# Acceleration due to gravity

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}
m^{3} kg^{−1} s^{−2},
*M*_{E} is the total mass of Earth, and *R*_{E} 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 *g _{n}*.

^{[2]}

^{[3]}The value of the

*standard acceleration due to gravity*

*g*is 9.80665 m s

_{n}^{−2}. This value of

*g*was the conventional reference for calculating the now obsolete unit of force, the kilogram force, as the force needed for one kilogram of

_{n}*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