earth's surface, known as {{nowrap|[[standard gravity]]}} is, by definition, 9.80665 m/s<sup>2</sup>{{Citation needed|date=December 2013}} (about 32.1740 ft/s<sup>2</sup>). This quantity is denoted variously as ''g''<sub>n</sub>, ''g''<sub>e</sub> (though this sometimes means the normal equatorial value on Earth, 9.78033 m/s<sup>2</sup>), ''g''<sub>0</sub>, gee, or simply ''g'' (which is also used for the variable local value). The symbol ''g'' should not be confused with g, the abbreviation for gram (which is not italicized).<ref>{{cite paper
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| |author=Bureau International des Poids et Mesures
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| |year=2006
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| |url=http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf
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| |title=The International System of Units (SI)
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| |version=8th ed.
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| |accessdate=2009-11-25
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| |chapter=Chapter 5
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| |quote=Unit names are normally printed in roman (upright) type ... Symbols for quantities are generally single letters set in an italic font, although they may be qualified by further information in subscripts or superscripts or in brackets.}}</ref><ref>{{cite web
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| |url=http://physics.nist.gov/cuu/Units/checklist.html
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| |quote=Variables and quantity symbols are in italic type. Unit symbols are in roman type.
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| |title=SI Unit rules and style conventions
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| |author=
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| |date=September 2004
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| |work=
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| |publisher=National Institute For Standards and Technology (USA)
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| |accessdate=2009-11-25}}</ref>
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| ==Variation in gravity and apparent gravity==
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| A perfect [[sphere]] of [[shell theorem|spherically uniform density]] (density varies solely with distance from centre) would produce a gravitational field of uniform magnitude at all points on its [[surface]], always pointing directly towards the sphere's centre. However, the Earth deviates slightly from this ideal, and there are consequently slight deviations in both the magnitude and direction of gravity across its surface. Furthermore, the [[net force]] exerted on an object due to the Earth, called "effective gravity" or "apparent gravity", varies due to the presence of other factors, such as inertial response to the Earth's rotation. A scale or [[plumb bob]] measures only this effective gravity.
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| Parameters affecting the apparent or actual strength of Earth's gravity include [[latitude]], [[altitude]], and the local [[topography]] and [[geology]].
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| Apparent gravity on the earth's surface varies by around 0.7%, from 9.7639 m/s<sup>2</sup> on the [[Nevado Huascarán]] mountain in Peru to 9.8337 m/s<sup>2</sup> at the surface of the [[Arctic Ocean]].<ref>{{cite web|title=New ultra-high resolution picture of Earth's gravity field|url=http://onlinelibrary.wiley.com/doi/10.1002/grl.50838/abstract|work=Geophysical Research Letters DOI: 10.1002/grl.50838|author=Hirt,Claessens et. al.|date=Aug 6, 2013}}</ref> In large cities, it ranges from 9.766 in [[Kuala Lumpur]], [[Mexico City]], and [[Singapore]] to 9.825 in [[Oslo]] and [[Helsinki]].
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| ===Latitude===
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| [[Image:Southern ocean gravity hg.png|thumb|right|300px|The differences of Earth's gravity around the Antarctic continent.]]
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| The surface of the Earth is rotating, so it is [[Non-inertial reference frame|not an inertial frame of reference]]. At latitudes nearer the Equator, the outward [[Centrifugal force (rotating reference frame)|centrifugal force]] produced by Earth's rotation is larger than at polar latitudes. This counteracts the Earth's gravity to a small degree – up to a maximum of 0.3% at the Equator – and reduces the apparent downward acceleration of falling objects.
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| The second major reason for the difference in gravity at different latitudes is that the Earth's [[equatorial bulge]] (itself also caused by inertia) causes objects at the Equator to be farther from the planet's centre than objects at the poles. Because the force due to gravitational attraction between two bodies (the Earth and the object being weighed) varies inversely with the square of the distance between them, an object at the Equator experiences a weaker gravitational pull than an object at the poles.
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| In combination, the equatorial bulge and the effects of the Earth's inertia mean that sea-level gravitational acceleration increases from about 9.780 m·s<sup>−2</sup> at the Equator to about 9.832 m·s<sup>−2</sup> at the poles, so an object will weigh about 0.5% more at the poles than at the Equator.<ref>{{cite conference
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| |first=Richard
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| |last=Boynton
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| |title=''Precise Measurement of Mass''
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| |booktitle=Sawe Paper No. 3147
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| |publisher=S.A.W.E., Inc.
