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# Gravitational field strength derivation

The gravitational field strength $(g)$ is a quantity that describes the gravitational effect of a mass on objects around it.

Specifically, $g$ is the magnitude of the gravitational force per unit mass (i.e. $1\text{ kg}$) at a point. $g$ is often casually referred to as the gravitational force on a unit mass.

This ignores the difference between a force (a vector) and the magnitude of the force (a scalar).

The equation for $g$ is derived from the equation for the law of universal gravitation:$$F=\frac{GMm}{r^2}$$Both sides of the equation are divided by $m$: $$g=\frac{F}{m}=\frac{GM}{r^2}$$

$F=$magnitude of force; $G=$universal gravitational constant; $M$ or $m=$mass; $r=$distance from a point mass.