Escape Velocity

Potential Wells

If we were to plot a graph of distance from a mass against gravitational potential, it would look like a funnel dropping down at the point of the mass, and approaching zero as the distance from the point approaches infinity. (If you have read the Altitude Analogy page, this should sound familiar!)

Escape Velocity

In order for a mass to escape a potential well, it needs to have a sufficiently high velocity. The gravitational potential will have an effect on the velocity of an object trying to escape, decreasing it - however, because of the way the gravitational potential approaches zero the further you get from the mass, the total influence on the velocity of the escaping object will approach a fixed number. (This can be shown by integrating the gravitational potential formula between the position of the mass and infinity with respect to $r$.) This is the escape velocity - the minimum velocity needed for an object to escape a gravitational pull. In theory, if an object was launched from a potential well with precisely the escape velocity, then as it approached infinity, its velocity would also approach zero.