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The question is not only escape velocity, if you want to fly away from the Moon, you still need to escape Earth and the Sun. The other part of the problem on Earth is atmosphere with its drag and the fact that some kind of propulsion, like ionic, is impossible.

Edit: hmmm... it seems that escaping Earth and the Sun would be easier from the Moon, since the Moon trajectory components include already the 9 km/s and 30 km/s of Moon and Earth's orbits. Once in Moon's orbit, with the right angle and a little push, you should be able to escape Sun.

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