Consider an isolated system consisting of a planet with mass $M$ and radius $R$ some distance $x$ away from an asteroid with radius $r$ and mass $m$. The two bodies are initially at rest, and will start falling towards each other due to gravitational attraction.
In terms of the given variables and the universal gravitation constant $G$, what is the speed the asteroid will have when it reaches the planet's surface?
Note: The distance $x$ between them initially represents the distance between their centers of mass. Take both bodies to be uniform and spherical.