Dimension of Universal Gravitational Constant

Theorem
The dimension of the gravitational constant $G$ is $M^{-1} L^3 T^{-2}$.

Proof
From Newton's Law of Universal Gravitation:
 * $\mathbf F = \dfrac {G m_1 m_2 \mathbf r} {r^3}$

We have:
 * The dimension of force is $M L T^{-2}$;
 * The dimension of displacement is $L$;
 * The dimension of mass is $M$.

Let $x$ be the dimension of $G$.

Then we have:
 * $M L T^{-2} = x \dfrac {M^2 L}{L^3}$

Hence, after algebra:
 * $x = M^{-1} L^3 T^{-2}$