This is the last in a series of four posts on the stars of the summer night sky: bright stars like Vega and Arcturus; middling stars like Polaris (the North Star) and Mizar (the star in the “bend” of the Big Dipper’s handle); and faint stars like Rho Leo and the companion of Mizar, Alcor. These posts have asked what it is we see when we look at the summer stars. They have questioned the idea that the sun is a star, and have asked if the stars are suns. And they have asked how we even know anything about the stars at all.
We have learned how we know what the stars are, and using that knowledge we have seen that while the sun is certainly a star, the summer stars themselves vary wildly in size and in power or luminosity. Among such incredible stellar diversity are many bodies that are very different from the sun. But all this knowledge about the stars came from just three measurements:
- An annual motion of a star (parallax).
- The magnitude of that star.
- The color of that star.
We do not measure the size of a star like we might measure the size of a window with a ruler. We do not measure the distance to a star like we might measure the distance to a friend’s house with our car’s odometer. We do not measure the power output of a star like an engineer might measure the output of a new kind of light bulb. We have never been to a star to make such direct measurements, and we are not likely to go to one in the near future. Rather, we measure movement, magnitude, and color, and from these things we reason mathematically to determine the star’s size, distance, temperature, and luminosity. 
We reason by analogy—the light of stars matches the light given off by a dense, incandescent object like a piece of hot iron. We suppose that stars and incandescent iron behave in the same basic ways: the luminosity of an iron ball increases as the square of its radius and the fourth power of its temperature, thus so does the luminosity of a star. In short, we suppose that the heavens and the Earth are under the same rule.
If we are wrong about the specific supposition that stars and glowing iron have something in common, we may be very wrong about the sizes and luminosities of stars now, but we can hope to figure things out better in the future. And we can imagine why there might be limits to this sort of supposition. For example, my fellow blogger Brenda Frye has noted that there is a limit to how massive a star can be, and that limit is only about 150 times the mass of the sun. But Antares takes up much, much more than 150 times the volume of the sun. Antares must be a lot less dense than the sun. How much less dense can Antares be before it stops being a “dense, incandescent body,” and the analogy to iron breaks down, throwing off our mathematical reasoning? On the other hand, if we are wrong about the general supposition that the heavens and the Earth are under the same rule, so that in fact maybe the stars are controlled by magic Elves who choose the coloring and brightness and motion of the stars for their own inscrutable Elvish reasons, that would do more than throw off our reasoning a bit. That would mean that we could never hope to know anything about the stars other than their motion, their magnitude, and their color. That would really stink.
Keep this in mind when you look up at the summer stars, or when you hear about how far away a certain star is, or how large or powerful it might be. It is cool, cool, cool to be able to look up at the summer sky and see the stars, and know something about what you are looking at, and to know how you know what you know, and to know why it is even possible to know what you know. There is so much to see and think about in the stars of the summer sky.
