A Paper Celestial Sphere

A spherical "map of outer space" to print, draw on, cut out, and tape together.

The "World Map of all the Constellations"

When I teach astronomy to children, we spend a good part of the year (off and on) going over the individual stars and constellations that they can see in the night sky after dinner. Sometimes students will try taping the paper charts of different constellations next to each other to represent how they go together. Somewhere along the way, after we have learned a few constellations over there and over there and over there, a student will often ask if it is possible to make a "world map" of all the constellations. If nobody asks, I wonder it aloud for them. If we could make such a map, what shape would it have to have? (We might have a problem with the fact that the constellations move, and are in different parts of the sky in different times. We have a few questions of motion to figure out, but it turns out that we can make a "world map of stars", in the shape of a sphere, as long as we remember that it has to spin the right way.) And if we can make such a "world map of stars", wouldn't it be almost as useful as a globe map of the earth? The globe is our map of all of our home world, and a spherical "globe" of constellations would be our map of all outer space.

And some time after Christmas, after we have finally covered all of the bright and helpful landmarks in the sky, it is finally time to see if we can put all the pieces together and make our "world map" of all constellations, our map of outer space.

The Terrestrial and Celestial Spheres

Perhaps you are familiar with The School of Athens, Raphael's tribute to the seekers of wisdom in the ancient world. Do you notice anything if you look closely at the right side?

The School of Athens, by Raphael

In the lower right-hand corner of the painting, we see two figures holding two spheres. One sphere is a mélange of blue and brown-green regions. The other sphere has lots of tiny white or yellow spangles on a dark, maybe dark blue, background. What do you suppose these two spheres are supposed to represent? (For some reason I haven't figured out yet, young children often say the earth and the moon, despite the fact we've spent the last class period or two talking about the "world map of stars". I wonder if maybe 2nd or 3rd grade is the youngest we should expect children to be able to grasp the concept of a spherical map of the constellations surrounding us...)

Among many aspects of wisdom depicted in the painting, these two spheres represent Greek knowledge of the structure of our cosmos. They represent our two maps of the universe. The blue-green sphere is obviously a depiction of the earth, our home world. The Ancient Greeks figured out long ago that the world had the shape of a sphere, despite having only mapped out less than an eighth of the surface. What was on the other side of the sphere was a total mystery, but they knew their world was round, and composed of land and sea. That's the first of the two spheres. The second sphere is our map of outer space, our neighborhood in all directions. Whether there is a physical "crystal sphere" surrounding us and spinning, or whether there are just a bunch of stars scattered around in space with us spinning as we watch them, was a challenging question to answer. But the immediately useful point is that we can make a map of outer space as a sphere around us, and to this day, we refer to this map as the "celestial sphere".

The Terrestrial and Celestial Spheres

Manufactured Celestial Spheres

So if we wish to admire a celestial sphere, a "constellation globe", what can we do? A few manufacturers of globes also make celestial spheres as well, such as:

It is also not too difficult for stone-workers to produce polished stone spheres, and sometimes people turn these stone spheres into globes. Even better, if you rest the sphere on a concave water fountain, they will "float", allowing you (with lots of effort) to spin them and turn them any way you wish. Such things are called Kugel Fountains, and I really wish there were more of them around. This is an example of a kugel fountain globe at my local car wash:

A Kugel Fountain Globe

And even better, this is an example of a kugel fountain celestial sphere at Johnson Space Center in Florida.

"Reaching For the Stars", from Wikimedia Commons

However, despite how impressive such manufactured celestial globes might be, they have a fundamental drawback. There is a basic flaw in making a globe of stars that we can hold in our hands (or in a stone cradle) and look at. Can you see the flaw? Whenever we look at spheres like this, we are on the outside looking in, when we should be on the inside looking out. These celestial globes are supposed to represent the sphere of constellations surrounding us, so if we draw them as a sphere with us on the outside, everything will appear backwards. All of the constellations will be inverted. You could draw the sphere "inside-out", so the constellations look normal, as they did when they made the Johnson Space Center Kugel Fountain, but then it isn't really the true celestial sphere, but a mirror-image version of it.

Paper Celestial Spheres

I wanted a way for students to be able to make their own celestial spheres in the classroom, out of paper, and I wanted them to be able to look at them from the inside, as if they were really looking at the sky. The main problem was that you can't make a spherical shape from a normal flat piece of paper without a lot of tearing or crumpling. So how do the manufacturers of classroom globes do it? Most manufactured globes have a paper layer containing the printing, and the globes are made by printing the colors into a shape that resembles a flower, with "petals" radiating in all directions from a central point. The starting shape looks something like this:

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Unmarked Celestial Hemispheres

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Marked Celestial Hemispheres

These "petals" are then folded down over a hemispherical form and pressed into a hemispherical shape. Examine a globe closely sometime and you will find the seams. In the classroom, we can't achieve the same beautiful result without the forming and pressing process, but if we start from the right shape, we can cut out a flower shape and fold the "petals" into a reasonable approximation of a hemisphere. If we print the stars on the inner surface, we can make a Northern Hemisphere of stars, and a Southern Hemisphere of stars.

Paper Celestial Hemispheres

For classroom hemispheres, the most difficult thing about making these things is drawing the initial figure. Figuring out the proper shape to draw the outline and the proper place to draw the stars requires a lot of fancy math. But I think I've done a pretty good job of that, and I'm offering the results in the downloads section. Once you have that, the rest is fairly straightforward. Just cut out the shape around the outline, and then tape the bottoms of the "petals" together side by side. You can also fold an extra piece of tape and stick it to the top to use as a handle. When I do this as a project with students, I use it as a chance to review all the constellations, and maybe add a few that we've never seen before in the southern hemisphere, and before we cut out the flowers I make the students draw in the stick figures of the constellations. I might or might not make them write in the names of stars and constellations, considering that there isn't a great deal of room to draw without cluttering up the map.

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