What is escape velocity?

So it relates to objects escaping Earth Gravitational field.

So if you had a tower and you stood on top of the tower and threw a ball, what velocity would you need to throw the ball to do the following. Please note this is assuming Wind resistance was zero. I think the calculation was based on Gravity being the only force acting on the ball.

So the thrown ball could do 1 of 3 things.

1). The ball was not thrown fast enough and the forces of gravity are able to pull the ball back to the earth.

2). The ball was thrown with precisely the amount of force that it is traveling so fast that gravity is not able to return the ball to the earth. This is the Idea of orbiting. The ball is always falling , but never hits the ground because its horizontal velocity is so great. (If the ball is thrown just a little bit harder it will escape the earths gravity field this is known as escape velocity)

3). The ball is thrown with too much force and it escapes Earths gravity and leaves earth on the trajectory and flies off into space.

the speed at which a small object will need to travel to escape the gravitational pull of a bigger object

the velocity of escaping duhhh