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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.