# How do you solve for d in G=(Gme)/d^2?

May 13, 2016

$d = \pm \sqrt{m e}$

#### Explanation:

Turn everything upside down giving:

$\frac{1}{G} = {d}^{2} / \left(G m e\right) \text{ ....an alternative at this stage is} \frac{1}{\cancel{G}} = {d}^{2} / \left(\cancel{G} m e\right)$

Multiply both sides by $G m e$

$\frac{1 \times G m e}{G} = {d}^{2} \times \frac{G m e}{G m e}$

But $\frac{G m e}{G m e} = 1$

${d}^{2} = \frac{\cancel{G} m e}{\cancel{G}}$

Take the square root of both sides

$d = \pm \sqrt{m e}$