Part 1 - Sun, Moon & Planets

Part 2 - The Stars

Part 3 - Seasons & the Celestial Sphere

Part 4 - Conclusion - Teaching Science Inductively

The Inductive Way to Understand the Sky

"This course is an unusual combination of elementary science and advanced epistemology."


Part 2 - The Stars

How many stars can we see on a clear night?

Of course, it depends where you are. If you’re in the mountains on a very clear, moonless night, then you will see many more stars than someone at sea-level in a populated area with a lot of background light. But let’s just consider the typical viewing conditions encountered by most people. On a clear night, such an observer might see 100 to 200 stars, depending on the time of year and whether the moon is out. Notice that this is not a huge number.

Now let’s consider the really bright stars, the ones that stand out from the others. Astronomers call these “first magnitude stars.” As it turns out, there are only 15 first magnitude stars that can be seen from the continental United States. This is a small number; it’s easy for us to learn and remember 15 items. Every child learns the 50 states and their capitals, which is much harder. And, unlike the states, the stars are directly available for our observation. So why doesn’t everybody know the bright stars?

It isn’t only because the material is taught badly. If the stars didn’t move—in other words, if each bright star was always seen in the same place—then it would be so easy to identify them that everybody would be able to do it even if schools never taught the subject at all. But, of course, the stars do move. They move east to west across the sky every night, so the sky looks different at nine in the evening than it does at midnight. Even worse, the stars have an annual motion relative to the sun, so they rise and set at different times during different months of the year. It’s complicated enough so that, if material isn’t presented the right way, most people never learn it.

So what is the right way to present it? The key is for the stargazer to be able to orient himself no matter when he is viewing the night sky. And the way to do that is to use what we call “guidepost” constellations. These are easily recognized constellations that are spaced such that you can always see at least one of them, and usually two. If you know how the guideposts are related to each other and to the most prominent surrounding constellations, then you can always orient yourself and identify what you see in the sky.

One of these key constellations is Orion. When it is high above the horizon at nighttime, it serves as an excellent guidepost. Of course, this isn’t always the case. In early summer, Orion rises and sets with the sun, and so we never see it. During normal viewing hours, it’s a great guidepost in the winter, but by spring it is getting a little too low in the western sky. Then we need another guidepost to take over.

Fortunately, we have the Big Dipper, which is high in the sky when Orion is low in the west. It is very distinctive and easily recognized; it’s made up of seven 2nd magnitude stars that are similar in brightness. During the evening hours, the Big Dipper is a very good guidepost in the spring.

By summer, the Big Dipper is getting lower in the sky and there is a better guidepost: the constellation Swan. Now, it turns out that Swan only looks like a swan if you can see all the stars, even the dim ones. Under normal conditions, we usually see only the four brightest stars, which form a T-shape. The brightest star is called Deneb, which is Arabic for “tail” of the swan. The other three stars are similar in brightness and visible on any clear night. Swan isn’t as spectacular as Orion and the Big Dipper, but it is easy to find and it makes an excellent guidepost when you can’t see Orion and the Big Dipper is getting low.

When Swan starts to get low in the western sky, there is a fourth constellation that can guide us: It’s called Cassiopeia. This constellation is supposed to represent a beautiful Queen, but in truth it just looks like an M. It consists of five stars that are bright enough to be seen on any clear night, and Cassiopeia is high in the sky during fall evenings.

These are the four main guideposts. In the evenings, we have a guidepost for each season: Orion in winter, Big Dipper in spring, Swan in summer, and Cassiopeia in fall. Now, how do we remember this?

First, remember that Orion rises and sets with the sun at summer solstice—that is, at the beginning of summer. That means that six months earlier or later, Orion is directly opposite the sun; in other words, around Christmas time it reaches its maximum height at midnight. This is why Orion is our guidepost during the winter.

Second, we can use a story to help us remember the order of our guideposts. Orion the hunter is the most spectacular constellation in the sky. As the next best constellation in the sky, the Big Dipper is jealous; it follows Orion and tries to dump its water on him. The Swan is thirsty, so it follows the Big Dipper to get a drink. Cassiopeia the Queen loves beauty, so she follows the beautiful swan in the attempt to capture it. Orion the hunter pursues the beautiful Queen—well, because that’s just the sort of thing men do. And that completes the cycle. Round and round they go, year after year. The jealous Big Dipper chases Orion, the thirsty Swan pursues the Big Dipper, the Queen pursues the beautiful Swan, and Orion chases the Queen.

