Acceleration due to gravity: Difference between revisions
imported>Milton Beychok m (More of the same) |
imported>Paul Wormer (Commented out 2 paragraphs [see talk]) |
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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. | 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: | 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: | ||
:<math>f = G \frac{M}{r^2}. </math> | :<math>f = G \frac{M}{r^2}. </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}. | \vec{f} = - G \frac{M}{r^2} \vec{e}_r \quad \hbox{with}\quad \vec{e}_r \equiv \frac{\vec{r}}{r}. | ||
</math> | </math> | ||
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==References== | ==References== | ||
<references/> | <references/> | ||
Revision as of 01:45, 28 February 2008
In the sciences, the term acceleration due to gravity refers to a constant g describing the magnitude of the gravitation on Earth, the planets, and on other extraterrestrial bodies. The constant 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 has an inverse squared dependence on the distance.
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)