Acceleration due to gravity: Difference between revisions
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An object with mass ''m'' near the surface of the Earth experiences a downward gravitational | |||
force of magnitude ''mg'', where ''g'' is the '''acceleration due to gravity'''. The quantity ''g'' has the dimension of acceleration, m | |||
s<sup>−2</sup>, hence its name. | |||
[[Gravitation#Newton's law of universal gravitation|Newtons's gravitational law]] gives the following formula for ''g'', | |||
:<math> | |||
g = G \frac{M_{\mathrm{E}}}{R^2_{\mathrm{E}}}, | |||
</math> | |||
where ''G'' is the universal gravitational constant, ''G'' = 6.67428 | |||
× 10<sup>−11</sup> | |||
m<sup>3</sup> kg<sup>−1</sup> s<sup>−2</sup>, | |||
''M''<sub>E</sub> is the total mass of the Earth, and ''R''<sub>E</sub> | |||
is the radius of the Earth. This equation gives a good approximation, | |||
but is not exact. Deviations are caused by the [[centrifugal force]] | |||
due to the rotation of the Earth around its axis, non-sphericity of the | |||
Earth, and the non-homogeneity of the composition of the Earth. These | |||
effects are the cause that ''g'' varies roughly ±0.01 around the | |||
value 9.8 m s<sup>−2</sup> from place to place on the surface of the Earth. | |||
The quantity ''g'' is therefore referred to as the ''local gravitational | |||
acceleration''. | |||
The 3rd General Conference on Weights and Measures (Conférence Générale | |||
des Poids et Mesures, CGPM) defined in 1901 a standard value denoted as | |||
''g<sub>n</sub>''.<ref>[http://physics.nist.gov/Document/sp330.pdf The | |||
International System of Units (SI), NIST Special Publication 330, 2001 | |||
Edition] (pdf page 29 of 77 pdf pages) | |||
</ref><ref>[http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf#page=51 | |||
Bureau International des Poids et Mesures] (pdf page 51 of 88 pdf | |||
pages)</ref> The value of the ''standard acceleration due to gravity'' ''g<sub>n</sub>'' | |||
is 9.80656 m s<sup>−2</sup>. | |||
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In the [[science]]s, the term '''acceleration due to gravity''' refers to a quantity '''g''' describing the strength of the local gravitational field. The quantity has dimension of [[acceleration]], i.e., m/s<sup>2</sup> (length per time squared) whence its name. | In the [[science]]s, the term '''acceleration due to gravity''' refers to a quantity '''g''' describing the strength of the local gravitational field. The quantity has dimension of [[acceleration]], i.e., m/s<sup>2</sup> (length per time squared) whence its name. | ||
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Any object of [[mass]] ''m'' near the [[Earth]] (for which the [[altitude]] ''h'' << ''R''<sub>Earth</sub>) is subject to a [[force]] ''m g'' in the downward direction that causes an [[acceleration]] of magnitude '''g<sub>n</sub>''' toward the surface of the earth. This value serves as an excellent approximation for the local acceleration due to [[gravitation]] at the surface of the earth, although it is not exact and the actual acceleration '''g''' varies slightly between different locations around the world. | Any object of [[mass]] ''m'' near the [[Earth]] (for which the [[altitude]] ''h'' << ''R''<sub>Earth</sub>) is subject to a [[force]] ''m g'' in the downward direction that causes an [[acceleration]] of magnitude '''g<sub>n</sub>''' toward the surface of the earth. This value serves as an excellent approximation for the local acceleration due to [[gravitation]] at the surface of the earth, although it is not exact and the actual acceleration '''g''' varies slightly between different locations around the world. | ||
--> | |||
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More generally, the acceleration due to gravity refers to the magnitude of the force on some test object due to the mass of another object. Under [[Gravitation#Newton's law of universal gravitation|Newtonian gravity]] the gravitational field strength, due to a [[spherical symmetry|spherically symmetric]] object of mass ''M'' is given by: | More generally, the acceleration due to gravity refers to the magnitude of the force on some test object due to the mass of another object. Under [[Gravitation#Newton's law of universal gravitation|Newtonian gravity]] the gravitational field strength, due to a [[spherical symmetry|spherically symmetric]] object of mass ''M'' is given by: | ||
Revision as of 00:16, 25 March 2008
An object with mass m near the surface of the Earth experiences a downward gravitational force of magnitude mg, where g is the acceleration due to gravity. The quantity g has the dimension of acceleration, m s−2, hence its name.
Newtons's gravitational law gives the following formula for g,
where G is the universal gravitational constant, G = 6.67428 × 10−11 m3 kg−1 s−2, ME is the total mass of the Earth, and RE is the radius of the Earth. This equation gives a good approximation, but is not exact. Deviations are caused by the centrifugal force due to the rotation of the Earth around its axis, non-sphericity of the Earth, and the non-homogeneity of the composition of the Earth. These effects are the cause that g varies roughly ±0.01 around the value 9.8 m s−2 from place to place on the surface of the Earth. The quantity g is therefore referred to as the local gravitational acceleration.
The 3rd General Conference on Weights and Measures (Conférence Générale des Poids et Mesures, CGPM) defined in 1901 a standard value denoted as gn.[1][2] The value of the standard acceleration due to gravity gn is 9.80656 m s−2.
References
- ↑ [http://physics.nist.gov/Document/sp330.pdf The International System of Units (SI), NIST Special Publication 330, 2001 Edition] (pdf page 29 of 77 pdf pages)
- ↑ [http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf#page=51 Bureau International des Poids et Mesures] (pdf page 51 of 88 pdf pages)