The nearest star, beyond the Sun, is Alpha Centauri – an unfamiliar star for most of us because it is more than 60° south of the equator. It is a star system: Alpha Centauri A and B, a binary pair, 4.34 light-years from us; and a red dwarf we call Proxima, in a long orbit around the other two and, in our age, the nearest, 4.25 light-years from us.
Space out to 12 light-years from the Sun. Grid lines 4 light-years apart on the equatorial plane. See the end note about enlarging illustrations.
A question came from a reader of the famous EarthSky website:
“If Alpha Centauri is the third brightest star in our sky what is our Sun’s ranking of brightness of a hypothetical planet orbiting around say Alpha Centauri A? I would assume Alpha Centauri B and Alpha Proxima would be significantly brighter than our Sun due to their proximity to Alpha Centauri A. Given our proximity to the Alpha Centauri cluster I would guess we’re maybe 5th after Sirius and Canopus.”
My cover picture story for Astronomical Calendar 1989 was about the “View from Alpha Centauri,” so I thought I might have worked on this subject then; but I had only partially done so.
I’ll call it allocentric, “other-centered,” as distinct from geocentric, “Earth-centered,” and heliocentric, “Sun-centered.” The word already exists, according to the Oxford English Dictionary, but with uses in medicine and psychology. I can use -ACEN- in my programming algebra, suggesting both “allocentric” and “Alpha Centauri.”
The question is: given the position (right ascension and declination), distance, and magnitude (brightness) of stars A and B as seen from the Sun, what is the distance and magnitude of B as seen from A?
It’s easy to see this algorithm – outline of the problem – and there’s a chain of equations for the steps in the procedure (finding, on the way, the rectangular coordinates from the polar ones and the absolute magnitudes from the apparent ones, and then back). What is tangled is that it’s a multidimensional situation, in which numbers have to be stored in arrays so as to be sorted into order, the combinations growing exponentially with the number of stars being compared. Imagine, in my space diagram, a sight-line from every star to every other star. A cat-s cradle, like the connections of neurons in a small brain! This is mostly what has taken me ten days of program-rewriting.
We can’t consider all the stars in the sky – that would take a super-computer – so I consider some of the nearest, and some of the brightest. Here’s a list, with their distances in light-years and apparent magnitudes.
from Sun by distance dily mag 1 Proxima Centauri 4.2465 10.43 2 Alpha Centauri A 4.344 0.01 3 Alpha Centauri B 4.344 1.33 4 Barnard's Star 5.9629 4.83 5 Sirius 8.60 -1.46 6 Procyon 11.4 0.38 7 Vega 26.4 0.03 8 Arcturus 36 -0.04 9 Canopus 310 -0.72 10 Deneb 2600 1.25
There are other small stars nearer to us than Procyon; and others in the “top twenty” of brightness above the extraordinary Deneb.
Now to study them allocentrically. For example, their order of distance from Alpha Centauri A:
from Alpha Centauri A by distance dily mag 1 Alpha Centauri B 0.0003 -19.16 2 Proxima Centauri 0.1907 3.69 3 Sun 4.3440 0.45 4 Barnard's Star 6.4656 5.01 5 Sirius 9.5366 -1.24 6 Procyon 13.6481 0.77 7 Vega 28.3313 0.18 8 Arcturus 37.7179 0.07 9 Canopus 311.5053 -0.71 10 Deneb 2617.4569 1.25
And the Centarocentric order of brightness:
from Alpha Centauri A by magnitude dily mag 1 Alpha Centauri B 0.0003 -19.16 2 Sirius 9.5366 -1.24 3 Canopus 311.5053 -0.71 4 Arcturus 37.7179 0.07 5 Vega 28.3313 0.18 6 Sun 4.3440 0.45 7 Procyon 13.6481 0.77 8 Deneb 2617.4569 1.25 9 Proxima Centauri 0.1907 3.69 10 Barnard's Star 6.4656 5.01
Compare this with the apparent magnitude of the Sun as seen from Earth: -26.8.
