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    $\begingroup$ Calculations like the above are not really in my wheelhouse, so please take the above numbers with a grain of salt, and if someone would be so kind as to check my work I'd be grateful. $\endgroup$ Commented Feb 3, 2023 at 22:19
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    $\begingroup$ I disagree on your math--you are assuming a star as bright as our own and in reality most stars are red dwarfs and you are neglecting the luminosity drop off as you approach the limbs of the star. However, I fully agree with the basic concept, you're at most a few zeroes off and that doesn't meaningfully change the basic concept. The sky must be empty or we cook. $\endgroup$ Commented Feb 3, 2023 at 23:01
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    $\begingroup$ Also seems to ignore redshift. $\endgroup$
    – ProfRob
    Commented Feb 3, 2023 at 23:26
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    $\begingroup$ By that, I mean that every sight line does end up on something that had the surface temperature of a star - it's the cosmic microwave background. The argument presented at the moment is only that the sky cannot be (geometrically) full of the discs of unredshifted stars. $\endgroup$
    – ProfRob
    Commented Feb 4, 2023 at 8:40
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    $\begingroup$ @ProfRob: I tweaked my preamble just now to mention "a sufficiently large telescope." :-) $\endgroup$ Commented Feb 4, 2023 at 14:28