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| |year=2001
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| |location=Arlington, Texas
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| |url=http://www.space-electronics.com/Literature/Precise_Measurement_of_Mass.PDF
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| |accessdate=2007-01-21}}</ref><ref>[http://curious.astro.cornell.edu/question.php?number=310 "Curious About Astronomy?"], Cornell University, retrieved June 2007</ref>
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| The same two factors influence the direction of the effective gravity. Anywhere on Earth away from the Equator or poles, effective gravity points not exactly toward the centre of the Earth, but rather perpendicular to the surface of the [[geoid]], which, due to the flattened shape of the Earth, is somewhat toward the opposite pole. About half of the deflection is due to inertia, and half because the extra mass around the Equator causes a change in the direction of the true gravitational force relative to what it would be on a spherical Earth.
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| ===Altitude===
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| [[Image:Erdgvarp.png|thumb|The graph shows the variation in gravity relative to the height of an object]]
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| 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 {{convert|30000|ft|m|sigfig=1|disp=flip}} causes a weight decrease of about 0.29%. (An additional factor affecting apparent weight is the decrease in air density at altitude, which lessens an object's buoyancy.<ref>[http://www.npl.co.uk/reference/faqs/i-feel-'lighter'-when-up-a-mountain-but-am-i-(faq-mass-and-density) "I feel 'lighter' when up a mountain but am I?"], National Physical Laboratory FAQ</ref> This would increase a person's apparent weight at an altitude of 9,000 metres by about 0.08%)
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| 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 {{convert|400|km|mi}}, equivalent to a typical orbit of the [[Space Shuttle]], gravity is still nearly 90% as strong as at the Earth's surface. Weightlessness actually occurs because orbiting objects are in [[free-fall]].<ref>[http://science.nasa.gov/science-news/science-at-nasa/2003/24jan_micro-g/ "The G's in the Machine"], NASA, see "Editor's note #2"</ref>
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| The effect of ground elevation depends on the density of the ground (see [[#Slab correction|Slab correction]] section). A person flying at 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.
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| The following formula approximates the Earth's gravity variation with altitude:
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| :<math>g_h=g_0\left(\frac{r_e}{r_e+h}\right)^2</math>
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| Where
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| *''g<sub>h</sub>'' is the gravitational acceleration at height <math>h\,</math> above sea level.
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| *''r<sub>e</sub>'' is the [[Earth radius|Earth's mean radius]].
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| *''g<sub>0</sub>'' is the [[standard gravitational acceleration]].
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| This formula treats the Earth as a perfect sphere with a radially symmetric distribution of mass; a more accurate mathematical treatment is discussed below.
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| ===Depth===
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| {{See also|Shell theorem}}
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| An approximate depth dependence of density in the Earth can be obtained by assuming that the mass is spherically symmetric (it depends only on depth, not on latitude or longitude). In such a body, the gravitational acceleration is towards the center. The gravity at a radius ''r'' depends only on the mass inside the sphere of radius ''r''; all the contributions from outside cancel out. This is a consequence of the [[inverse-square law]] of gravitation. Another consequence is that the gravity is the same as if all the mass were concentrated at the center of the Earth. Thus, the gravitational acceleration at this radius is<ref>{{cite book|last=Tipler|first=Paul A.|title=Physics for scientists and engineers.|year=1999|publisher=W.H. Freeman/Worth Publishers|location=New York|isbn=9781572594913|pages=336–337|edition=4th ed.}}</ref>
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| :<math>g(r) = -\frac{GM(r)}{r^2}.</math>
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| where ''G'' is the [[gravitational constant]] and ''M(r)'' is the total mass enclosed within radius ''r''. If the Earth had a constant density ''ρ'', the mass would be {{nowrap|''M(r)'' {{=}} (4/3)π''ρr''<sup>3</sup>}} and the dependence of gravity on depth would be
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| :<math>g(r) = \frac{4\pi}{3} G \rho r.</math>
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| If the density decreased linearly with increasing radius from a density ''ρ''<sub>0</sub> at the centre to ''ρ''<sub>1</sub> at the surface, then {{nowrap|''ρ(r)'' {{=}} ρ<sub>0</sub> − (ρ<sub>0</sub> − ρ<sub>1</sub>) ''r'' / ''r''<sub>e</sub>}}, and the dependence would be
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| :<math>g(r) = \frac{4\pi}{3} G \rho_0 r - \pi G \left(\rho_0-\rho_1\right) \frac{r^2}{r_e}.</math>
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| The actual depth dependence of density and gravity, inferred from seismic travel times (see [[Adams–Williamson equation]]), is shown in the graphs below.
