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The Earth is quite a lot smaller that 1/3000th the volume of the Sun. If it was producing 1/3000th the total energy output of the Sun, it would explode.

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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.

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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