# Acceleration due to gravity

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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,[1] 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.[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

1. The International System of Units (SI), NIST Special Publication 330, 2001 Edition (pdf page 29 of 77 pdf pages)
2. 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