Why is there an escape velocity?

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I can’t wrap my mind around why you need to be going a certain speed to escape the pull from earth’s gravity.

In my mind I envision 5 people playing tug of war with a bull. The people are exerting a pulling force but the bull would be able to overcome it. Let’s say the humans never get tired but the bull will be able to exceed the forces pulling it back and continue to move forward. That can happen at 22mph or 2mph.

Outside of it being severely inefficient (I’m guessing), why can’t an object just travel upwards at low speeds and eventually overcome the pull of the earth because it has lots of… torque (for lack of a better word)?

In: Physics

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>In my mind I envision 5 people playing tug of war with a bull. The people are exerting a pulling force but the bull would be able to overcome it. Let’s say the humans never get tired but the bull will be able to exceed the forces pulling it back and continue to move forward. That can happen at 22mph or 2mph.

Imagine the bull has a short attention span – he pulls hardest when people are nearby, but when they are far away, he gets less motivated to put in any effort.

If the people are moving away at 2mph, he will pull them back. But if they move fast enough, he pulls back just as hard at the beginning, but the people are fast enough that they only lose some of their speed, then they are far enough away that the bull loses interest, and they can escape.

>why can’t an object just travel upwards at low speeds and eventually overcome the pull of the earth 

In theory it can. The “escape velocity” only strictly applies when there are no other forces except gravity at work. If we build a tall ladder to space, we could (in principle) climb up it at a leisurely pace. Or we could build a rocket that gave just enough acceleration to overcome gravity, and zoom slowly upwards into space.

However, “escape velocity” is still a useful idea even in those situations: it gives you an idea of the minimum “total force” you’ll need to apply over time.

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