# Standard gravity

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{{short description|Standard gravitational acceleration on Earth}}
{{broader|Gravity of Earth}}
The '''standard acceleration of gravity''' or '''standard acceleration of free fall''', often called simply '''standard gravity''', is the nominal [gravitational acceleration](/source/gravitational_acceleration) of an object in a [vacuum](/source/vacuum) near the surface of the [Earth](/source/Earth). It is a constant defined by [ISO standard 80000](/source/ISO%2FIEC_80000) as {{cvt|9.80665|m/s2||sigfig=7|disp=x| (about |)|comma=gaps}}, denoted typically by {{math|''ɡ''<sub>0</sub>}} (sometimes also {{math|''ɡ''<sub>n</sub>}}, {{math|''ɡ''<sub>e</sub>}},{{efn|Though this sometimes means the normal gravity at the equator, {{convert|9.7803267715|m/s2|abbr=on}}),<ref>{{cite journal | last1 = Moritz | first1 = Helmut | date = 2000 | title = Geodetic Reference System 1980 | journal = [Journal of Geodesy](/source/Journal_of_Geodesy) | volume = 74 | issue = 1 | pages = 128–133 | doi = 10.1007/s001900050278 | s2cid = 195290884 | url = https://link.springer.com/article/10.1007/s001900050278 | access-date = 2023-07-26 | quote = γe = 9.780 326 7715 m/s² normal gravity at equator | url-access = subscription }}</ref>}} or simply {{mvar|ɡ}}). This value was established by the third [General Conference on Weights and Measures](/source/General_Conference_on_Weights_and_Measures) (1901, CR 70) and used to define the standard [weight](/source/weight) of an object as the product of its mass and this nominal [acceleration](/source/acceleration).<ref>{{cite report |editor1-first=Barry N.|editor1-last=Taylor|editor2-first=Ambler|editor2-last=Thompson |date=March 2008 |title=The international system of units (SI) |url=https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication330e2008.pdf|publisher=[National Institute of Standards and Technology](/source/National_Institute_of_Standards_and_Technology) |page=52 |docket=NIST special publication 330, 2008 edition }}</ref><ref>{{cite book |url=http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf#page=51 |title=The International System of Units (SI) |publisher=[International Bureau of Weights and Measures](/source/International_Bureau_of_Weights_and_Measures) |edition=8th |year=2006 |isbn=92-822-2213-6 |pages=142–143}}</ref> The acceleration of a body near the surface of the Earth is due to the combined effects of [gravity](/source/gravity) and [centrifugal acceleration](/source/centrifugal_force) from the rotation of the Earth (but the latter is small enough to be negligible for most purposes); the total (the apparent gravity) is about 0.5% greater at the [poles](/source/geographical_pole) than at the [Equator](/source/Equator).<ref name="Boynton">{{cite conference
|first=Richard
|last=Boynton
|title=''Precise Measurement of Mass''
|book-title=Sawe Paper No. 3147
|publisher=S.A.W.E., Inc.
|date=2001
|location=Arlington, Texas
|url=http://www.space-electronics.com/Literature/Precise_Measurement_of_Mass.PDF
|access-date=2007-01-21
|archive-date=2007-02-27
|archive-url=https://web.archive.org/web/20070227132140/http://www.space-electronics.com/Literature/Precise_Measurement_of_Mass.PDF
|url-status=dead
}}</ref><ref>[https://curious.astro.cornell.edu/question.php?number=310 "Curious About Astronomy?"], Cornell University, retrieved June 2007</ref>

Although the symbol {{math|''ɡ''}} is sometimes used for standard gravity, {{math|''ɡ''}} (without a suffix) can also mean the local acceleration due to local gravity and centrifugal acceleration, which varies depending on one's position on Earth (see [Earth's gravity](/source/Earth's_gravity)). The symbol {{math|''ɡ''}} should not be confused with {{math|''G''}}, the [gravitational constant](/source/gravitational_constant), or g, the symbol for [gram](/source/gram). The {{math|''ɡ''}} is also used as a unit for any form of acceleration, with the value defined as above ({{xref|see also: [g-force](/source/g-force)}}).

