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.
|+ Kescape = 0|
For the Earth this is 11.2 km/s ≈ 25,000 mph!