Acceleration due to gravity

From Citizendium
(Redirected from Gravitational acceleration)
Jump to navigation Jump to search
This article is a stub and thus not approved.
Main Article
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
This editable Main Article is under development and subject to a disclaimer.

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 m3 kg−1 s−2, ME is the total mass of Earth, and RE 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 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, as the force needed for one kilogram of mass to accelerate at this value.