About 4000 stars are visible on a really dark, clear night. If you know that stars, you can mention them by name. "There's Sirius, the brightest star in our night sky." Or, "Over there is Polaris, it's only the fiftieth brightest star, but it always shows which way is north." (If you want to drive your friends mad, suggest they count out the first 49 bright stars to find Polaris.)
Sirius as a name come from ancient Greek, and means bright in that language. The star is located in the constellation of Canis Major, the Big Dog. There are two other dog constellations, Canis Minor, the small dog, which has a very bright star named Procyon in it. Procyon means the leading dog. Finally we have Canes Venatici, the hunting dogs, which lacks bright stars, although it has three visible stars with names, Cor Caroli, Chara, and La Superba. There are also four named galaxies, the Whirlpool, Sunflower, Croc's Eye, and Silver Needle. Note the galaxies all have names in English. That is because other galaxies were only recognized after 1923. The names do not come down from centuries ago.
Ursa Major, the Big Bear, has the most named stars, 22, also with four named galaxies. Most of the star names, as is true throughout the sky, derive from Arabic. Dubhe, for example, simply is the Arabic word for bear (perhaps not the most useful Arabic word to know if you find yourself in Cairo). Megrez means base of the tail. This is typical of most star names, which either describe the star, or its location in its constellation.
Of course, there are some oddities, such as a star whose name means hyena in Draco the dragon, or monkey in Columba the dove. These names are remnants of ancient constellations that have been lost, eliminated or ignored.
Some names present challenges in various ways. Libra has five named stars: Zubeneschamali, Zubenelgenubi, Zubenelgubi, Zubenhakrabi, and Mulizi. Zuben means claw in Arabic, and the rest of the names mean north, south, or just "of the crab." Mulizi snuck in from the Akkadian language of 3000 years ago, and means "man of fire." (I used to rattle those names off to my classes, and then say they would be on their next test, "spelling counts." Strictly to see who was awake.)
About a dozen stars are named for astronomers who either discovered them or did major studies of them. The eminent Dutch astronomer Jacobus Kapteyn (1851-1922) has a star in the southern constellation of Pictor, a crater on the Moon, and an asteroid named for him, an impressive celestial trifecta.
There are 88 constellations recognized by the astronomical community today, based on recommendations made about 130 years ago by Benjamin S. Gould, the first American to earn a PhD in astronomy (he got it from Heidelberg University in Germany, where they have been giving such degrees for centuries). Gould selected the 48 ancient constellations and 40 that had been invented mostly between 1500 and 1800 to fill gaps left by the ancients. 81 of these constellations have one or more stars with a name more interesting than a Greek letter or catalog number. Most of the seven with no named stars are modern, dim, southern constellations, such as Antlia and Circinus.
Around 1600 a German mapmaker, Johannes Bayer, created a map of the sky, and for no known reason attached Greek letters to many of the stars. His idea was popular, and thus we have such names as Alpha Centauri. The first Astronomer Royal, John Flamsteed had a different idea, and around 1690 started the practice of numbering stars within each constellation, going from west to east. Thus Sirius is also Alpha Canis Majoris and 8 Canis Majoris (neither of these is a particularly popular alternative). Later catalogs have introduced additional ways to designate a star, the result being that the average star has as many pseudonyms as the average hard working bank robber.
Notice that there is no mention of purchased names. These are totally ignored by the astronomy profession, and it is a source of annoyance to have people walk into a planetarium and ask to be shown a star they think they purchased. (If they bought the Brookyn Bridge it would be as meaningful.) In my many years of training students to work in the planetarium field, one of the things I have had to advise is how to handle people with negative reactions to learning they wasted their money, particularly bereaved parents who had hoped to create a lasting memorial to a deceased child.
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