Astronomy question about temperature and distance?

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have_hope89

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I am having trouble figuring out how to go about this question; I think I need a formula, but I'm not sure which to use. If someone can guide me on how to get the answer, I would really appreciate it!
"Evil aliens increase the temperature of the sun by a factor of 2 (double the temp.). Good aliens can't stop them but do offer to move the earth to a new orbit. What orbit should they move the earth to so that the new hotter sun would appear as bright as the normal sun appears to us now? Half of this question is being able to tell me closer/further and why. The second half of this question is being able to tell me precisely how much closer/further. Show work.
 
According to the Stephan Boltzman law the brightness of a star is proportional to T^4, or a factor 16. As the apparent brightness falls off as the distance squared, the Earth should be positioned 4 times further away from the Sun.
 
Intensity is proportional to 1/distance^2. That's the principle you are supposed to be using here.

Does the temperature go up or down as you get closer to a hot object? If you are near a fire or an oven and it's too hot, which way do you go to get cooler? Closer or farther?

So if the temperature of the sun is doubled, which way would you go to get cooler?

Now reasoning mathematically, that intensity is proportional to 1/r^2, you have to figure out how to change r so that intensity goes down by a factor of 2, so it's the same as it was before.
 
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