The value of {{math|''ɡ''<sub>0</sub>}} defined above is a nominal midrange value on Earth, originally based on the acceleration of a body in free fall at sea level at a [geodetic latitude](/source/latitude) of 45°. Although the actual acceleration of free fall on Earth varies according to location, the above standard figure is always used for [metrological](/source/metrological) purposes. In particular, since it is the ratio of the [kilogram-force](/source/kilogram-force) and the [kilogram](/source/kilogram), its numeric value when expressed in [coherent](/source/Coherence_(units_of_measurement)) SI units is the ratio of the kilogram-force and the [newton](/source/newton_(unit)), two [units of force](/source/Force).

== History ==
Already in the early days of its existence, the [International Committee for Weights and Measures](/source/International_Committee_for_Weights_and_Measures) (CIPM) proceeded to define a standard [thermometric](/source/Thermometer) scale, using the [boiling point](/source/boiling_point) of water. Since the boiling point varies with the [atmospheric pressure](/source/atmospheric_pressure), the CIPM needed to define a standard atmospheric pressure. The definition they chose was based on the weight of a column of [mercury](/source/mercury_(element)) of 760&nbsp;mm. But since that weight depends on the local gravity, they now also needed a standard gravity. The 1887 CIPM meeting decided as follows:

{{quote|The value of this '''''standard acceleration due to gravity''''' is equal to the acceleration due to gravity at the International Bureau (alongside the [Pavillon de Breteuil](/source/Pavillon_de_Breteuil)) divided by 1.0003322, the theoretical coefficient required to convert to a latitude of 45° at sea level.<ref>{{cite book |title=From Artefacts to Atoms: The BIPM and the Search for Ultimate Measurement Standards |author=Terry Quinn |page=127 |publisher=[Oxford University Press](/source/Oxford_University_Press) |year=2011 |isbn=978-0-19-530786-3}}</ref>}}

All that was needed to obtain a numerical value for standard gravity was now to measure the gravitational strength at the [International Bureau](/source/International_Bureau_of_Weights_and_Measures). This task was given to Gilbert Étienne Defforges of the Geographic Service of the French Army. The value he found, based on measurements taken in March and April 1888, was 9.80991(5)&nbsp;m⋅s<sup>−2</sup>.<ref>{{cite conference |author=M. Amalvict |chapter=Chapter 12. Absolute gravimetry at BIPM, Sèvres (France), at the time of Dr. Akihiko Sakuma |title=Gravity, Geoid and Earth Observation: IAG Commission 2: Gravity Field |editor=Stelios P. Mertikas |pages=84–85 |publisher=Springer |year=2010 |isbn=978-3-642-10634-7}}</ref>

This result formed the basis for determining the value still used today for standard gravity. The third [General Conference on Weights and Measures](/source/General_Conference_on_Weights_and_Measures), held in 1901, adopted a resolution declaring as follows:

{{quote|The value adopted in the International Service of Weights and Measures for the standard acceleration due to Earth's gravity is 980.665&nbsp;cm/s<sup>2</sup>, value already stated in the laws of some countries.<ref>{{cite web |title=Resolution of the 3rd CGPM (1901) |url=https://www.bipm.org/en/committees/cg/cgpm/3-1901/resolution-2 |publisher=[BIPM](/source/BIPM) |access-date=July 19, 2015}}</ref>}}

The numeric value adopted for {{math|''ɡ''<sub>0</sub>}} was, in accordance with the 1887 CIPM declaration, obtained by dividing Defforges's result – 980.991&nbsp;cm⋅s<sup>−2</sup> in the [cgs](/source/cgs) system then ''en vogue'' – by  1.0003322 while not taking more digits than are warranted considering the uncertainty in the result.

== Conversions ==
{{Acceleration conversions}}

== See also ==
* [Gravity of Earth](/source/Gravity_of_Earth)
* [Gravity map](/source/Gravity_map)
* [Seconds pendulum](/source/Seconds_pendulum)
* [Theoretical gravity](/source/Theoretical_gravity)

== Notes ==
{{notelist}}

== References ==
{{reflist}}

Category:Physical quantities
Category:Gravity
Category:Units of acceleration
Category:Constants

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Adapted from the Wikipedia article [Standard gravity](https://en.wikipedia.org/wiki/Standard_gravity) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Standard_gravity?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.