Let’s try our brightest star as the allocenter:
from Sirius by magnitude dily mag 1 Canopus 311.5841 -0.71 2 Arcturus 38.4343 0.11 3 Vega 29.2816 0.25 4 Procyon 15.5344 1.05 5 Deneb 2617.4575 1.25 6 Alpha Centauri A 9.5366 1.72 7 Sun 8.6000 1.94 8 Alpha Centauri B 9.5363 3.04 9 Barnard's Star 14.4241 6.75 10 Proxima Centauri 9.3622 12.15
And the most distant of our bright stars:
from Deneb by magnitude dily mag 1 Canopus 2305.9745 3.64 2 Arcturus 2579.9517 9.24 3 Vega 2589.4104 9.99 4 Sirius 2617.4575 10.95 5 Procyon 2604.4140 12.17 6 Alpha Centauri A 2617.4569 13.91 7 Sun 2615.8296 14.35 8 Alpha Centauri B 2617.4568 15.23 9 Barnard's Star 2615.8933 18.04 10 Proxima Centauri 2617.3804 24.38
Two remarks for the accuracy-minded: Don’t let it bother you that some of my numbers are given to ridiculous levels of precision; rounding them depending on their size is a lot more trouble. And: You may find different recent figures for the distance or magnitude of some of the stars. They shouldn’t make much difference.
Comparing the lists, you can see that – well, I’m going to take a rest from cogitation. Let us know if you can make any generalization about the changes in these orders of brightness from different viewpoints.
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ILLUSTRATIONS in these posts are made with precision but have to be inserted in another format. You may be able to enlarge them on your monitor. One way: right-click, and choose “View image” or “Open image in new tab”, then enlarge. Or choose “Copy image”, then put it on your desktop, then open it. On an iPad or phone, use the finger gesture that enlarges (spreading with two fingers, or tapping and dragging with three fingers). Other methods have been suggested, such as dragging the image to the desktop and opening it in other ways.
This is a thought, not a request. I wonder how the orders of apparent magnitude would change if a red supergiant, Antares or Betelgeuse, either about 600 light years from our neighborhood, were added to the list. I think they would be about equally bright from the Sun or Alpha Centauri, and either would be the brightest star on the list as seen from Deneb.
I’ll think into it more when I, as I hope, turn this topic into an “astronomical miscellany” page.
One easy generalization is that from a very distant star, such as Deneb, all our close neighbors would form a group in which their order of apparent magnitude is the same as their order of absolute magnitude.
The term allosaurus jumped to mind.LOL. June is the month to see Alpha Cent skim your southern horizon in the evening hours. In 2017 I saw Canopus skimming from Big Bend NP in Texas. From the Gulf coast at say Galveston, Alpha Cent would be lifted by refraction and be half a degree up. With atmospheric extinction it would be a challenge. From Sydney it transits 60 degrees up before 10 pm and forms a horizontal line with Beta.
The creatures of the planet around Alpha Centauri that you portrayed in 1989 might have a tougher time learning about astronomy because they would only be able to properly see the night sky when it was night AND Alpha Centauri B was out of the sky as well; if their planet had a satellite like our Moon it would be even more challenging to see a properly dark sky.
Alpha Centauri is obviously very well known to those of us living in the southern hemisphere. For the past few months, during my evening walks, I’ve been enjoying the spectacle of it and the three other brightest stars, Sirius, Canopus and Arcturus spread out gloriously across the night sky.
Very bright stars are bright, even from a great distance. Very dim stars are dim, even from a close distance. Middling stars are bright when you’re close to them and dim from farther away.
Thanks for doing the math!
What I find most interesting is the Sun comes in about 7th brightest in each list even from Deneb! Though I’m sure that has more to do the selection of stars chosen for comparison.
Not that unfamiliar a star for although I can’t see Alpha Centauri now I spent my childhood in South Africa and have seen it loads of times plus more recently on trips to southern hemisphere nations and places technically in the northern hemisphere but under the Tropic of Cancer where it rises.Due it’s closeness it’s probably the best known southern hemisphere star although possibly beaten by Sirius due to it being the brightest star?AC is certainly more famous than Canopus.Beta Centauri, not to be confused with Alpha B,is very bright but pretty remote.