How long to freeze a planet?
If some advanced race were to make a solid opaque shell around our Sun, say around Mercury's orbit, something like a Dyson Sphere, how long would it take for Earth to freeze over and end most life?
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1 answer
Here, it is useful to treat the planet as a black body. The Stefan-Boltzmann law states that a black body will have a luminosity
This shows us that luminosity is a function of temperature. Luminosity is expressed in units of watts per second, meaning that it is a energy over time:
There are other corrections you have to make, though - for example, taking the atmosphere into account, as well as the fact that the Dyson Sphere, too, will radiate.
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