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

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

Step 1

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

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

Step 2

Simplify.

Combine $G$ and $\frac{m M}{r^{2}}$ .

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

Remove parentheses.

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

Step 3

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

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

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

Simplify the left side.

Multiply the numerator by the reciprocal of the denominator.

$\frac{G m M}{r^{2}} \cdot \frac{1}{G} = \frac{F}{G}$

Combine.

$\frac{G m M \cdot 1}{r^{2} G} = \frac{F}{G}$

Cancel the common factor of $G$ .

Cancel the common factor.

$\frac{G m M \cdot 1}{r^{2} G} = \frac{F}{G}$

Rewrite the expression.

$\frac{m M \cdot 1}{r^{2}} = \frac{F}{G}$

Multiply $m$ by $1$ .

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

Step 4

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

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

Step 5

Simplify.

Simplify the left side.

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Combine $\frac{F}{G}$ and $r^{2}$ .

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

Step 6

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

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

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

Simplify the left side.

Cancel the common factor of $M$ .

Cancel the common factor.

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

Divide $m$ by $1$ .

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

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$m = \frac{F r^{2}}{G} \cdot \frac{1}{M}$

Combine.

$m = \frac{F r^{2} \cdot 1}{G M}$

Multiply $F$ by $1$ .

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

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

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