5. Escape Velocity

Definitions

Escape Velocity

• Velocity at which an objects kinetic energy is equal to its gravitational potential energy
• Same for all masses in the same gravitational field

Derivations

The work done to escape the gravitational field is

$$w = -Um = \dfrac{GMm}{r}$$

so the kinetic energy we need is equal to $w$

$$\dfrac{1}{2}mv^2 = \dfrac{GMm}{r}$$

so our escape velocity comes out to

$$v = \sqrt{\dfrac{2GM}{r}}$$