In pop astronomy when the sun expands in its last throes the Earth gets hotter.
But this can't be right.
The sun's surface radiates as much as it does due to its heat energy escaping through it's surface. Its heat is stable over time because the escaped energy is being replaced by fusion.
But when it expands and the fusion stops the heat energy has to be distributed over a larger volume so the surface tempreture goes down while the surface area goes up. The energy radiated is no longer being replaced but the sun still has a lot of internal heat so the surface access to the remaining heat. If that were the only consideration the volume of the expanded sun and its new surface would radiate only a little less to the Earth as it did before.
But The heat energy of the volume now has a lower surface area to volume ratio so the energy has a smaller route from which to escape the sun. It takes longer to escape from an expanded sun than it did from the smaller Sun.
So unless the Earth comes into direct contact with the surface of the red expanded Sun The radiant energy from the Sun to the Earth should decrease not increase. It would be as if, by expanding, the Sun is wraping itself in insulation preventing as much energy from escaping as did when it was smaller.



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