Newton's Law of Gravitation states that two bodies with masses $M$ and $m$ attract each other with a force $$F=G\frac{Mm}{r^2},$$ where $r$ is the distance between the bodies and $G$ is the gravitational constant.

Find the escape velocity $v_0$ that is needed to propel a rocket of mass $m$ out of the gravitational field of a planet with mass $M$ and radius $R$. Use Newton's Law of Gravitation (given above) and the fact that the initial kinetic energy of $\frac{1}{2}mv_0^2$ supplies the needed work.

Note: Your answer could contain $M$, $m$, $G$, and $R$.

Work =