DanielLC comments on Stupid Questions December 2014 - Less Wrong
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This is a fascinating question. Very speculatively, I could imagine somehow using energy gained by pushing other objects closer to the Sun, to move the Earth away from the Sun. Like some sort of immense elastic band stretching between Mars and Earth, pulling Earth "up" and Mars "down".
That is essentially what would happen if you used gravitational assistance and orbited asteroids between Mars and Earth.