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| {|
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| |-
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| |[[Image:RadialDensityPREM.jpg|thumb|300px|right|Earth's radial density distribution according to the Preliminary Reference Earth Model (PREM).<ref name="prem">{{cite journal|author=A. M. Dziewonski, D. L. Anderson|pmc=411539|title=Preliminary reference Earth model |journal=Physics of the Earth and Planetary Interiors|year= 1981|volume=25|issue=4|pages=297–356|url=http://www.gps.caltech.edu/uploads/File/People/dla/DLApepi81.pdf|doi=10.1016/0031-9201(81)90046-7|issn=0031-9201}}</ref>]]
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| |[[Image:EarthGravityPREM.svg|thumb|300px|right|Earth's gravity according to the Preliminary Reference Earth Model (PREM).<ref name=prem/> Two models for a spherically symmetric Earth are included for comparison. The straight dashed line is for a constant density equal to the Earth's average density. The curved dotted line is for a density that decreases linearly from center to surface. The density at the centre 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.]]
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| |}
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| ===Local topography and geology===
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| {{See also|Physical geodesy}}
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| Local variations in [[topography]] (such as the presence of mountains) and [[geology]] (such as the density of rocks in the vicinity) cause fluctuations in the Earth's gravitational field, known as [[Gravity anomaly|gravitational anomalies]]. Some of these anomalies can be very extensive, resulting in bulges in [[sea level]], and throwing [[pendulum]] clocks out of synchronisation.
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| The study of these anomalies forms the basis of gravitational [[geophysics]]. The fluctuations are measured with highly sensitive [[gravimeter]]s, the effect of topography and other known factors is subtracted, and from the resulting data conclusions are drawn. Such techniques are now used by [[prospectors]] to find [[oil]] and [[mineral deposits]]. Denser rocks (often containing mineral [[ore]]s) cause higher than normal local gravitational fields on the Earth's surface. Less dense [[sedimentary rock]]s cause the opposite.
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| ===Other factors===
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| In air, objects experience a supporting [[buoyancy]] force which reduces the apparent strength of gravity (as measured by an object's weight). The magnitude of the effect depends on air density (and hence air pressure); see [[Apparent weight]] for details.
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| The gravitational effects of the [[Moon]] and the [[Sun]] (also the cause of the [[tide]]s) have a very small effect on the apparent strength of Earth's gravity, depending on their relative positions; typical variations are 2 µm/s<sup>2</sup> (0.2 [[Gal (unit)|mGal]]) over the course of a day.
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| ===Comparative gravities in various cities around the world===
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| The table below shows the gravitational acceleration in various cities around the world;<ref>[http://www.wolframalpha.com/widgets/view.jsp?id=d34e8683df527e3555153d979bcda9cf Gravitational Fields Widget as of Oct 25th, 2012] – [[WolframAlpha]]</ref> amongst these listed cities, it is lowest in Mexico City or Kuala Lumpur (9.776 m/s<sup>2</sup>) and highest in Anchorage, Alaska (9.826 m/s<sup>2</sup>).
