Newton's Law of Universal Gravitation states that the force $F$ between two objects is given by the formula $F=G\frac{m_1{m}_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the objects, and $r$ is the distance between their centers. Which of the following equations correctly expresses $G$ in terms of $F$, $m_1$, $m_2$, and $r$?