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Will the nature of the Earth moving to the Roche Limit possibly save life on it when the sun becomes hotter?

I don't suppose the gravity of the sun becomes greater too, thus putting the Roche Limit and a doomed Earth farther then expected?

Huh? The Roche limit of the sun is 696,000 km, just above the surface. If the sun expanded to twice its size, the Roche limit would decrease to half what it is now. So effectively, the Roche limit would be inside the sun.

Any planet that reaches the Roche limit gets torn apart into dust and rocks, by the tidal forces. And when the sun expands out to the Earth's orbit, the drag of the sun's atmosphere will cause the Earth to fall into the sun and vaporize.

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