Acceleration due to gravity: Difference between revisions
imported>John R. Brews (link) |
imported>Mark Widmer (1st para: Added statement about force per unit mass. Corrected variation in g to 0.02 (was 0.01). Added values at equater and poles.) |
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An object with mass ''m'' near the surface of | An object with mass ''m'' near the surface of 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. 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'', | [[Gravitation#Newton's law of universal gravitation|Newton's gravitational law]] gives the following formula for ''g'', | ||
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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> | 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 | ''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 equater 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> | 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> | ||
Revision as of 18:13, 5 May 2021
An object with mass m near the surface of 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. 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 equater 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.
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