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This looks fine, BUT, indeed have a good read of the wikipedia pages on the topic of habitable zones to see all the complications there are in deducing where around a star the conditions may be "habitable". In addition I recommend, if you are serious about this calculation, reading the short article by Kane & Gelino (2012) and visiting the accompanying ...


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Let me see if I understand the derivation. $$F=\frac{L}{4 \pi R^2}$$ becomes $$F_\odot=\frac{L_\odot}{4 \pi R_\odot^2}$$ and $$F_{\text{ other star}}=\frac{L_{\text{ other star}}}{4 \pi R_{\text{ other star}}^2}$$ and so setting them equal means $$\frac{L_\odot}{4 \pi R_\odot^2}=\frac{L_{\text{ other star}}}{4 \pi R_{\text{ other star}}^2}$$ and ...


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Gas giants start big and luminous and get smaller and less luminous. Their gravitational contraction gives them a luminosity. The virial theorem then demands that they must contract in response if their gas pressure is a function of temperature. However after evolving for some time, the cores of gas giants become partially and then nearly fully electron ...



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