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I was figuring out how to move the earth today for when the sun gets too hot to sustain life, and the asteroid gravity-assist is the method I arrived at as well.

I hadn’t yet figured how long it would take, but that seems reasonable.

Wouldn’t have thought of the solar sail as that seems much harder physics-wise.

Just a thought experiment. Humans will be long extinct in 300 million years, when the heating up really begins.