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| {|style="text-align: left;" class="wikitable sortable collapsible collapsed"
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| |-
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| !width="110px" |Location !!Acceleration in m/s<sup>2</sup>
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| |-
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| |[[Amsterdam]]
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| |9.817
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| |-
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| |[[Anchorage]]
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| |9.826
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| |-
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| |[[Athens]]
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| |9.800
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| |-
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| |[[Auckland]]
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| |9.799
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| |-
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| |[[Bangkok]]
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| |9.780
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| |-
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| |[[Brussels]]
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| |9.815
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| |-
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| |[[Buenos Aires]]
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| |9.797
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| |-
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| |[[Calcutta]]
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| |9.785
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| |-
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| |[[Cape Town]]
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| |9.796
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| |-
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| |[[Chicago]]
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| |9.804
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| |-
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| |[[Copenhagen]]
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| |9.821
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| |-
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| |[[Denver]]
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| |9.798
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| |-
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| |[[Frankfurt]]
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| |9.814
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| |-
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| |[[Havana]]
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| |9.786
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| |-
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| |[[Helsinki]]
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| |9.825
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| |-
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| |[[Hong Kong]]
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| |9.785
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| |-
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| |[[Istanbul]]
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| |9.808
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| |-
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| |[[Jakarta]]
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| |9.777
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| |-
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| |[[Kuala Lumpur]]
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| |9.776
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| |-
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| |[[Kuwait]]
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| |9.792
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| |-
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| |[[Lisbon]]
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| |9.801
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| |-
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| |[[London]]
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| |9.816
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| |-
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| |[[Los Angeles]]
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| |9.796
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| |-
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| |[[Madrid]]
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| |9.800
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| |-
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| |[[Manila]]
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| |9.780
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| |-
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| |[[Mexico City]]
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| |9.776
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| |-
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| |[[Montréal]]
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| |9.809
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| |-
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| |[[New York City]]
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| |9.802
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| |-
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| |[[Nicosia]]
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| |9.797
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| |-
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| |[[Oslo]]
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| |9.825
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| |-
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| |[[Ottawa]]
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| |9.806
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| |-
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| |[[Paris]]
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| |9.809
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| |-
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| |[[Rio de Janeiro]]
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| |9.788
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| |-
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| |[[Rome]]
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| |9.803
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| |-
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| |[[Helsinki]]
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| |9.825
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| |-
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| |[[Seattle]]
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| |9.811
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| |-
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| |[[Singapore]]
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| |9.776
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| |-
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| |[[Skopje]]
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| |9.804
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| |-
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| |[[Stockholm]]
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| |9.818
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| |-
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| |[[Sydney]]
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| |9.797
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| |-
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| |[[Taipei]]
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| |9.790
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| |-
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| |[[Tokyo]]
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| |9.798
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| |-
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| |[[Vancouver]]
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| |9.809
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| |-
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| |[[Washington, D.C.]]
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| |9.801
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| |-
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| |[[Wellington]]
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| |9.803
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| |-
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| |[[Zurich]]
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| |9.807
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| |}
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| ===Mathematical models===
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| ====Latitude model====
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| If the terrain is at sea level, we can estimate ''g'':
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| :<math>g_{\phi}=9.780327 \left(1+0.0053024\sin^2 \phi-0.0000058\sin^2 2\phi \right) \frac{\mathrm{m}}{\mathrm{s}^2} </math>
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| where
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| :<math> \ g_{\phi}</math> = acceleration in m·s<sup>−2</sup> at latitude :<math>\ \phi</math>
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| This is the [[International Gravity Formula]] 1967, the 1967 Geodetic Reference System Formula, Helmert's equation or Clairaut's formula.<ref name="IGF">[http://geophysics.ou.edu/solid_earth/notes/potential/igf.htm International Gravity formula]</ref>
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| Helmert's equation may be written equivalently to the version above as either:
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| :<math>\ g_{\phi}= \left(9.8061999 - 0.0259296\cos(2\phi) + 0.0000567\cos^2(2\phi)\right)\,\frac{\mathrm{m}}{\mathrm{s}^2}</math>
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| or
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| :<math>\ g_{\phi}= \left( 9.780327 + 0.0516323\sin^2(\phi) + 0.0002269\sin^4(\phi) \right)\,\frac{\mathrm{m}}{\mathrm{s}^2}</math>
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| An alternate formula for ''g'' as a function of latitude is the WGS ([[World Geodetic System]]) 84 Ellipsoidal [[gravity formula|Gravity Formula]]:
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| :<math>\ g_{\phi}= \left(9.7803267714 ~ \frac {1 + 0.00193185138639\sin^2\phi}{\sqrt{1 - 0.00669437999013\sin^2\phi}} \right)\,\frac{\mathrm{m}}{\mathrm{s}^2}</math>
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| The difference between the WGS-84 formula and Helmert's equation is less than 0.68·10<sup>−6</sup> m·s<sup>−2</sup>.
