It's much easier to move Earth to a higher orbit than it would be to refuel the Sun. In fact, we should de-fuel the Sun to prolong its life and move the Earth closer to it. One could move the Earth with a collection of bodies orbiting the Sun pulling the Earth in the right direction with gravity. Those bodies could obtain their own momentum from solar sails. It's not fancy technology beyond major bruteforce work (we'd need to disassemble the Moon, at least)
Remember the timeframes involved are of many million years. The Sun will change very slowly until the very end and moving the Earth any faster would create climate problems of their very own.
BTW, we'll have some problems before that, when the Milky Way merges with Andromeda. I imagine lots of stars will gain excessive mass from fast moving gas clouds and may decide to go nova/supernova in the millennia it will take for both galaxies to pass through each other.
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It's much easier to move Earth to a higher orbit than it would be to refuel the Sun. In fact, we should de-fuel the Sun to prolong its life and move the Earth closer to it. One could move the Earth with a collection of bodies orbiting the Sun pulling the Earth in the right direction with gravity. Those bodies could obtain their own momentum from solar sails. It's not fancy technology beyond major bruteforce work (we'd need to disassemble the Moon, at least)
Remember the timeframes involved are of many million years. The Sun will change very slowly until the very end and moving the Earth any faster would create climate problems of their very own.
BTW, we'll have some problems before that, when the Milky Way merges with Andromeda. I imagine lots of stars will gain excessive mass from fast moving gas clouds and may decide to go nova/supernova in the millennia it will take for both galaxies to pass through each other.