Acceleration due to gravity

In the sciences the term acceleration due to gravity commonly refers to the value

$g=9.807\ {\text{m/s}}^{2}\ .$

Any object near the earth is subject to a force in the downward direction that causes an acceleration of magnitude g 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 and direction of the acceleration of some test object due to the mass of another object. Under Newtonian gravity the gravitational field strength, or gravitational acceleration, due to a spherically symmetric object of mass M is given by

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

The magnitude of the acceleration is $g=GM/r^{2}$, with SI units of meters per second squared.

Here G is the gravitational constant, G = 6.67428×10⁻¹¹ Nm²/kg², ${\vec {r}}$ is the position of the test object in the field relative to the centre of mass M, and r is the magnitude (length) of ${\vec {r}}$.