Dimension of Gravitational Constant

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Theorem

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

Proof

$\mathbf F = \dfrac {G m_1 m_2 \mathbf r} {r^3}$

We have:

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

Then we have:

$M L T^{-2} = x \dfrac {M^2 L}{L^3}$

Hence, after algebra:

$x = M^{-1} L^3 T^{-2}$

$\blacksquare$