Acceleration due to gravity

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Where g is the acceleration due to gravity, an object with mass m near the surface of Earth experiences a downward gravitational force of magnitude mg. 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,

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

where G is the universal gravitational constant,^[1] G = 6.67428 × 10⁻¹¹ m³ 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 equator 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_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, as the force needed for one kilogram of mass to accelerate at this value.

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