The Escape Velocity calculator computes the escape velocity at some radius (R) distance from a massive body (M) using the.
INSTRUCTIONS: Choose units and enter the following:
Escape Velocity (v): The calculator returns the escape velocity (v) in kilometers per second. However, this can be automatically converted into other velocity units via the pull-down menu.
` V = sqrt( (2*G*M)/R)`
This function is very important in today's world of satellites. It defines for a mass lifting off the surface of the Earth for example, what velocity the launch vehicle must obtain to leave the pull of Earth's gravity. It shows you that if you were to specify your own mass, you could determine just how fast that gigantic slingshot would have to fling you to put you in outer space.
This equation then, solving for R also defines the event horizon distance for anything attempting to escape a black hole. Remember the event horizon is a distance from a black hole which once passed cannot be reversed. Since you cannot go faster than the speed of light, and so a black hole by definition has an escape velocity that cannot be achieved. See THIS EQUATION for that event horizon calculation.
University Physics 12th Edition, Chapter 12, Equation #12.29