How fast would you have to throw an object so it never came back down? Ignore air resistance. Let's find the escape speed - the minimum speed required to escape from a planet's gravitational pull.

Apply the master energy equation:

U_i + K_i = U_f + K_f

Set both terms on the right to zero. We want the object to reach infinity, where the potential energy is zero, and we want it to just reach infinity...so it can arrive there with negligible speed.

Basically the total initial energy must be at least zero for the object to escape.

For a planet of mass M and radius R, that 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

=

G m M R

vescape

=

(

2 G M R

)

½

For the Earth this works out to 11.2 km/s.