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| ====Free air correction====
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| The first correction to be applied to the model is the free air correction (FAC) that accounts for heights above sea level. Near the surface of the Earth (sea level), gravity decreases with height such that linear extrapolation would give zero gravity at a height of one half the radius is 9.8 m·s<sup>−2</sup> per 3,200 km.<ref>The rate is calculated by differentiating ''g''(''r'') with respect to ''r'' and evaluating at ''r''=''r''<sub>Earth</sub>.</ref>
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| Using the mass and radius of the [[Earth]]:
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| :<math>r_\mathrm{Earth}= 6.371 \times 10^{6}\,\mathrm{m} </math>
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| :<math>m_\mathrm{Earth}= 5.9736 \times 10^{24}\,\mathrm{kg} </math>
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| The FAC correction factor (Δ''g'') can be derived from the definition of the acceleration due to gravity in terms of G, the [[Gravitational Constant]] (see Estimating ''g'' from the law of universal gravitation, below):
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| :<math>g_0 = G \, m_\mathrm{Earth} / r_\mathrm{Earth}^2 = 9.8331\,\frac{\mathrm{m}}{\mathrm{s}^2}</math>
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| where:
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| :<math>G = 6.67428 \times 10^{-11}\,\frac{\mathrm{m}^3}{\mathrm{kg}\cdot\mathrm{s}^2}.</math>
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| At a height ''h'' above the nominal surface of the earth ''g<sub>h</sub>'' is given by:
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| :<math>g_h = G \, m_\mathrm{Earth} / \left( r_\mathrm{Earth} + h \right) ^2</math>
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| So the FAC for a height ''h'' above the nominal earth radius can be expressed:
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| :<math>\Delta g_h = \left [ G \, m_\mathrm{Earth} / \left( r_\mathrm{Earth} + h \right) ^2 \right ] - \left[G \, m_\mathrm{Earth} / r_\mathrm{Earth}^2 \right]</math>
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| This expression can be readily used for programming or inclusion in a spreadsheet. Collecting terms, simplifying and neglecting small terms (''h''<<''r''<sub>Earth</sub>), however yields the good approximation:
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| :<math>\Delta g_h \approx - \, \dfrac{ G \, m_\mathrm{Earth}}{ r_\mathrm{Earth} ^2} \times \dfrac{ 2 \,h}{r_\mathrm{Earth}}</math>
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| Using the numerical values above and for a height ''h'' in metres:
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| :<math>\Delta g_h \approx - 3.084 \times 10^{-6}\, h</math>
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| Grouping the latitude and FAC altitude factors the expression most commonly found in the literature is:
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| :<math>g_{\phi, h}=9.780 327 \left( 1+0.0053024\sin^2 \phi-0.0000058\sin^2 2\phi \right) - 3.086 \times 10^{-6}h</math>
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| | |
| where <math> \ g_{\phi, h}</math> = acceleration in m·s<sup>−2</sup> at latitude <math>\ \phi</math> and altitude ''h'' in metres. Alternatively (with the same units for ''h'') the expression can be grouped as follows:
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| :<math>g_{\phi, h}=9.780327 \left[ \left( 1+0.0053024\sin^2 \phi-0.0000058\sin^2 2\phi \right) - 3.155 \times 10^{-7}h \right] \,\frac{\mathrm{m}}{\mathrm{s}^2} </math>
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| | |
| ====Slab correction====
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| ::<small>Note: The section uses the [[Galileo (unit)|galileo]] (symbol: "Gal"), which is a cgs unit for acceleration of 1 centimeter/second<sup>2</sup>.</small>
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| For flat terrain above sea level a second term is added for the gravity due to the extra mass; for this purpose the extra mass can be approximated by an infinite horizontal slab, and we get 2π''G'' times the mass per unit area, i.e. 4.2{{e|−10}} m<sup>3</sup>·s<sup>−2</sup>·kg<sup>−1</sup> (0.042 μGal·kg<sup>−1</sup>·m<sup>2</sup>)) (the Bouguer correction). For a mean rock density of 2.67 g·cm<sup>−3</sup> this gives 1.1{{e|−6}} s<sup>−2</sup> (0.11 mGal·m<sup>−1</sup>). Combined with the free-air correction this means a reduction of gravity at the surface of ca. 2 µm·s<sup>−2</sup> (0.20 mGal) for every metre of elevation of the terrain. (The two effects would cancel at a surface rock density of 4/3 times the average density of the whole earth. The density of the whole earth is 5.515 g·cm<sup>−3</sup>, so standing on a slab of something like iron whose density is over 7.35 g·cm<sup>−3</sup> would increase one's weight.)
