A Flat Celestial Sphere
A globe of the world is a useful visual summary of all of the lands and seas across the surface of our world, and can be a beautiful addition to a library or a school. But globes aren't easy to fold or carry around, and they aren't useful for detailed study of nations. For some purposes, flat maps are better than globes. In the same way, a celestial sphere or constellation globe is a useful visual summary of the arrangement of everything in outer space around our world. A celestial sphere is our map of all outer space. But it isn't very practical for detailed study of constellations, or for predicting which stars will be up and which will be down at any given time. For some purposes, flat celestial maps are better than celestial globes.
What if we wanted a flat version of a celestial sphere, for some reason? What if we wanted a celestial equivalent of a flat ‘world map’? One way to make a flat ‘world map of stars’ would be to cut the celestial sphere into two halves, the Northern Hemisphere of Stars, and the Southern Hemisphere of Stars, press both hemispheres flat, and print the two hemispheres on opposite sides of a disk. You would then have your whole celestial sphere in the shape of a flat planar double-sided disk — a planisphere—, with the North Star (effectively marking the ‘North Pole of Stars’) at the center on one side, and the South Celestial Pole (the ‘South Pole of Stars’) at the center of the other side.
Note that if we were to cut the celestial sphere in half exactly at the celestial equator, we would have to cut Orion in half at the waist, among other problems. Instead, it is usually helpful to extend both sides of the map a little into the opposite hemisphere, creating an overlap region. This is what I have done in the examples above. The Equator of Stars is not the perimeter around each star map, but the dashed line inset from the edges.
A Celestial Calendar
What if we want to make a celestial clock or calendar? What if we want to show, not just a ‘world map of stars’, but also which stars are actually up in our sky and which are down, and where in the sky to look for them? To do this, we have to cover one half of our celestial sphere, to hide the hemisphere of stars that are down, and we have to be able to cover different parts at different times. In other words, we need to spin the celestial sphere behind the cover, in a way that represents the tilted spinning motion of the celestial sphere in the sky above us, and thus show stars setting below the ‘horizon’, and emerging from behind it as they rise.
If we have a flat celestial planisphere, we could make a partial sleeve or slipcover to cover half of the disk and hide the half of the stars that are down. The top edge of the cover cutting across the disk would represent the horizon cutting off our view of the stars, and we could turn the disk to represent the spinning motion of the stars. As we spin the disk, it would show stars rising above the horizon on one side, and setting on the other.
But exactly what shape should the top of the slipcover be? If we live in northern mid-latitudes, we need to leave the center of the northern side exposed. There are stars close to the North Star, like the Guardians and the Big Dipper (depending on your exact latitude), which turn forever in counter-clockwise circles in the northern sky, never setting below the horizon. (These are the ‘North Circumpolar Stars’.) Our cover for the northern hemisphere of stars needs to leave the central portion of stars exposed, no matter which way we turn the disk. On the other hand, the cover for the southern side needs to always hide the central portion of stars (the ‘South Circumpolar Stars’) which never rise above the southern horizon.
Thus if we draw a concave bowl-shaped curve on the northern side of our ‘horizon sleeve’, and then turn the wheel counterclockwise behind this cover, this will represent the daily motion of the stars in the north. The stars in the center will never be covered no matter which way we turn the disk, and the stars farther away will rise in the east, arc counterclockwise across the sky (since you are facing north), and set in the west. If we flip the disk over and draw the opposite horizon, a convex hill-shaped curve covering the center of the wheel, and turn the wheel clockwise, this will represent the daily motion of the southern hemisphere of stars. We will never get to see the stars closest to the center, because they never rise, and constellations like Scorpius and Sagittarius that are farther away from the center will rise in the east, make a low clockwise arc across the southern sky, and set in the west.
