Acceleration due to gravity

In the sciences, the term acceleration due to gravity commonly 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. It is also often referred to as the local gravitational acceleration or the standard gravity.

Any object near the earth is subject to a force 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 gravity at the surface of the earth, although it is not exact and the actual acceleration varies slightly between different locations around the world.

More generally the acceleration due to gravity refers to the magnitude of some test object due to the mass of another object. Under Newtonian gravity the gravitational field strength, due to a spherically symmetric object of mass M is given by:

$g=G{\frac {M}{r^{2}}}$

The magnitude of the acceleration is in SI units of meters per second squared. Here G is the universal gravitational constant, G = 6.67428×10⁻¹¹ Nm²/kg², $r$ is the distance of the test object to the centre of mass of the Earth and M is the mass of the Earth.

In physics acceleration is a vector, with an absolute value (magnitude, length) g and a direction from the center of mass of Earth toward the test object, hence as a vector the acceleration is,

${\vec {g}}=-G{\frac {M}{r^{2}}}{\vec {e}}_{r}\quad {\hbox{with}}\quad {\vec {e}}_{r}\equiv {\frac {\vec {r}}{r}}.$