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Given two environments that are identical, except for air density (e.g. Cape Canaveral, but at Mount Everest's height), would launching a rocket require more or less fuel at the lower air density?

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At the start of the launch, the rocket has the largest mass of its entire flight. Any rocket that can make it to orbit necessarily is fairly big, making its fully loaded mass enormous. The combination of large size and large mass makes its relative air drag smaller than compared to a smaller and less massive rocket.

The rocket's speed is also a consideration. At maximum acceleration, the rocket becomes supersonic only after it has reached the very upper limits of the troposphere. This means it only start moving really fast after it has climbed above the most dense parts of the atmosphere. Since air resistance depends quadratically on speed, but the air density drops roughly exponentially with altitude, air resistance is hardly a consideration at all (for large rockets).

Naturally, if there is no air at all, there is no air resistance, so less propellant would be required in all. But with regard to fuel efficiency: for any rocket that can make it to orbit, removing the whole atmosphere would be less effective than launching that rocket from the top of Mt. Everest :)

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I know your question, however the question is not proper, but only who can see the point correctly can answer the question.

You original question is, at the moment of the launch, if all air disappears suddenly, then the rocket's gets slower or same or faster speed.

My answer is slower and the rocket can not get out the globe. 99% people would say same but I say its worst answer.

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All other things being equal (initial and final altitudes and velocities), you need somewhat (but not much) less fuel with less dense air, as air drag will be less at the initial stage of the flight.

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And we do actually do this en.wikipedia.org/wiki/Pegasus_(rocket) –  Martin Beckett Aug 26 '12 at 5:42
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protected by Qmechanic Feb 6 '13 at 14:15

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