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| For the gravity below the surface we have to apply the free-air correction as well as a double Bouguer correction. With the infinite slab model this is because moving the point of observation below the slab changes the gravity due to it to its opposite. Alternatively, we can consider a [[Shell theorem|spherically symmetrical Earth]] and subtract from the mass of the Earth that of the shell outside the point of observation, because that does not cause gravity inside. This gives the same result.
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| ==Estimating ''g'' from the law of universal gravitation==
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| From the [[law of universal gravitation]], the force on a body acted upon by Earth's gravity is given by
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| :<math>F = G \frac{m_1 m_2}{r^2}=\left(G \frac{m_1}{r^2}\right) m_2</math>
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| where ''r'' is the distance between the centre of the Earth and the body (see below), and here we take ''m''<sub>1</sub> to be the mass of the Earth and ''m''<sub>2</sub> to be the mass of the body.
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| Additionally, [[Newton's second law]], ''F'' = ''ma'', where ''m'' is mass and ''a'' is acceleration, here tells us that
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| :<math>F = m_2g\,</math>
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| Comparing the two formulas it is seen that:
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| :<math>g=G \frac {m_1}{r^2}</math>
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| So, to find the acceleration due to gravity at sea level, substitute the values of the [[gravitational constant]], ''G'', the Earth's [[mass]] (in kilograms), ''m''<sub>1</sub>, and the Earth's [[radius]] (in metres), ''r'', to obtain the value of ''g'':
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| :<math>g=G \frac {m_1}{r^2}=(6.6742 \times 10^{-11}) \frac{5.9736 \times 10^{24}}{(6.37101 \times 10^6)^2}=9.822 \mbox{m} \cdot \mbox{s}^{-2}</math>
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| Note that 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 ''r''.
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| The value obtained agrees approximately with the measured value of ''g''. The difference may be attributed to several factors, mentioned above under "Variations":
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| *The Earth is not [[Homogeneous (chemistry)|homogeneous]]
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| *The Earth is not a perfect sphere, and an average value must be used for its radius
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| *This calculated value of ''g'' 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 "used up" in providing the [[centripetal acceleration]]
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| There are significant uncertainties in the values of ''r'' and ''m''<sub>1</sub> as used in this calculation, and the value of ''[[Gravitational constant|G]]'' is also rather difficult to measure precisely.
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| If ''G'', ''g'' and ''r'' are known then a reverse calculation will give an estimate of the mass of the Earth. This method was used by [[Henry Cavendish]].
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| ==Comparative gravities of the Earth, Sun, Moon, and planets==
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| The table below shows comparative gravitational accelerations at the surface of the Sun, the Earth's moon, each of the planets in the Solar System and their major moons, Pluto, and Eris. The "surface" is taken to mean the cloud tops of the [[gas giants]] (Jupiter, Saturn, Uranus and Neptune). For the Sun, the surface is taken to mean the [[photosphere]]. The values in the table have not been de-rated for the inertia effect of planet rotation (and cloud-top wind speeds for the gas giants) and therefore, generally speaking, are similar to the actual gravity that would be experienced near the poles. For reference the time it would take an object to fall 100 metres, the height of a skyscraper, is shown, along with the maximum speed reached. Air resistance is neglected.
