Ah the wonders of the formula:
2 4
Luminosity = 4 pi R x sigma T
If the radius of the Sun, R, stayed the same, the luminosity would increase by a
factor of (10,000/6,000)^4 = 39 for the high temperature case, and decrease by a
factor of (3,000/6,000)^4 = 0.062 times for the low temperature. The Earth
would instantly loose its oceans to evaporation and turn into a twin to Venus,
while on the cool end, the oceans would freeze. To simulate these conditions
today, for the high temperature scenario, we would have to move the Earth
to about (1/39)^1/2 = 0.16 AU, or just inside the orbit of Mercury. For the
cold situation, we would move to (1/.062)^1/2 = 4.0 AU or between the orbit of
Mars and Jupiter. I would take the cooler scenario any day! Better skiing!