Solve for m F=(G(mM))/(r^2)

$F = \frac{G (m M)}{r^{2}}$

Step 1

Rewrite the equation as $\frac{G m M}{r^{2}} = F$ .

$\frac{G m M}{r^{2}} = F$

Step 2

Multiply both sides by $r^{2}$ .

$\frac{G m M}{r^{2}} r^{2} = F r^{2}$

Step 3

Simplify the left side.

Cancel the common factor of $r^{2}$ .

Cancel the common factor.

$\frac{G m M}{r^{2}} r^{2} = F r^{2}$

Rewrite the expression.

$G m M = F r^{2}$

Step 4

Divide each term in $G m M = F r^{2}$ by $G M$ and simplify.

Divide each term in $G m M = F r^{2}$ by $G M$ .

$\frac{G m M}{G M} = \frac{F r^{2}}{G M}$

Simplify the left side.

Cancel the common factor of $G$ .

Cancel the common factor.

$\frac{G m M}{G M} = \frac{F r^{2}}{G M}$

Rewrite the expression.

$\frac{m M}{M} = \frac{F r^{2}}{G M}$

Cancel the common factor of $M$ .

Cancel the common factor.

$\frac{m M}{M} = \frac{F r^{2}}{G M}$

Divide $m$ by $1$ .

$m = \frac{F r^{2}}{G M}$