How fast would you have to throw an object so it never came back down? This is the escape speed - the minimum speed required to escape a planet's gravitational pull.

To find the escape velocity, apply energy conservation:  U_i + K_i = U_f + K_f

For escape, set both terms on the right to zero. We want the object to barely reach infinity, where the potential energy is zero.

For a planet of mass M and radius R, the potential energy of an object of mass m at the planet's surface is:   U= - G m M/R.

Therefore:

- G m M R

+ Kescape = 0

½ mv²_escape = G m M/ R.

vescape

=

(

2 G M R

)

½

For the Earth this is 11.2 km/s ≈ 25,000 mph!