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Ringworlds and habitability on other planets

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This is the second part of a question here that I've broken up because they are two very distinct problems. Assuming a perfectly stable ringworld:

Assume a more traditional flat ringworld that is not quite so massive (Niven's first description was of one only a kilometer thick & the mass of Jupiter) and is much closer to the star, well outside the habitable zone. A planet in a discrete orbit "behind" the ringworld has all sunlight occluded by the ring. What kind of heat could this planet receive to make it habitable? Would radiation from the sun spill over the sides? Could the (metallic) ringworld itself, absorbing energy from the sun, radiate an appreciable amount of energy from its dark side into space and create a habitable zone that this planet would be within?

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This post was sourced from https://worldbuilding.stackexchange.com/q/79717. It is licensed under CC BY-SA 3.0.

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