Aug. 26th, 2016

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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 true: the picture one article painted of Proxima Centauri, a relatively dim red dwarf, hanging in the sky like a dull glowing ember. It's a faint star, true, but it's still a star, so how bright would it seem from Proxima b?

To start, some basic data.

Proxima Centauri is visual magnitude 11.13 and is 4.25 light years away. Its diameter is 0.141 x that of the Sun.

Proxima b orbits at 0.0485 astronomical units.

1 light year = 63,241 AU, so Proxima b is closer to Proxima Centauri than we are by a factor of

(4.25 x 63,241) / 0.0485 = 5,541,737, or 5.54 x 106

This means that Proxima Centauri's brightness from Proxima b, as compared to Earth, will be increased by this factor squared

= 3.07 x 1013 times brighter

Converting that to stellar magnitudes gives us

2.5 log (3.07 x 1013) = 33.72 magnitudes brighter

So, the visual magnitude of Proxima Centauri from Proxima b would be

11.13 - 33.72 = -22.59

Now, the apparent visual magnitude of the Sun is -26.7, so in comparison to the Sun, this is

-26.7 - (-22.59) = -4.11 magnitudes fainter

That corresponds in actual brightness ratio to

10(-4.11 / 2.5) = 0.0226 = 1/44

So from Proxima b, Proxima Centauri would look 44 times less bright than the Sun does from Earth.

At first, that might seem surprising; after all, isn't Proxima b meant to be in Proxima Centauri's habitable zone? Surely that means that it ought to be getting the roughly the same energy from Proxima Centauri as we get from the Sun? Well, it does - but far more of it is in infra-red rather than visible, because Proxima Centauri is an M6 class red dwarf with a surface temperature of about 3,000K, whereas the sun is a G2 yellow dwarf with a surface temperature of 6,000K. Standing on the surface of Proxima b in daylight would feel as warm as standing in daylight does on Earth.

It wouldn't even look much darker. A factor of 44 times sounds a lot, but that corresponds to a dull overcast on Earth. Day on Proxima b would still look like day, although a bit odd.

But back to the question of how bright Proxima Centauri would look. It is much smaller than the Sun, but Proxima b is proportionately even closer to it than we are to the Sun. The ratio in apparent diameter is

0.141 / 0.0485 = 2.9

- Proxima Centauri is nearly three times larger in angular diameter in the sky than the Sun is for us. That means it occupies the square of that in terms of area of the sky

2.92 = 8.45 times the area of the Sun

This means that the brightness of Proxima Centauri is not only 1/44th that of the Sun in our sky, but is spread over 8.45 times the area, so the apparent surface brightness is reduced even further

44 x 8.45 = 372 times less bright per area of sky

That, mind you, is still very bright. To put it in perspective, the full moon is 14 magnitudes less bright than the Sun, or about 400,000 times. In terms of apparent intensity, Proxima Centauri as seen from Proxima b would still be a thousand times brighter-looking than the full Moon seems. Bearing in mind that you would see it in a rather dimmer sky, I suspect it would look to all intents and purposes as bright as the Sun does from Earth.

This isn't surprising. 3,000K is still way past red-hot by normal standards. In fact, heat something to that temperature and it will be white-hot to the naked eye. 3,000K is about the temperature of the filament of an incandescent light bulb, the light from which looks white unless you are comparing it to sunlight (when, as photographers know, it looks yellowish by comparison).

So, Proxima b won't have a 'glowing ember' in the sky. It will have a sun that would look at first glance like our own. It won't be as intense - in fact, I'd hazard a guess that you could probably look straight at it without discomfort - and it would be noticeably bigger in the sky, but it would still seem like a big white-hot thing.

Photography will be a pain, though. What would be a picture at f/16 on a sunny day on Earth will have to be taken at about f/2 on Proxima b - and remember to set your camera to 'indoor tungsten' light temperature.

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Simon Bradshaw

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