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

12 Answers

Anonymous 0 Comments

There is one thing that you don’t take into the account. The bull’s strength is lower the further you are from said bull. And it falls with the _square_ of the distance. So if you get 2 times further from the bull, it pulls you 4 times weaker. This is according to the Newton’s law of gravitation, which uses inverse square.

The force that the bull exerts slows you down linearly. So after you travel 2 times further, you are losing speed with a 4 times lower ratio. There exists an initial speed where you only reach 0 speed once you travel to infinity (we need calculus to calculate this rigorously). This speed is called escape velocity.

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