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Consider a planet with effective temperature $T$ radiating as a blackbody, emitting a total luminosity $L=4 \pi \sigma R^2 T^4$. At distance $a$ the power per square meter will be $$P = \frac{L}{4\pi a^2} = \sigma \left(\frac{R}{a}\right)^2 T^4.$$ If we demand a sun-like energy flow of $P_{required}$, we get a necessary temperature T=\left[\frac{P_{...