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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>the surface of the planet at 1 m/s without any change in acceleration would it not eventually end up in space?
If there’s no change in acceleration you are constantly putting energy into the system to counteract gravity. When we talk escape velocity we are essentially talking if you were launched into space at a start velocity. Why do we think this way? Well your rocket has a limited amount of fuel, and thus energy. So you want to calculate so you have (at least) enough fuel to escape gravity.
The way to think about it is to think about energy instead of velocity.
Being on the ground you have what we call a negative potential energy. You need to put in energy to be in a neutral state. The reason its negative is because the reference frame would be your state where you are infinitely far away from the object and thus not effected by its gravity.
The energy is defined as 1/m * intregal from x to inf of G*m*M/(x^2)
G is the universal gravity constant, x is the height from the center of the object(Height from center of earth in this case), m is your mass and M is the mass of the earth in this case.
You get some massive amount of negative energy. In order to completely escape this, you need a kinetic energy equal to that potential energy. Kinetic energy is calculated by e=1/2 * m * v^2.
You take these two equations and solve for v, and get:
v_esc = sqrt(2*G*m/x)
You can get input your current height from center of earth, G and mass of earth to get the escape velocity.
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