Acceleration due to gravity

In the sciences, the term acceleration due to gravity refers to a quantity g describing the strength of the local gravitational field. The quantity has dimension of acceleration, i.e., m/s² (length per time squared) whence its name.

In the article on gravitation it is shown that for a relatively small altitude h above the surface of a large, homogeneous, massive sphere (such as a planet) Newton's gravitational potential V is to a good approximation linear in h: V(h) = g h, where g is the acceleration due to gravity. This aproximation relies on h << R_sphere (where R_sphere is the radius of the sphere). The exact gravitational potential is not linear, but is inversely proportional to the distance, r, from the centre of the Earth: $V_{G}={\frac {GM}{r}}$.

On Earth, the term standard acceleration due to gravity refers to the value of 9.80656 m/s² and is denoted as g_n. That value was agreed upon by the 3rd General Conference on Weights and Measures (Conférence Générale des Poids et Mesures, CGPM) in 1901. The actual value of acceleration due to gravity varies somewhat over the surface of the Earth; g is referred to as the local gravitational acceleration .

Any object of mass m near the Earth (for which the altitude h << R_Earth) is subject to a force m g in the downward direction that causes an acceleration of magnitude g_n toward the surface of the earth. This value serves as an excellent approximation for the local acceleration due to gravitation at the surface of the earth, although it is not exact and the actual acceleration g varies slightly between different locations around the world.