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# Law of universal gravitation

The magnitude of gravitational force between two point masses is given by the law of universal gravitation: $$F=\frac{GMm}{r^2}$$

A point mass is a mass concentrated at one point in space (i.e. it has no physical dimensions).

Non-point masses can be thought of to be comprised of a multitude of point masses (each of which exerts separate gravitational forces). However, they are often approximated as point masses for simplicity.

The law states that the force is directly proportional to the masses of the two bodies ($M$ and $m$) and inversely proportional to the square of the distance between the two bodies $(r)$.

The coefficient of proportionality is the universal gravitational constant $(G)$: $$G=6.674\times 10^{-11} \text{ N} \text{ m}^2 \text{ kg}^{-2}=6.674\times 10^{-11} \text{ m}^3 \text{ kg}^{-1}\text{s}^{-2}$$

Two masses exert gravitational forces on each other. The magnitude (but not the direction) of the two forces is equal even if the masses are different.