Dimension of Gravitational Constant

From ProofWiki
Jump to: navigation, search

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:

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

Then we have:

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

Hence, after algebra:

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

$\blacksquare$