Now, consider an important epistemological point. Notice something strange about the presentation so far: It’s still two-dimensional. I have been describing how constellations move across the sky, but ignoring variations in north-south position. Of course, later we will discuss the north-south variations and how the stars are positioned on the whole celestial sphere. We start, however, with a simplified, “sun-puppet” type presentation.

Earlier I pointed out that the reason people don’t already know the stars is because the stars don’t stay put; their daily and annual movements across the sky make the subject more complicated. This is what you have to master if you are going to learn the sky. So we start out discussing only the main direction of the movement, and to the extent possible we postpone discussing the north-south positions. (Of course, we have to say something; for example, we tell students that they should face south to look for Orion, and north to look for the other guidepost constellations.)

Now, a guidepost is supposed to guide you somewhere; otherwise, it’s not very useful. Our guidepost constellations are supposed to direct us to the other important constellations in that general area of the sky. And we will use stories to help us integrate and remember the entire group of constellations. Let’s see how it works.

[Start with the summer group and the story: The Archer battles the Scorpion, while the Eagle flies away to warn Swan of the danger. Point out the summer triangle (three first magnitude stars) and Antares.

Now sketch out the winter story: The Gemini Twins hold hands and toss a bone to Orion’s dog, while Orion protects the Twins from a charging Bull. A charioteer in the north leads Orion’s hunting party. Point out the great winter hexagon (seven first magnitude stars).]

You get the idea of how we use these guidepost constellations to orient ourselves and remember a whole section of the sky. Our book, The Stars, explains it all in detail. If you learn the four guideposts and their surrounding constellations, you will know most of the stars that can be seen in the continental United States under typical conditions. So, with just this much, you can become a fairly expert stargazer.

Let’s take another break from astronomy to identify the main epistemological point here. I mentioned earlier that the principle of hierarchy has a counterpart on the perceptual level; the fact that certain items stand out in our perceptual field implies that there can be a correct order of presentation. Now, the principle of integration also has a counterpart on the perceptual level. It’s useless to present a long series of unrelated observations—it simply can’t be retained. So we need to present the observations in an integrated framework that is easy to remember. That is exactly what is done in the Falling Apple book on the stars. We present the entire complexity by means of four guideposts related by a master story, and then a simple story relating each guidepost to the most important surrounding constellations. And the individual stories include maybe five constellations. So, it turns out, with less than 20 constellations, we cover all of the 1st magnitude stars and most of the 2nd magnitude stars. Contrast this with the usual approach of stating at the outset that there are 88 constellations, and then just plowing through them, one after another.

Now we need to talk about one more star. There is a very important star that I have left out so far: Polaris, the north star. Now, Polaris is a 2nd magnitude star, and it belongs to a constellation—the Little Dipper—that is faint and nothing to write home about. Polaris is important for only one reason: It marks the direction of north and is almost exactly on the axis of the celestial sphere, so as the other stars turn around, it never moves. It’s very convenient to have a star at this location, and for a long time travelers have used Polaris to determine their direction.

Polaris turns out to be useful for another reason: it tells you something about your location on Earth. At the North Pole, Polaris is seen directly overhead; at the equator, it is on the horizon. At locations in between, Polaris is seen at an angle above the horizon that is equal to the angle of that location above the equator—in other words, the elevation of Polaris is equal to the latitude of the observer.

Because of its importance and special status, it’s common for books on the stars to discuss Polaris and the north pole of the celestial sphere right at the outset. But we think this is a mistake. As a general rule, the stars move from east to west across the sky. To begin by presenting the exception—the one star that doesn’t move—is confusing. Instead, the student should learn about Polaris as the exception, after learning about the movements of the brighter stars and main constellations. Then, for us, Polaris provides a good segue into expanding the sun-puppet presentation to the whole celestial sphere. And that’s what we’ll do in the next class.

Let’s wrap up. The bottom-line is: If you choose the right material, present it in the right order, and find a way to tie it together into an interrelated whole—then even a complex topic can come across as transparently clear and easy. But this is a tricky business, involving a lot of choices that are far from obvious, and some clever innovations designed to achieve the integration. So it’s not difficult to understand why, in general, educators have not been able to do it. It’s the new frontier in education.

Book 2: The Stars

Part 3 - Seasons & the Celestial Sphere