At least fifty of the brightest stars have names that are either of Greek or Latin origin (Sirius, Castor, Pollux), or Arabic (Altair, Fomalhaut). Many of the brighter naked-eye stars in the constellations, however, are designated not by name but by small letters of the Greek alphabet. In this system, introduced in 1603 by Johannes Bayer, the brightest star in a constellation generally is labeled Alpha or a, the second-brightest star is Beta or p, and so on down to Omega or ra. (There are important exceptions to this, however, as I will soon describe.)
The name of a star in the Bayer system is the Greek letter designation followed by the possessive of the constellation's Latin name. And, in fact, this is how astronomers still refer to these stars. For example, the brightest star in the constellation Canis Major, besides being called Sirius, is Alpha (a) Canis Majoris. (However, astronomers typically refer to the proper name of a star of that magnitude.) In the essays, I use both the Greek symbol as well as the name of the Greek letter to aid in helping you find the star on a star map.
As mentioned, the Bayer system, in a general sense, goes in order of descending brightness. But not always. For example, the seven brightest stars in Ursa Major, which comprise the Big Dipper, are lettered in order of their position from the cup, because they are not much different in brightness from one another. Thus, the brightest star in Ursa Major is fifth down, Epsilon (e) Ursa Majoris, rather than Alpha. There are other exceptions as well. In Orion, Rigel is quantitatively the brightest star in that constellation, but Betelgeuse, the second-brightest, is designated Alpha, while Rigel is designated Beta. The same is true in Gemini, in which Pollux, the constellation's brightest star, is designated Beta, while Castor, the second-brightest star, is designated Alpha.
For now, these things are all you need to know to get started observing the night sky. The few remaining terms relating to distances, types of stars, and other astronomical nomenclature will be defined in the text. You don't need to be versed in astronomical jargon to enjoy the night sky purely from an aesthetic point of view, but just as knowing where each of the cardinal directions lie from your home or how to read a road map can help you find your way from one place to another, these modest terms will help you move effortlessly from star to star until you know the heavens as well as your own neighborhood.
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