Escape Speed is the minimum initial speed required for an object to escape a body’s gravitational field. We can find the escape speed using Conservation of Energy.
Since we want the minimum speed, the final energy of our object will be 0. In other words, the object has no Energy left after escaping the field. Our final Kinetic Energy will be 0 and our final Potential Energy will be 0.
Our initial states will use the normal kinetic energy equation and Gravitational Potential Energy.
Solving for