Acceleration due to gravity: Difference between revisions
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[[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'', | ||
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g = G \frac{M_{\mathrm{E}}}{R^2_{\mathrm{E}}}, | g = G\, \frac{M_{\mathrm{E}}}{R^2_{\mathrm{E}}}, | ||
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due to the rotation of the Earth around its axis, non-sphericity of the | 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 | Earth, and the non-homogeneity of the composition of the Earth. These | ||
effects cause ''g'' to vary roughly ±0.01 around the | 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. | 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 quantity ''g'' is therefore referred to as the ''local gravitational acceleration''. | ||
Revision as of 00:22, 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, 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.[1] [2] The value of the standard acceleration due to gravity gn is 9.80656 m s−2.
References
- ↑ 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)