The announcement of the discovery of a planet orbiting Proxima Centauri is absolutely fascinating; we finally have a (roughly) Earth-size world orbiting in the (notionally) habitable zone of a (by astronomical standards) close star. There's been a lot of speculation about what Proxima b might be like, but one description I saw didn't quite ring
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Pluto's daylight actually ranges from two hundred to six hundred times brighter than moonlight on Earth, comparable to a badly overcast day on Earth or the lighting in an average home. It generally appears to be much darker because the Sun is perceived as a bright star, there is no atmospheric scattering of light, shadows are completely dark, and most of the surface materials absorb light with minimal reflections.
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Unless of course you're standing in whatever Cthulhu Regio is made of.
(Snoozing Shoggoths, presumably).
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Can you mock up a picture: Earth daytime, Earth moonlight and Proximity's daytime?
There's an artist's impression on the Wikipedia entry, but that 'sun' looks the same size as ours. There's a comparison further down, so I guess that does the trick.
What difference does Alpha Centauri A and B make to all this? Are they bright enough to make a sunny day? One thought, if Proximity is tidally locked, then Alpha Centauri A and B will rise and fall every 11 days.
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From Earth, at a distance of 4.37 light years, Alpha Centauri A has a magnitude of 0.01 and Alpha Centauri B a magnitude of 1.33. The brightness increase from Proxima Centauri will be
2.5 log (4.37 / 0.21)2 = 6.6 magnitudes
So, Alpha Centauri A would be Mag -6.6 and Alpha Centauri B would be Mag -5.3. That's about three times brighter and about half as bright again than Venus at its brightest respectively.
From Proxima Centauri, the maximum separation of Alpha Centauri A and B would be about 0.15 degrees at most. Much of the time they would probably look like one bright star perhaps four times brighter than Venus. In other words, not enough to affect how bright daylight seemed on Proxima b.
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Of course, dependent upon any atmosphere, which I'd have thought likely given that Proximity is slightly bigger than the Earth. If Proxima gives a dull daylight day, then on a dull day, it would be very gloomy.
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In terms of the sky, this is my guess at Earth (top) and Proxima B. It's hard to do a real comparison as of course your eyes would adjust in dimmer light, but it would seem dimmer and yellower.
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