Acceleration due to gravity: Difference between revisions
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Where ''g'' is the '''acceleration due to gravity''', an object with mass ''m'' near the surface of Earth experiences a downward gravitational force of magnitude ''mg''. The quantity ''g'' has the dimension of acceleration, m s<sup>−2</sup>, hence its name. Equivalently, it can be expressed in terms of force per unit mass, or N/kg in SI units. | |||
[[Gravitation#Newton's law of universal gravitation|Newton's gravitational law]] gives the following formula for ''g'', | |||
:<math>g = G\, \frac{M_{\mathrm{E}}}{R^2_{\mathrm{E}}},</math> | |||
:<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''<sub>E</sub> is the total mass of Earth, and ''R''<sub>E</sub> is the radius of Earth. This equation gives a good approximation, but is not exact. Deviations are caused by the [[centrifugal force]] due to the rotation of Earth around its axis, non-sphericity of Earth, and the non-homogeneity of the composition of Earth. These effects cause ''g'' to vary roughly ± 0.02 around the value 9.8 m s<sup>−2</sup> from place to place on the surface of Earth. The quantity ''g'' is therefore referred to as the ''local gravitational acceleration''. It is measured as 9.78 m s<sup>−2</sup> at the equator and 9.83 m s<sup>−2</sup> at the poles. | |||
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 Bureau International des Poids et Mesures] (Brochure on SI, pdf page 51 of 88 pdf pages) From the website of the [[Bureau International des Poids et Mesures]]</ref> The value of the ''standard acceleration due to gravity'' ''g<sub>n</sub>'' is 9.80665 m s<sup>−2</sup>. This value of ''g<sub>n</sub>'' was the conventional reference for calculating the now obsolete unit of force, the kilogram force, as the force needed for one kilogram of ''mass'' to accelerate at this value. | ||
==References== | |||
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Latest revision as of 09:12, 14 September 2024
Where g is the acceleration due to gravity, an object with mass m near the surface of Earth experiences a downward gravitational force of magnitude mg. The quantity g has the dimension of acceleration, m s−2, hence its name. Equivalently, it can be expressed in terms of force per unit mass, or N/kg in SI units.
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 Earth, and RE is the radius of Earth. This equation gives a good approximation, but is not exact. Deviations are caused by the centrifugal force due to the rotation of Earth around its axis, non-sphericity of Earth, and the non-homogeneity of the composition of Earth. These effects cause g to vary roughly ± 0.02 around the value 9.8 m s−2 from place to place on the surface of Earth. The quantity g is therefore referred to as the local gravitational acceleration. It is measured as 9.78 m s−2 at the equator and 9.83 m s−2 at the poles.
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 9.80665 m s−2. This value of gn was the conventional reference for calculating the now obsolete unit of force, the kilogram force, as the force needed for one kilogram of mass to accelerate at this value.
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 (Brochure on SI, pdf page 51 of 88 pdf pages) From the website of the Bureau International des Poids et Mesures