Acceleration due to gravity: Difference between revisions
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In the [[science]]s, the term '''acceleration due to gravity''' refers to a | 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 article on [[Gravitation#Gravitational potential|gravitation]] it is shown that for a relatively small altitude ''h'' above the surface of a large, homogeneous, massive sphere (such as a planet) [[Isaac Newton|Newton's]] [[Gravitation#Gravitational potential|gravitational potential]] ''V'' is to a good approximation linear in ''h'': ''V''(''h'') = ''g h'', where '''g''' is the '''acceleration due to gravity'''. This aproximation relies on ''h'' << ''R''<sub>sphere</sub> (where ''R''<sub>sphere</sub> is the radius of the sphere). The exact gravitational potential is not linear, but | In the article on [[Gravitation#Gravitational potential|gravitation]] it is shown that for a relatively small altitude ''h'' above the surface of a large, homogeneous, massive sphere (such as a planet) [[Isaac Newton|Newton's]] [[Gravitation#Gravitational potential|gravitational potential]] ''V'' is to a good approximation linear in ''h'': ''V''(''h'') = ''g h'', where '''g''' is the '''acceleration due to gravity'''. This aproximation relies on ''h'' << ''R''<sub>sphere</sub> (where ''R''<sub>sphere</sub> is the radius of the sphere). The exact gravitational potential is not linear, but is inversely proportional to the distance, ''r'', from the centre of the Earth: <math>V_G = \frac{G M}{r}</math>. | ||
On Earth, the term ''standard acceleration due to gravity'' refers to the value of 9.80656 m/s<sup>2</sup> and is denoted as '''g<sub>n</sub>'''. That value was agreed upon by the 3rd General Conference on Weights and Measures (Conférence Générale des Poids et Mesures, CGPM) in 1901.<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 actual value of acceleration due to gravity varies somewhat over the surface of the Earth; '''g''' is referred to as the ''local gravitational acceleration'' . | On Earth, the term ''standard acceleration due to gravity'' refers to the value of 9.80656 m/s<sup>2</sup> and is denoted as '''g<sub>n</sub>'''. That value was agreed upon by the 3rd General Conference on Weights and Measures (Conférence Générale des Poids et Mesures, CGPM) in 1901.<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 actual value of acceleration due to gravity varies somewhat over the surface of the Earth; '''g''' is referred to as the ''local gravitational acceleration'' . | ||
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==References== | ==References== | ||
<references/> | <references/> | ||
Revision as of 02:32, 19 March 2008
In the sciences, 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/s2 (length per time squared) whence its name.
In the article on gravitation it is shown that for a relatively small altitude h above the surface of a large, homogeneous, massive sphere (such as a planet) Newton's gravitational potential V is to a good approximation linear in h: V(h) = g h, where g is the acceleration due to gravity. This aproximation relies on h << Rsphere (where Rsphere is the radius of the sphere). The exact gravitational potential is not linear, but is inversely proportional to the distance, r, from the centre of the Earth: .
On Earth, the term standard acceleration due to gravity refers to the value of 9.80656 m/s2 and is denoted as gn. That value was agreed upon by the 3rd General Conference on Weights and Measures (Conférence Générale des Poids et Mesures, CGPM) in 1901.[1][2] The actual value of acceleration due to gravity varies somewhat over the surface of the Earth; g is referred to as the local gravitational acceleration .
Any object of mass m near the Earth (for which the altitude h << REarth) is subject to a force m g in the downward direction that causes an acceleration of magnitude gn 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.
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)