Why is there a velocity associated with escaping from earth’s atmosphere? If an object were to fly from the surface of the planet at 1 m/s without any change in acceleration would it not eventually end up in space?
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It’s all to do with energy. Specifically, gravitational potential energy. To go up, you need to do work, turn energy into gravitational potential energy. When you go down, that potential energy turns into kinetic energy.
You can calculate how much gravitational potential energy you would need to create going from your current position all the way to infinity (and beyond!). It’s GMm/r, where G is a constant, M is the Earth’s mass, m is your mass, and r is the distance to the centre of the Earth. (Actually doing the calculation requires doing an integration, so I won’t get into it, but it’s a pretty simple integration)
Now, imagine you had exactly that much kinetic energy. You could go straight up, and that kinetic energy all converting into gravitational potential energy would be enough to get you to infinity. Kinetic energy is 0.5 mv^2. So, let’s equate those two numbers.
GMm/r = 0.5 mv^2
We can rearrange and cancel out the ‘m’s…
v = sqrt(2GM/r)
Which is the definition of escape velocity, and it depends only on distance from the centre of a body (r) and the mass of that body (M) and a constant. It’s just the speed at which your kinetic energy is enough that without any other force acting you can completely escape a body’s gravity out to infinity.
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