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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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I've been interested in space and astronomy all my life, and I'm a lawyer. As such I've been thinking about the question - back in the public eye again with the Pluto encounter - of what the rules should be for defining a planet.

Here is my suggestion on the 'what is a planet' question in light of what we saw at Pluto.

A planet is a celestial body that:

1) Orbits the sun, not any other body.

2) Has achieved hydrostatic equilibrium (i.e. its own gravity has squashed it to be round).

3) Has one of the following properties:

3a) Is a gas giant*; or

3b) Has a surface modified by self-generated geological processes.

(*A more formal definition might be along the lines of 'more than half its mass is not in solid phase')

Point (1) excludes geologically active moons such as Io, Triton or Enceladus.

Point (2) excludes comets.

Point (3a) is probably obvious but ensures that Jupiter etc count despite not having a 'surface' for the purposes of point (3b).

Point (3b) is what distinguishes a planet from a large asteroid and also excludes Io etc as their geological activity is generated externally (tidal forces from their primary body).

On this definition, Jupiter, Saturn, Uranus and Nepture are all planets by virtue of point (3a). Mercury, Venus, Earth, Mars and Pluto (as seen in the last couple of days) are all planets by virtue of point (3b).

Pluto and Charon probably count as a 'double planet' given that Charon seems to meet (3b) too.

Ceres is not a planet because it doesn't meet (3b). Vesta is not a planet because it doesn't meet (2) or (3b).

Until we see their surfaces, we cannot class Eris, Haumea or Makemake as planets because we do not know that they meet (3b).

This definition returns us to the nine-planet solar system. It allows for Kuiper belt objects to be defined as planets if it turns out that they have been geologically active, but until we send probes to them they remain dwarf planets. Finally, in my view it is not an arbitrary criterion: having an active self-generated geology is a significant factor.
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Martin Mobberley’s biography of Sir Patrick Moore is saddled with perhaps the most ungainly title ever for such a work, and the first impression that the title conveys is only amplified by the subtitle: ‘A Fan’s Biography of Sir Patrick Moore.’ In the face of such, a reader could be forgiven for expecting a hagiography heavy on anecdote and light on research, and that is certainly what I was prepared for. I was pleasantly surprised to find that Mobberley has produced a well-researched, very thorough (640 pages) and, frankly, surprisingly honest examination of the life of the man who from the late 1950s onwards was synonymous with astronomy in the public eye.

Read more... )

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Simon Bradshaw

May 2017

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