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:
 * $$\mathbf F = \frac {G m_1 m_2 \mathbf r} {r^3}$$

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:
 * $$M L T^{-2} = x \frac {M^2 L}{L^3}$$

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