Acceleration due to gravity

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,

$g=G\,{\frac {M_{\mathrm {E} }}{R_{\mathrm {E} }^{2}}},$

where G is the universal gravitational constant, G = 6.67428 × 10⁻¹¹ m³ kg⁻¹ s⁻², M_E is the total mass of the Earth, and R_E 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 g_n. The value of the standard acceleration due to gravity g_n is 9.80665 m s⁻². This value of g_n was the conventional reference for calculating the now obsolete unit of force, the kilogram force.