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| {|class="wikitable sortable"
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| |-
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| !Body
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| !data-sort-type="number"|Multiple of<br>Earth gravity
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| !data-sort-type="number"|m/s<sup>2</sup>
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| !data-sort-type="number" colspan=2|Time to fall 100 m and<br/>maximum speed reached<!-- Note: limited decimal places are shown for this field because it's meant to help with intuition and smaller amounts are difficult to imagine -->
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| |-
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| |[[Sun]]
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| |27.90
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| |274.1
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| |0.85 s || {{convert|843|km/h|abbr=on}}
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| |-
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| |[[Mercury (planet)|Mercury]]
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| |0.3770
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| |3.703
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| |7.4 s || {{convert|98|km/h|abbr=on}}
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| |-
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| |[[Venus]]
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| |0.9032
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| |8.872
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| |4.8 s || {{convert|152|km/h|abbr=on}}
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| |-
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| |[[Earth]]
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| |1
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| |9.8067<span style="margin-left:0.2em"><ref></span>This value excludes the adjustment for centrifugal force due to Earth's rotation and is therefore greater than the 9.80665 m/s<sup>2</sup><span> value of [[standard gravity]].</ref>
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| |4.5 s || {{convert|159|km/h|abbr=on}}
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| |-
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| |[[Moon]]
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| |0.1655
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| |1.625
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| |11.1 s || {{convert|65|km/h|abbr=on}}
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| |-
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| |[[Mars]]
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| |0.3895
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| |3.728
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| |7.3 s || {{convert|98|km/h|abbr=on}}
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| |-
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| |[[Jupiter]]
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| |2.640
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| |25.93
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| |2.8 s || {{convert|259|km/h|abbr=on}}
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| |-
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| |[[Io (moon)|Io]]
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| |0.182
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| |1.789
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| |10.6 s || {{convert|68|km/h|abbr=on}}
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| |-
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| |[[Europa (moon)|Europa]]
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| |0.134
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| |1.314
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| |12.3 s || {{convert|58|km/h|abbr=on}}
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| |-
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| |[[Ganymede (moon)|Ganymede]]
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| |0.145
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| |1.426
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| |11.8 s || {{convert|61|km/h|abbr=on}}
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| |-
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| |[[Callisto (moon)|Callisto]]
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| |0.126
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| |1.24
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| |12.7 s || {{convert|57|km/h|abbr=on}}
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| |-
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| |[[Saturn]]
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| |1.139
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| |11.19
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| |4.2 s || {{convert|170|km/h|abbr=on}}
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| |-
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| |[[Titan (moon)|Titan]]
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| |0.138
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| |1.3455
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| |12.2 s || {{convert|59|km/h|abbr=on}}
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| |-
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| |[[Uranus]]
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| |0.917
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| |9.01
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| |4.7 s || {{convert|153|km/h|abbr=on}}
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| |-
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| |[[Titania (moon)|Titania]]
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| |0.039
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| |0.379
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| |23.0 s || {{convert|31|km/h|abbr=on}}
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| |-
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| |[[Oberon (moon)|Oberon]]
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| |0.035
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| |0.347
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| |24.0 s || {{convert|30|km/h|abbr=on}}
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| |-
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| |[[Neptune]]
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| |1.148
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| |11.28
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| |4.2 s || {{convert|171|km/h|abbr=on}}
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| |-
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| |[[Triton (moon)|Triton]]
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| |0.079
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| |0.779
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| |16.0 s || {{convert|45|km/h|abbr=on}}
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| |-
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| |[[Pluto]]
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| |0.0621
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| |0.610
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| |18.1 s || {{convert|40|km/h|abbr=on}}
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| |-
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| |[[Eris (dwarf planet)|Eris]]
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| |0.0814 (approx.)
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| |0.8 (approx.)
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| |15.8 s || {{convert|46|km/h|abbr=on}}
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| |}
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| ==See also==
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| {{Portal|Gravitation}}
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| *[[Earth's magnetic field]]
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| *[[Gravitation]]
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| *[[Gravity anomaly]], [[Bouguer anomaly]]
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| *[[Gravitation of the Moon]]
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| *[[Gravitational acceleration]]
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| *[[Gravity Field and Steady-State Ocean Circulation Explorer]]
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| *[[Gravity Recovery and Climate Experiment]]
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| *[[Newton's law of universal gravitation]]
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| ==References==
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| {{Reflist|2}}
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| ==External links==
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| *[http://hyperphysics.phy-astr.gsu.edu/hbase/orbv.html Altitude gravity calculator]
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| *[http://www.csr.utexas.edu/grace/ GRACE – Gravity Recovery and Climate Experiment]
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| *[http://geodesy.curtin.edu.au/research/models/GGMplus/ GGMplus high resolution data (2013)]
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| {{Geophysics navbox}}
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| [[Category:Gravimetry]]
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| [[Category:Gravitation]]
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| [[Category:Earth]]
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| [[eo:Gravita akcelo]]
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