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As we know, velocity to escape from an orbit is in proportional with the orbital velocity:

$$v_\mathrm{escape}=\sqrt{2}v_\mathrm{orbit}$$

Since, orbital velocity decreases as we move away so should be velocity to escape from it. In other words farther is an orbit lesser will be velocity to escape from it.

Thus, as we move away the value of velocity with which we need to escape decreases. Now isn't that actually negative acceleration? We need to have that acceleration in order to escape.

Why then we call it as escape velocity instead of escape acceleration?

(And, if I am correct is it just opposite of gravitational acceleration?)

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    $\begingroup$ It doesn't matter how the velocity is achieved; if you have it, you escape; if not, you are stuck. Thus the acceleration is not the deciding factor. $\endgroup$ – Peter Diehr Feb 16 '16 at 13:30
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    $\begingroup$ Gravity is a constant (negative) acceleration. Technically anything with a positive acceleration is an escape acceleration given enough time. It doesn't make much sense to reason in those terms though, otherwise one could argue that to fly, you need only build a device that grants you constant positive acceleration. $\endgroup$ – Neil Feb 16 '16 at 14:20
  • $\begingroup$ Are the dimensions of the quantity in question those of velocity or those of acceleration? $\endgroup$ – dmckee Feb 16 '16 at 17:40
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I think this is just down to a minor misunderstanding of terminology.

If I place a rock, say, near the Earth, with a velocity high enough to escape the Earth's gravity. It will only have acceleration based on gravity; as it is unpowered, but whether or not it escapes will depend entirely on whether its velocity is above the escape velocity for the position it is in.

That velocity will change, and Earth's gravity will continue to slow the rock as it heads away from the Earth. But the rock isn't going to be able to accelerate against gravity - it's a rock. It can still escape though...

Yes, the velocity required will reduce in proportion with the orbital velocity, but that in no way defines an escape acceleration.

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I think the issue is a lot clearer if you think in terms of energy. When you're on the surface of the Earth, you're in a gravitational potential well. You need a certain amount of kinetic energy to "climb out" of the potential well, and since velocity is a visible (and less abstract) proxy for kinetic energy, it's common to speak of escape velocity.

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