Now we have, in the ‘window’ above the northern horizon of the sleeve, a picture of what the northern sky looks like, and above the horizon of the southern side of the cover, we have a picture of what the southern sky looks like. The only thing that remains, if we wish to show what our sky will look like at any particular time, is to figure out which way to turn the disk to represent that particular time. For this, we need to notice where the sun is among the stars, and where the sun is above or below our horizon, and match the one to the other. We can list the months in a circle around the outside edge of our celestial hemispheres, naming where the sun is among the stars during those months, and we can list the times of day around the perimeter of the horizon cover, showing where the sun is in our sky (or rather, below our horizon) at those times. With these labels in place, all we have to do is match the date and time we desire, and then the portion of the planisphere revealed above the cover will show us what the sky looks like at that date and time.
Practical vs Educational Planispheres
A common astronomy toy sold by science education companies and available in many museum gift shops is a ‘planisphere’, or ‘star wheel’, similar to mine. These planispheres are not good for detailed study of constellations — a constellation atlas is better for that — but they are great for giving you a quick overview of the what the sky will look like tonight after sunset or tomorrow morning before sunrise. When I first started teaching astronomy many years ago, there were a number of options available, but many of them were single-sided. They were intended for viewers in the northern hemisphere, and showed only the northern hemisphere of stars (plus an overlap region, depending on latitude), and covered this disk with an oval window. These single-sided planispheres tried to represent the entire dome of the sky within one oval on the map and had several drawbacks. For one thing, trying to hold the map upside-down over your head, with the correct corner facing North, and trying to match up the drawn constellations with the real ones while your head is in this position was inconvenient. For another thing, the constellations along the outer edge of the dial, the ones near the ‘southern horizon’, were highly stretched and distorted. This is an unavoidable consequence of trying to draw a flat picture of a round thing, but it was especially bad in these single-sided planispheres that tried to include too many southern constellations on a northern map. As an example, compare the appearance of Scorpius and Sagittarius in reality with their appearance on an old planisphere:
However, in the last decade or so, these inferior single-sided planispheres have apparently disappeared in favor of David Chandler’s Night Sky. Whenever I visit a museum gift shop or search online, this is the planisphere that I usually find. It’s a double-sided planisphere, like mine, and instead of trying to show the entire sky at once, it shows the northern sky and the southern sky separately on reverse sides. Instead of awkwardly holding it straight over your head, you hold up the northern side in front of you and face north, or hold up the southern side and face south. The northern side of the double-sided planisphere is much like a single-sided planisphere with the outer edges trimmed back, and because it doesn’t try to reach so far into the southern sky, the constellations near the edge are less distorted. The southern side of the double-sided planisphere gives you views of the southern sky in a far more natural, far less distorted, and far more comfortable way than the single-sided planisphere can.
If I wanted a planisphere for practical outdoor use, I would probably buy one of David Chandler’s dials. But as a teacher I wanted to make a blank version that I could print out onto card stock with a computer printer, and then have students label and assemble on their own. I wanted students to become more familiar with identifying stars and using planispheres by making their own personalized planispheres. One day I stumbled across a wonderful design by Toshimi Taki and decided to make my own version of it. Toshimi Taki’s original design is here, and my design is available in the downloads section.
This design, with the ‘celestial sphere’ and slipcover as separate pieces, may not be the best for practical outdoor use by astronomers, but I think it is wonderful for teaching purposes. The removable double-sided disk provides a nice model of the celestial sphere, and if you want to take out the star disk and doodle your own labels on it, you can. Unlike single-sided versions, this one includes all stars and constellations. (David Chandler’s double-sided version does also, you just have to lift up the cover and look underneath to see the hidden ones.) The slip cover nicely models the earth, or rather the horizon of any particular latitude on earth. The time-of-year markings on the star wheel measure the passage of the sun through the stars, and the time-of-day markings on the horizon cover measure the passage of the sun around the horizon. Being able to make it yourself and to draw on it yourself can be a fun educational project. Being able to write your own time markings on the cover also means that, if you are unfortunate to live somewhere where clock time and solar time are very different, you can just shift all your time labels to whatever you need them to be. And if you move to a different city, all you have to do is replace the slipcover with one representing your new latitude.
