What's the brightness of Alpha Centauri from Proxima Centauri?
Self-explanatory, but I would like a comparison as well. Is the light enough to see by? How disrupted will the pitch darkness on the spot opposite of the 'solar pole' be?
Not close to being able to read by.
Proxima Centauri is about 13,000 AU from the two binary Centari stars. Together they have about twice the luminosity of the sun but at 13,000 AU, that's roughly 2/169,000,000 the visible light that the Earth gets from the Sun.
The brightness variation of the full moon to the Sun is about 1 to 440,000, so, some rough math, the two stars would shine about 1/190th as bright as the full moon. That would make those 2 stars by far the brightest stars in the Proxima Centauri sky, but far short of reading light. Together, the two stars would be about 10 times as bright as Venus at Venus' peak. (Venus is about 1/2000th as bright as the moon, -4.4 apparent magnitude to -12.6 for the moon).
That would, I think, be bright enough to be visible during the day under an earth like sky a lot of the time.
The two stars would be quite close to each other too, maximum visible distance between them would be roughly 1/4 the diameter of the full moon, where they would still be visible separate stars when far apart, but they would pass close to each other too, perhaps appearing to touch to the naked eye.
The two stars complete a full orbit around each other in 79.9 years, so the variation would be noticeable over a human lifetime.