Look at a picture of a spiral galaxy. I happen to think that spiral galaxies are about the most beautiful things in the universe. Look at what you see in the picture. It is a gravitationally bound system of billions of stars, all orbiting the center of mass in the center. At this scale we see only the largest blue giant stars; the rest merge into a glorious glowing mass of gas clouds and color. As far as we know, the Milky Way Galaxy looks something like this. For perspective, the Sun would not be visible in a photograph like this.
In the night sky, the Milky Way is a softly glowing ragged band of light that circles the entire celestial sphere. It is quite obvious and lovely in a dark sky (of course, from in the city you can't see it at all). Look at the photograph of it at the bottom of page 392. The dark blotches are dark dust clouds. It suggests that the Galaxy, whatever its shape, is at least flattened. Looking at pictures of other spiral galaxies gives us good reason to suspect that the Milky Way is similar to other spiral galaxies. Look at a picture of a spiral galaxy edge-on. Notice the resemblance to the Milky Way.
To imagine the shape of such a galaxy, imagine a really perfect fried egg, with the white being perfectly circular and the yolk exactly in the center. Take two of these and put them back to back and you have it. The Galaxy is disk-shaped (like the egg whites) and has a central bulge (the yolks).
One note: when you see the word galaxy capitalized, as Galaxy, astronomers are referring to the Milky Way. If astronomers refer to a galaxy (not capitalized), they are referring to an exterior galaxy (beyond the Milky Way).
Discovering the true shape of the Milky Way is not easy - we are buried inside it! We can see lots of ISM that blocks our view. In the 18th century, William (Wilhelm) Herschel attempted to determine the shape by counting stars by apparent brightness (this was over 100 years before the H-R diagram was known). The resulting counts led Herschel to postulate that the Galaxy looked like the drawing in Figure 14.3. Strange looking thing, isn't it? It has one very suspicious property - the Sun is near the center. This weird shape does suggest that the Galaxy is flattened (correct), but the shape and size are not right. There are two assumptions in this technique, both of which are wrong. One is that the stars are all the same luminosity and the other is that space is empty and transparent. We now know that stars vary widely in luminosity and that space (at least in the Galaxy) is loaded with ISM (gas and dust). The strange shape of Herschel's estimate is due to these factors. Truth is that Herschel came nowhere close to locating the center.
There are some evolved stars which pulsate (vary) all by themselves. They go through a cycle of expansion and contraction because of the behavior of helium in the star. There are two types of these: Cepheid variables and RR Lyrae variables. These are called intrinsic variables because they actually change brightness, as opposed to eclipsing binaries, where one star blocks out the light of its companion for a short time. These two types of intrinsic variable are post-main-sequence stars; Cepheids are large former blue giants on the way to their red giant phase and RR Lyrae stars are lower mass stars that have reached the Horizontal Branch on the H-R diagram. The wonderful property of these stars that makes them so valuable is the fact that their luminosities and their periods of variation are related. You can see this for Cepheids in Figure 14.6. RR Lyrae stars are all very similar in luminosity. Examination of the light curve and spectrum of the variable star will identify it. With that knowledge, measurement of its period of variation will yield an estimate of its absolute magnitude (M), from which a distance can be computed. That's why these variable stars are so important - their distances can be found.
Here's a nice spread of a Cepheid variable in M100.
The distance ladder isn't exactly a ladder - it is a structure of distance-measuring techniques, each one built on the one below it on the ladder. It's all based on the AU, which has been measured to 8 significant figures using modern radar! The principle of radar is simple; a radio pulse goes out and an echo comes back. The next method up the ladder is parallax, which is based on knowledge of the AU. The limit for parallax measurement is our ability to measure the small angles of parallax; when distance makes the parallax less than our uncertainty of measurement, we have reached the limit of about 200 parsecs. A few orbiting spacecraft have extended this to over 500 parsecs by avoiding the effects of the atmosphere.
Remember that parallax measurements of distance, when combined with spectral analysis of nearby stars, yielded the H-R diagram and the knowledge of stars that it revealed. The H-R diagram allows the use of spectroscopic parallax to find distances. This technique applied to star clusters allowed the approximate calibration of the Cepheid variables. In the 21st century the Hubble Space Telescope has actually gotten parallax measurements for a handful of Cepheids and therefore reduced the uncertainty to about 10%. The Cepheids are enormously useful, and even better calibration will only improve their accuracy.
Check out the "Early Computers" box on page 371. This is a glimpse into how some very important astronomy was done over 100 years ago. Those women, known as "computers," examined and analyzed huge numbers of plates and star images. It's not that the observatory director hired them because he was so progressive at the end of the 19th century, but that the women would work for less than men and were better at the repetitive analysis chore. They did a prodigious amount of basic work and made some significant discoveries. The box lists some of them. By the way, the lady sitting in the back left, under the pictures on the wall and facing to your right, looks like Henrietta Swan Leavitt, the discoverer of the period-luminosity relationship of Cepheid variables.
The key to the Galaxy's shape lay in globular clusters. These spherical aggregations of stars swarm around the other galaxies we can see and are also known to exist around the Milky Way; over 120 are known. Fortunately for astronomers, globular clusters contain lots of RR Lyrae variable stars. The presence of those allowed Harlow Shapley to determine the distribution of those clusters in three dimensions. The center of that distribution revealed where the center of the Galaxy was.
How does this work? The globular clusters must be orbiting the Galaxy; if they were NOT moving they would have fallen in to the center long ago. If they ARE orbiting, they must be orbiting a center of mass (ALL orbiting bodies do that). Next, you have to assume that the distribution of the clusters is reasonably random, with the clusters distributed rather evenly all around. Given that, the center of the cluster distribution will be quite close to the center of mass of the Galaxy.
Once Shapley located the center of the Galaxy, it was obvious that we are NOT in the center, or even near the center. We are about 8 kpc (26,000 LY) out from the center. The Sun is out in the disk of the spiral galaxy. We are not able to see the center of the Galaxy, at least with visible light, because of the 8 kpc of ISM that is in the way. It blocks the light quite thoroughly. The galactic center has, however, been observed in infrared and radio wavelengths; these pass through the ISM quite freely. This image of the Milky Way's center was made in infrared wavelengths. This X-Ray image made by the Chandra X-ray telescope, schows a jet coming from the black hole at the center.
You can at least look toward the center of the Galaxy. It's in the summer sky, above the scorpion's tail and the spout of the teapot (Sagittarius).