Acceleration due to gravity: Difference between revisions
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imported>Milton Beychok m (No changes. Just eliminated the odd spacing of the edit page to make it easier to read.) |
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An object with mass ''m'' near the surface of the Earth experiences a downward gravitational | 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. | ||
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|Newton's gravitational law]] gives the following formula for ''g'', | [[Gravitation#Newton's law of universal gravitation|Newton's gravitational law]] gives the following formula for ''g'', | ||
:<math> | :<math>g = G\, \frac{M_{\mathrm{E}}}{R^2_{\mathrm{E}}},</math> | ||
where ''G'' is the universal gravitational constant,<ref> Source: [http://physics.nist.gov/cgi-bin/cuu/Value?bg|search_for=Gravitational CODATA 2006, retrieved 2/24/08 from NIST website]</ref> ''G'' = 6.67428 × 10<sup>−11</sup> | |||
</math> | |||
where ''G'' is the universal gravitational constant,<ref> Source: [http://physics.nist.gov/cgi-bin/cuu/Value?bg|search_for=Gravitational CODATA 2006, retrieved 2/24/08 from NIST website]</ref> ''G'' = 6.67428 | |||
× 10<sup>−11</sup> | |||
m<sup>3</sup> kg<sup>−1</sup> s<sup>−2</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> | ''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 cause ''g'' to vary 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''. | ||
is the radius of the Earth. | |||
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. | |||
effects cause ''g'' to vary 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 | 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> | ||
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 Bureau International des Poids et Mesures] (pdf page 51 of 88 pdf | <ref>[http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf 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>'' | pages)</ref> The value of the ''standard acceleration due to gravity'' ''g<sub>n</sub>'' is 9.80656 m s<sup>−2</sup>. | ||
is 9.80656 m s<sup>−2</sup>. | |||
==References== | ==References== | ||
Revision as of 13:53, 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.
Newton's gravitational law gives the following formula for g,
where G is the universal gravitational constant,[1] 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 cause g to vary 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.[2] [3] The value of the standard acceleration due to gravity gn is 9.80656 m s−2.
References
- ↑ Source: CODATA 2006, retrieved 2/24/08 from NIST website
- ↑ The International System of Units (SI), NIST Special Publication 330, 2001 Edition (pdf page 29 of 77 pdf pages)
- ↑ Bureau International des Poids et Mesures (pdf page 51 of 88 pdf pages)