Gravitational systems are particularly interesting because there are so many examples of such systems. The formation of our universe from immense galactic structures, to solars systems with planets and moons, and even asteroids and comets are all examples of gravitational systems. In these notes, you will read about a particular gravitational phenomenon: how a small object can escape the gravitational bounds of a much more massive object. This object must move with at least the escape speed.

Consider trying to throw a rock with a speed $v$ away from an airless planet. There's three possible outcomes:

1. $v<v_{esc}$; the rock will rise to a maximum height above the surface and fall back down.
2. $v>v_{esc}$; the rock will be moving with some speed at $r=\infty$.
3. $v=v_{esc}$; the rock will have just enough kinetic energy to escape the planet (as $r \rightarrow 0$; $v \rightarrow 0$)

The final outcome defines the escape speed ($v_{esc}$).