imported>Milton Beychok |
imported>Paul Wormer |
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| 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>. |
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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.
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| 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>.
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| 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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| 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:
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| :<math>f = G \frac{M}{r^2}. </math>
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| The magnitude of the acceleration ''f'' is expressed in [[SI]] units of [[meter]]s per [[second]] squared. Here ''G'' is the [[universal gravitational constant]] ''G'' = 6.67428×10<sup>−11</sup> Nm<sup>2</sup>/kg<sup>2</sup> <ref> Source: [http://physics.nist.gov/cgi-bin/cuu/Value?bg|search_for=Gravitational CODATA 2006, retrieved 2/24/08 from NIST website]</ref> and <math>r</math> is the distance from the test object to the centre of mass of the Earth and ''M'' is the mass of the Earth.
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| In [[physics]], it is common to see [[acceleration]] as a vector, with an absolute value (magnitude, length) ''f'' and a direction from the test object toward the center of mass of the Earth (antiparallel to the position vector of the test object), hence as a vector the acceleration is:
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| :<math>
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| \vec{f} = - G \frac{M}{r^2} \vec{e}_r \quad \hbox{with}\quad \vec{e}_r \equiv \frac{\vec{r}}{r}.
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| </math>
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| ==References== | | ==References== |
Revision as of 10:06, 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
