Why does an object have to reach escape velocity to leave the Earth?

Seems strange doesn't it? But when you're trying to attain orbit, you're trying to "fall" so fast that you just keep missing the Earth. In other words, you're really not trying to get away from earth at a 90 degree angle to the surface you're on right now. You're trying to eventually move parallel to the ground, but so fast that the curve of the Earth falls away from you so fast that you never hit it. The velocity that allows you to pull off that stunt is "escape velocity."

The next thing you'll wonder about is getting away from the Earth and not worrying about orbit. OK, then the escape velocity is the speed you need to get to that will keep you moving away from the Earth (i.e., overcoming gravity) once all your fuel runs out. If you could have an infinite supply of fuel (without corresponding infinite weight), you could do just as you thought and continue into space at a slow speed with a rocket motor.

(P.S. running out of fuel is not the same thing as an empty tank. You're out of fuel when you no longer have enough to do what you want to do next--like return to Earth in one piece.)

Escape velocity is the (theoretical) velocity an object would need to be travelling at initially when it left the surface of the earth to overcome acceleration by gravity. Escape velocity is NOT the velocity an object must be going as it is leaving the atmosphere. This is assuming there are no other forces acting on it, aside from its weight (gravity).

If you take a ball and throw it directly upwards, as soon as it leaves your hand gravity starts accelerating the ball back towards the ground. Initially you see this as the ball decelerating while moving upwards, but eventually it will have slowed down so much it becomes stationary, at the top of its path. After this, of course it starts accelerating back down again. Escape velocity is how fast you would have to throw that ball so that it is never slowed down so much that it stops and starts coming back down again.

The example you gave with your hand is fine. If you were helping the ball (or stone) all the way out you could go as slow as you liked. The key difference here is that you're continually providing an upwards force to overcome gravity, so escape velocity doesn't apply.

An object doesn't have to reach escape velocity to leave earth. Escape velocity is theoretically the the velocity something would have to be travelling at initially (assuming no air resitance) to totally escape the earth's gravity. It is the same as the velocity an object falling from infinity would have when it reached the earth.

In other words, it's the speed a bullet would have to be fired at to go on forever and not fall back to earth.

However, an object doesn't need this velocity if it is being continuously propelled with e.g a rocket. Also, the escape velocity is the speed it would need to leave the earth's gravitational field totally. Satellites are in orbit and need a lower speed than escape velocity to achieve this orbit. That's why it's easier to get a satellite into low earth orbit than the higher geostationary orbit.

You could get out of the atmosphere with less thrust. Escape velocity is simply the Minimum amount of energy you need to leave Earth's orbit. You can't quite get this to a true Minimum because there will be losses going through the atmosphere.

Another way of thinking about it is that escape velocity is simply a ballistic trajectory. The same as if you fired a bullet out of a gun. With anything less than escape velocity the bullet will either fall back to Earth or go into orbit. You have to reach escape velocity for the bullet to completely leave the Earth and not come back.

Now, that is the minimum and we like minimums when we have to pay for rocket fuel so we try to get as close as possible. However, as long as you have a greater than 1:1 thrust to weight you will rise and as long as the thrust maintains greater than 1:1 you will continue to rise. If it ever becomes possible to build a space ladder then these objects would rise at much less than escape velocity. As long as you have some way to give more force than gravity it will work, but this would mean continuously adding energy. Right now, we don't have any way to do it besides fuel rockets and, at low thrust, these would either burn more fuel or even run out before they got into orbit.

This is one of the areas that people tend to get confused about. For example, what is the escape velocity of a black hole? Well, it is at least the speed of light but it can be higher. Most people will insist that this means that nothing can leave a black hole because the escape velocity is the speed of light and nothing can travel faster than the speed of light. However, this isn't actually true. The event horizon of a black hole is the same as a Rindler horizon and it can be demonstrated that both information and physical objects can cross both ways over a Rindler horizon. A Rindler Horizon simply says that if two spaceships are accelerating in the same direction at the same rate that there is a distance such that light will not reach from the spaceship in back to the spaceship in front. What actually happens is that light from the rear spacecraft gets red-shifted until there is nothing left.

A Rindler horizon can be overcome by having a series of spaceships all excelerating at the same rate and stretching across the distance between the front spaceship and the rear one. In other words, these ships in the middle span the Rindler Horizon that exists between the front spaceship and the rear one. By having each one relay something up or down the chain both information and physical objects can cross both ways over the Rindler Horizon.

However, there doesn't seem to be any handy black hole equivalent. You would need some way to add energy to an object to get it out of a black hole and there is no obvious way to do this. In other words, there doesn't seem to be any way to have intermediate steps like you can with a Rindler Horizon. Still, given the equivalence of a Rindler Horizon with an Event Horizon if it is possible with one it is theoretically possible with the other.

So, escape velocity is the minimum amount of energy required. You can escape gravitational influence at lower velocity if you use more energy.

Not quite the same question, but the reason that a rocket has to reach escape velocity is because conventional rocket fuel does not have enough energy to lift its own weight into orbit.

Consequently, most of the fuel has to be burnt close to the ground, and the rocket has to reach a velocity that enables it to achieve orbit without burning any more fuel.

In theory, if you could generate enough power from a small weight of fuel (e.g. using nuclear fission) and could continue to provide more thrust than the weight of the vehicle all the way up to orbit, you would not need to reach escape velocity at all.

I think you could make a small fortune if you could lift objects out into orbit at 3cm/sec.

I think escape velocity is the speed an object needs to get to so that Earth's gravity does not pull it back - so it escapes.

Can you throw a stone out of the atmosphere? Yes you can if you can throw at 25, 000 MPH. To reach that velocity the object continues to accelerate and fight the pull of gravity until it no longer needs to. Slower than that the pull of gravity wins out. Ever see that stone just stay in mid air?

You are right. If you had a ladder long enough then you could just climb It and pop an object into orbit. Unfortunately, no such ladder exists and so we have to take a step back and give the object a mighty heave in order to overcome gravity and air friction.

Yeah but if you throw the stone up in the air it falls back down, doesn't it? That's why you need to go really really fast to escape the earth's atmosphere and be free of gravitational pull

Lower speeds would require more fuel. More fuel weighs more, requiring more energy. More energy requires larger engines. Larger engines weighs more, requiring more fuel. You get the drift.

There is a graph line of optimum weight/power that equals a certain speed. This speed is escape velocity.