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Standard gravity

From Wikipedia, the free encyclopedia

Thestandard acceleration of gravityorstandard acceleration of free fall,often called simplystandard gravityand denoted byɡ0orɡn,is the nominalgravitational accelerationof an object in avacuumnear the surface of theEarth.It is a constantdefined by standardas9.80665m/s2(about32.17405ft/s2). This value was established by the 3rdGeneral Conference on Weights and Measures(1901, CR 70) and used to define the standardweightof an object as the product of its mass and this nominalacceleration.[1][2]The acceleration of a body near the surface of the Earth is due to the combined effects ofgravityandcentrifugal accelerationfrom 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 thepolesthan at theEquator.[3][4]

Although the symbolɡis sometimes used for standard gravity,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 (seeEarth's gravity). The symbolɡshould not be confused withG,thegravitational constant,or g, the symbol forgram.Theɡis also used as a unit for any form of acceleration, with the value defined as above; seeg-force.

The value ofɡ0defined above is a nominal midrange value on Earth, originally based on the acceleration of a body in free fall at sea level at ageodetic latitudeof 45°. Although the actual acceleration of free fall on Earth varies according to location, the above standard figure is always used formetrologicalpurposes. In particular, since it is the ratio of thekilogram-forceand thekilogram,its numeric value when expressed incoherentSI units is the ratio of the kilogram-force and thenewton,twounits of force.

History

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Already in the early days of its existence, theInternational Committee for Weights and Measures(CIPM) proceeded to define a standardthermometricscale, using theboiling pointof water. Since the boiling point varies with theatmospheric pressure,the CIPM needed to define a standard atmospheric pressure. The definition they chose was based on the weight of a column ofmercuryof 760 mm. But since that weight depends on the local gravity, they now also needed a standard gravity. The 1887 CIPM meeting decided as follows:

The value of thisstandard acceleration due to gravityis equal to the acceleration due to gravity at the International Bureau (alongside thePavillon de Breteuil) divided by 1.0003322, the theoretical coefficient required to convert to a latitude of 45° at sea level.[5]

All that was needed to obtain a numerical value for standard gravity was now to measure the gravitational strength at theInternational Bureau.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) m⋅s−2.[6]

This result formed the basis for determining the value still used today for standard gravity. The thirdGeneral Conference on Weights and Measures,held in 1901, adopted a resolution declaring as follows:

The value adopted in the International Service of Weights and Measures for the standard acceleration due to Earth's gravity is 980.665 cm/s2,value already stated in the laws of some countries.[7]

The numeric value adopted forɡ0was, in accordance with the 1887 CIPM declaration, obtained by dividing Defforges's result – 980.991 cm⋅s−2in thecgssystem thenen vogue– by 1.0003322 while not taking more digits than warranted considering the uncertainty in the result.

Conversions

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Conversions between common units of acceleration
Base value (Gal,or cm/s2) (ft/s2) (m/s2) (Standard gravity,g0)
1 Gal, or cm/s2 1 0.0328084 0.01 1.01972×10−3
1 ft/s2 30.4800 1 0.304800 0.0310810
1 m/s2 100 3.28084 1 0.101972
1g0 980.665 32.1740 9.80665 1

See also

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References

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  1. ^Taylor, Barry N.; Thompson, Ambler, eds. (March 2008).The international system of units (SI)(PDF)(Report).National Institute of Standards and Technology.p. 52. NIST special publication 330, 2008 edition.
  2. ^The International System of Units (SI)(PDF)(8th ed.).International Bureau of Weights and Measures.2006. pp. 142–143.ISBN92-822-2213-6.
  3. ^Boynton, Richard (2001)."Precise Measurement of Mass"(PDF).Sawe Paper No. 3147.Arlington, Texas: S.A.W.E., Inc.Retrieved2007-01-21.
  4. ^"Curious About Astronomy?",Cornell University, retrieved June 2007
  5. ^Terry Quinn (2011).From Artefacts to Atoms: The BIPM and the Search for Ultimate Measurement Standards.Oxford University Press.p. 127.ISBN978-0-19-530786-3.
  6. ^M. Amalvict (2010). "Chapter 12. Absolute gravimetry at BIPM, Sèvres (France), at the time of Dr. Akihiko Sakuma". In Stelios P. Mertikas (ed.).Gravity, Geoid and Earth Observation: IAG Commission 2: Gravity Field.Springer. pp. 84–85.ISBN978-3-642-10634-7.
  7. ^"Resolution of the 3rd CGPM (1901)".BIPM.RetrievedJuly 19,2015.