Making the Double-Sided Paper Planisphere
In the downloads section you will find a series of designs for double-sided planispheres, for latitudes ranging from the equator to 60°. If you live in the southern hemisphere, choose the version for your numerical latitude, but reverse the north and south covers. In other words, label everything as I describe, but swap the shapes and use the bowl-shaped cover as the southern cover, and use the hill-shaped cover as the northern cover. You might also notice that the dials are identical in every version. The celestial sphere is always the same, and the only thing that changes with your latitude is the horizon cover.
In the download versions, I have included the ‘celestial equator’ as a dashed line, and I have included the circle of the ‘ecliptic’ as a faint dotted line. The celestial equator appears in the sky as a half-circle that touches the horizon at due west and due east, and tilts towards the south (if you live in the northern hemisphere), and is marked by the daily path of the sun near the equinoxes. The ecliptic you can describe variously (depending on your audience) as the line upon which the sun travels through the stars, a line marking the middle of the zodiac, or the ‘planet highway’ along which the sun, moon, and planets travel.
Printing the templates
Start by choosing the latitude closest to you, and printing the corresponding PDF file onto card stock. I tried to align the two celestial hemispheres within the rectangular page so that you could use the ‘double-sided’ option of modern printers to print them automatically on opposite sides of the same page, but I find that sometimes printers have tiny asymmetric gutters that cause the two sides to not line up well. You can try double-sided printing, but you may prefer to print the celestial hemispheres separately, and after you’ve labeled them, line them up back-to-back manually. The two pages containing the slipcover must be printed separately of course, because they are separate pieces.
Drawing the constellations (Northern Viewers)
It may be fun to print off several copies of the dial and have kids start by making up their own constellations, and it may be fun to consult a star atlas and try to find as many constellations as you can on the star map. (I recommend
The Stars and
Find The Constellations, by H.A. Rey, the same author who wrote Curious George.) But if your map is to be a useful sky guide, I recommend simply highlighting the brightest stars and constellations, the ones that make the useful visual landmarks in the sky. In the northern hemisphere of stars: The Big Dipper, Cassiopeia, The Summer Triangle, The Great Square of Pegasus, Capella and the Kids. Students should also familiarize themselves with the relationships between certain stars and constellations, especially the ‘Pointers’ in the Big Dipper, which point to the North Star. Arcturus and Spica are two stars off by themselves, with only faint surrounding constellations, and I teach my kids to identify them using the handle of the Big Dipper: “Arc to Arcturus, then speed on to Spica.” The Winter Triangle and the Winter Hexagon are also important things to recognize — bright landmarks, easy to find.
The months around the edge of the dial are to indicate where the sun is during that month of the year. I have also included marks dividing each month into four weeks, for those who may want slightly more precision in their dial. For elementary students, you may wish to try ignoring the months altogether and instead label the outer rim with the four seasons, or maybe even with pictures representing the four seasons. I had all of my students label the rim with months, but the younger students were basically following instructions without understanding the reasons, which is something I try to avoid as much as possible. I have also labeled the constellations of the zodiac in the following pictures, but you may want to ignore that unless you have an advanced group of students.
Assuming you live in northern latitudes, you will never see the stars in the middle of the southern hemisphere of stars. The two most important constellations on the southern side are Sagittarius (commonly identified as a teapot) and Scorpius, which are to be found low in the Southern Sky on summer evenings. Notice that the constellations overlying the equator on the northern disk are also present near the equator on the southern disk, although the reversed distortion makes them look a little different.
Filling out the covers
The following instructions are for viewers in the northern hemisphere. If you live in the southern hemisphere, follow the same instructions, but reverse the north and south cover plates, i.e. use the concave cover plate as the south side, and the convex cover plate as the north side.
Assuming you live in the northern hemisphere, the cover plate with the dip in the middle is the one for covering over the northern stars. The concavity in the middle reveals the stars in the center of the wheel: the North Star which is directly in the middle of the wheel and all of the ‘circumpolar stars’ around it that spin forever above the horizon in the North. When you are facing north, west will be on your left, and east on your right, so the horizon should be labeled that way: W, N, E. The precise points for West and East are marked by the dashed circle (i.e. where the celestial equator intersects the horizon).
