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I think I have learned in physics that escape velocity is defined as the speed at which objects going ballistic in the opposite direction of the main gravitational force are able to finally overcome that force (assuming the simplest case with two directly opposing forces).

This means objects ballistically moving away from Earth slower than that velocity would never be able to escape and will finally fall back to Earth.

I have heard in many documentaries that this is the reason that spacecraft must accelerate to that velocity to get into deeper space at all.

However, as far as I understand it, spacecraft are not purely ballistic objects and could be controlled and accelerated step by step as needed, so why is it not possible to escape from Earth with lower speed and just "keep going", i.e. "accelerating" (exerting force) only to not come to a halt ?

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You're absolutely correct - objects do not need to ever reach earth's escape velocity of 11.2 km/s, and many spacecraft that leave orbit, don't.

That being said, note that escape velocity depends on where you are: the velocity that a cannonball 1000 km above the earth's surface would need to escape is substantially lower than that needed by a cannonball on the surface. This is particularly obvious when you envision a cannonball fired at escape velocity from the surface: once it reaches 1000 km, it must be going slower, but it must still be at "escape velocity". In this sense, all objects intended to leave earth's orbit do reach escape velocity, but only at a great distance.

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  • $\begingroup$ I believe there's a recent what-if.xkcd which discusses the, ahem, difficulty in actually launching a cannonball with enough velocity to overcome atmospheric wind resistance and maintain escape velocity. $\endgroup$ – Carl Witthoft Apr 17 '14 at 23:25

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