Escape Velocity

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:  Ui + Ki = Uf + Kf

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.
- G m M
+ Kescape = 0
½ mv2escape = G m M/ R.

vescape = (
2 G M
) ½

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