The times are marked according to where the sun is relative to the horizon at that time. Sunrise corresponds to the right side of the horizon (east), noon to the top (high above the horizon), sunset to the left side (west), and midnight to the bottom (below the horizon). For an elementary version of this, you could try just ignoring the tick marks and write in ‘morning’, etc.
If you live in the northern hemisphere, the southern cover is the convex one, the one with the hump. The hump permanently covers the stars near the center of the star disk, just as the real southern horizon permanently covers stars near the south celestial pole. As you look south, east is on your left and west on your right, so the horizon hump needs to be labeled that way: E, S, W.
As with the northern cover, the time markings are to indicate where the sun is at that time. In this case, morning is on the left (east), and evening is on the right (west), which is the reverse of the northern cover.
Assembling the pieces
Once the pieces are labeled, you will need to cut them out and tape or glue the opposites together. If you have put a lot of effort into your planisphere and you wish to laminate it in one way or another, remember that the disk needs to fit within the assembled sleeve, and you need to be able to see through the windows in the sleeve. When you tape or glue your two star disks back-to-back, it isn’t absolutely necessary to rotate them to match up the edges with each other, but it is better if you do. If the front and back halves are properly matched to each other, then once you set your planisphere to a certain date and time on one side, it will automatically be set for the same time on the other side, and you won’t have to change anything to switch from viewing northern stars to southern stars. To align the two disks properly back-to-back, look for Orion, the Summer Triangle, and all of the months — everything around the edges, in fact — and spin one side until everything matches up with itself on the reverse side.
To create the horizon sleeve, cut out both pieces, remove the windows with a scissors and/or a hole punch and/or a hobby knife, and tape the two covers back-to-back. Bear in mind that the outer rim of months on the star disk needs to coincide with the calendar windows in the sleeve. I laminated the two halves of the sleeve separately, then cut them out and joined them by wrapping the outer rim — the margin between the outside edge and the window — with pieces of scotch tape, and this worked very nicely. The tape prevented the edges of the disk from slipping too far inside the sleeve and held the disk very nicely in exactly the proper place within the sleeve. You could also try gluing the two halves together–just keep all of the glue along the outermost rim, outside the radius of the windows.
Once the disk and the sleeve are prepared, all you have to do it slide the star wheel into the sleeve. Remember, however, that both pieces have a north and south side, and that it is possible to put the disk in backwards. The northern side of the star map — the one with the Big Dipper, Cassiopeia, and Polaris — needs to go behind the northern side of the horizon. The southern side of the star map — the one with Scorpius, Sagittarius, and a bunch of unfamiliar stars in the center — needs to go behind the southern side of the horizon.
Using the planisphere
Spinning the star disk within the horizon sleeve represents the spinning of the celestial sphere around us, apparent to us as the circling of stars through the sky. To make the planisphere represent the sky at a specific date and time, turn it until the desired month on the wheel lines up with the desired time of day on the cover, at which point it will show the arrangement of stars in the sky at that time. All of the stars above the northern horizon at that month and time will be above the “N” on the cover plate, all of the stars above the eastern horizon will be above the “E”s on the cover plate, and so on. For viewers in mid-northern latitudes, the stars directly overhead will be roughly in the center of the exposed window of the northern cover. When trying to match up constellations on the dial with constellations in the sky, bear in mind that the dial is small and the sky is huge. Pictures and distances on the planisphere can appear deceptively small, and you may have to turn sideways or bend backwards surprisingly far to find what you are looking for.
A Few Random Practice Questions:
- What does the sky look like right now?
- What will it look like after sunset tonight?
- What will it look like before sunrise tomorrow morning?
- If you want to see Orion high in the south in the evenings, you will have to wait until which month?
- In March, at what time will Cassiopeia be to the left of the North Star, and the Big Dipper to the right?
- In March, at what time will the Big Dipper be to the left of the North Star, and Cassiopeia to the right?
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