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DanArmak comments on Stupid Questions December 2014 - Less Wrong Discussion
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Is there any plausible way the earth could be moved away from the sun and into an orbit which would keep the earth habitable when the sun becomes a red giant?
I don't really know if it's plausible, but Larry Niven's far-future fiction A World Out of Time (the novel, not the original short story of the same name) deals with exactly this problem.
His solution is a "fusion candle": build a huge double-ended fusion tube, put it in the atmosphere of a gas giant, and light it up. The thrust downwards keeps the tube floating in the atmosphere. The thrust upwards provides an engine to push the gas giant around. In the book, they pushed Uranus to Earth, and then moved it outwards again, gravitationally pulling the Earth along.