My wife and her cousin were under the common misapprehension that Polaris is the brightest star in the sky. While proving them wrong, I mentioned that the apparant magnatude of Sirius is about -1.4 and the apparant magnatude of Polaris is about 2.
They wanted to knwo why brighter stars have lower magnatudes and all I could answer is, “because that’s how they do it”
Is there a reason for this?
From here:
The story of measuring and estimating star brightness goes back to around 129 BC, when the greek astronomer Hipparchus produced the first well known star catalog. Hipparchus ranked his stars in a simple way. He called the brightest ones “of the first magnitude”, simply meaning the biggest. Stars not so bright he called “of the second magnitude”. The faintest stars he could see he called “of the sixth magnitude”. This system was copied by Claudius Ptolemy in his list of stars around AD 140. Sometimes Ptolemy added the words “greater” or “smaller” to distinguish some stars within a magnitude class. Ptolemy’s catalogue remained the basic astronomy text for the next 1400 years and the same basic (backward) scale is still used.
The explanation I always heard was that before there were ways to accurately measure how much light was coming from a star, the stars were just classified into broad categories. The “first-magnitude” stars were the top tier of brightness; the “second-magnitude” stars the next highest tier; and so forth. Only once accurate methods of quantifying a star’s brightness came along did astronomers standardize things, and of course they wanted their new scale to look something like the old one.
Not much better than “they’ve always done it that way”, I know, but there you have it.
Well at least that makes some kind of sense.
So when did they establish the current ranking system and what did they base it on?
What I mean by that is there some object that is the starting point? Did they pick a star and say “ok that star is magnatude 1 so now we have to figure out the others based on that”
A short but decent explanation can be found here.
The magnitude system was originally a ranking of stellar brightnesses, done purely by eye, before the arrival of accurate photometry. It was later retrofitted to accommodate modern measuring techniques.
I believe Vega defines the zero point of the scale, with each 5 magnitude “units” signifying a ratio of 100 in brightness levels. (Like the earthquake scale, stellar magnitudes are a logarithmic mapping.)
Yet another good explanation can be found here.
Not an explanation for backwards numbering but a simple explanation (and calculator) can be found here:
http://www.1728.com/magntude.htm
This is correct. In fact, Vega (the fifth brightest nighttime star) is defined as being 0 magnitude in any filter, making it not only the astronomical standard for brightness but also for whiteness.
Of course, all of the stars with a magnitude of less than one would have been called first magnitude by Hipparchus, but there are only fourteen of these (and only nine viewable from Greece), so that doesn’t exactly shake up the system much.
Yep. So we’re in for a lot of expensive re-calibrating when Vega leaves the Main Sequence.
I know I won’t be typing in all those corrections. Dump that chore on some grad student.
Okay, that raises the question of which ones are brightest. Aside from the Sun, my list from memory is:
I know both Betelgeuse and Rigel are in or close to the top ten.
(By the way, I actually got to see Canopus – sometime last year was just barely above the southern horizon here at midnight, and we have an open view to the south.)
Name Magnitude
Sirius -1.46
Canopus -0.72
Rigil Kentaurus -0.27
Arcturus -0.04
Vega 0.03
Capella 0.08
Rigel 0.12
Procyon 0.38
Achernar 0.46
Betelgeuse 0.50 (var.)
Hadar 0.61 (var.)
Acrux 0.76
Altair 0.77
Aldebaran 0.85 (var.)
Antares 0.96 (var.)
In Hipparchus’ time (ca. 147 BC) because of the precession of the equinoxes, Hadar, Alpha Centauri, and Acrux would have been visible from Greece. 
Me too, no my way down here from Las Vegas. Stayed one night in a little town in northern AZ and it was just this little bright dot over the mountains. It was quite an exciting moment seeing it down there with Orion and Canis Major so high up in the sky above it. 
OK, my list puts Betelgeuse down between Altair and Aldebaran, and give slightly different magnitude values, but otherwise, that agrees.
Huh. I didn’t take precession into account, so I’ll take your word for it. But if Hipparchus was able to see alpha Cen and Acrux, and he surely noted they were bright ones, why do they have such boring names?