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I don't doubt that you're right, but to play devil's advocate Earth's surface to volume ratio is also much higher than the sun's so it cools quicker too.

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Perhaps, and furthermore Earth's surface-to-volume ratio would increase quite a lot more shortly afterward, as its shattered remains spread throughout the solar system. I imagine that the Earth would cool off rather quickly, or what's left of it anyway.

As they're both effectively spheres, don't they have the same surface-to-volume ratio?

The ratio is actually a function of the radius:

v = (4/3) * pi * r^3

s = 4 * pi * r^2

s / v => 3/r

This makes a kind of sense in terms of heat transfer: the sun's got a whole lot more insides for radiation to get through before it can even reach the surface to escape.

EDIT: line breaks unbreak formulas.

Ah, of course. Increase in volume is cubic, area is square.

Thanks.

http://en.wikipedia.org/wiki/Surface-area-to-volume_ratio

>For a given shape, SA:V is inversely proportional to size.

When an object grows in size its volume grows faster than its surface area.

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