Printable Double-Sided Planispheres

Conventional Single-Sided Planispheres

A common astronomy toy sold by science education companies is a “planisphere”, or “star wheel”, a movable map of the constellations that you can rotate into different positions to show what the firmament looks like at any given time. They are not very useful for detailed study of constellations (a constellation atlas is better for that), but they are very useful as an overall map of the sky, for figuring out which constellations will be up tonight, and where to look for them. Examples are Sky and Telescope’s Star Wheel, and David Chandler’s Night Sky. Commercial planispheres such as these are fine so far as they go, but 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.

I also preferred to avoid some of the awkward drawbacks of conventional one-sided planispheres, such as Sky and Telescope’s Star Wheel, that try to represent the entire dome of the sky within one oval on the map. For one thing, trying to hold the map upside-down over your head, with the correct side facing North, and trying to match up the drawn constellations with the real ones while in this position, is somewhat inconvenient. For another thing, the constellations along the outer edge of the dial, the ones near the “southern horizon” are highly stretched and distorted–an unavoidable consequence of trying to make a flat picture of the spherical star-globe surrounding us. As an example, compare the appearance of Scorpius and Sagittarius in reality with their appearance on a conventional planisphere:

The Teapot and the Scorpion above the Southern Horizon, Sept. 1, 8pm, at the latitude of Orange County, CA

Sagittarius and Scorpius on a conventional dial.

Sagittarius and Scorpius on a conventional dial.

If you wish to judge the accuracy of these pictures for yourself by finding Scorpius and Sagittarius in the sky, they are the brightest constellations in the southern evening skies from mid-summer to early fall.

Double-Sided Planispheres

A less common but more convenient variation of the conventional planisphere, is a “double-sided planisphere”, such as David Chandler’s Night Sky. Instead of trying to show the entire sky at once, such a planisphere shows the northern sky and the southern sky separately on reverse sides, and instead of 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. Furthermore, a one-sided planisphere centered on Polaris can’t display stars near the south celestial pole at all, which becomes a problem if you travel to the tropics or the Southern Hemisphere.

For a student-made planisphere, I decided to make templates for a double-sided planisphere, using my own version of a wonderful but little-known design by Toshimi Taki, which I stumbled across on the web. In this design, the two-sided disk representing the firmament, and the slip cover representing the horizon, are separate pieces. Not only does this simplify assembly, but it has some academic virtues that I like a lot. The completed version looks like this:

North Side

North Side

South Side

South Side

In design, the star disk is essentially an entire star globe representing all of the stars in the sky in all directions around us, with each hemisphere pressed flat into one side of the two-sided disk. On one side of the disk are the stars of the northern half of the star globe, with Polaris in the center, and on the other side of the disk are the stars of the southern celestial hemisphere with the south celestial pole in the center. (This would make the circumference of both sides correspond to the celestial equator. In practice, it is convenient to extend both sides a little into the opposite hemisphere, making the outer (equatorial) constellations on both sides overlap, and making the celestial equator a circle slightly smaller than the whole disk. In these pictures, the celestial equator is represented by the dashed circle.) This all-sky constellation disk is placed into a partial sleeve representing the horizon, with the northern horizon on one side and the southern horizon on the other. This sleeve covers the portion of the stellar globe which is below the horizon at any given time.

Some of the reasons I like this design are as follows: If for some abstract reason you just want a portable celestial sphere, a universal map of all constellations, you can just remove the star disk from the horizon sleeve. If you want to take out the star disk and doodle on it, you can. If you travel to a new latitude, and you want to figure out which constellations will be visible in your new latitude, you just need to obtain a new horizon sleeve–or perhaps carry a series of them–and place your star disk into whichever latitude sleeve you wish. I also find a very pleasing esthetic simplicity in this design–the disk corresponds very nicely to the “celestial sphere” around us, and the slip cover corresponds nicely to the earth, or rather to 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.

My Templates

With all of this in mind, I designed my own set of planisphere templates to be printed out, and used by students. The design given here was created by me using the mathematical software Mathematica, although I was inspired by a design by Toshimi Taki. The cover plates are designed for the latitude of Orange County (CA), Phoenix, Dallas, and Atlanta, but will work perfectly well for any child within five degrees of this latitude, and will be roughly accurate for anybody in the United States. I intend to produce additional cover plates for other latitudes in the future, but I ran out of time this summer before the school year started.

I have plotted all of the stars with relative sizes corresponding to their relative brightnesses in the sky, and I have included time-of-year and time-of-day markings which I think are appropriate for a Junior High class. I also included the “celestial equator” as a dashed line, and the circle of the “ecliptic” as a faint dotted line–I think they are appropriate for Junior High students, although you may want to ignore them depending on the interest and ability of your students. 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, and is more or less marked by the daily path of the sun, particularly in the spring and fall. The ecliptic you can describe variously as the line upon which sun travels through the stars, the planet-line, a line through the middle of the zodiac, the stellar highway through which the sun, moon, and planets travel.

I would like to make a simplified version of this planisphere for Elementary students, with only the brightest constellations and simplified time labels, but I haven’t worked out how to do it yet. If you really want a simplified star dial, the best I can give you at the present time is an earlier version of my double-sided star map, which omits many of the dimmer stars and makes it easier to focus on the brighter, more important constellations. It also omits the ecliptic, and includes less overlap across the equator, i.e. at the margins of the disk, making the constellations a bit larger and reducing relative distortion. It wasn’t designed to work with the slipcovers given above, so it is slightly too large, but it should still be usable with them.

Printing the templates:

To make a double-sided planisphere using my templates, start by printing them out onto card stock, each of the four pieces on a separate piece of paper. I tried to align the star-disks within the rectangular page so that you could use the “double-sided” option of modern printers to print them automatically on opposite sides of a page, but due to maddening page-alignment shifts between PDF, printer, and the software with which I created the PDF, I couldn’t get it to come out quite right. You’ll have to print them separately, and after you’ve labeled them, line them up back-to-back manually.

Drawing the northern constellations:

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 Big Dipper, Cassiopeia, The Summer Triangle, The Great Square of Pegasus. 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 find the following to be a useful mnemonic device for identifying them: “Arc to Arcturus, then speed on to Spica.” (The “arc” is the handle of the big dipper. I connected it to Arcturus and Spica with a dashed line in my examples below.) I think that the Winter Triangle and the Winter Hexagon are also useful things to know–bright landmarks, easy to find. (I leave these for you to look up yourself.) By the way, I find that students confuse Andromeda and the Great Square with the Big Dipper on the star disk. You can point out that the “bowl” of the “not-the-Big-Dipper” is shorter and more square-like, and the “handle” (which is actually Andromeda) curves the wrong way.

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. This is something I need to improve in the Elementary version.

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.

The northern constellations.

Drawing the southern constellations:

Assuming you live in northern latitudes, you will never see the stars in the middle of this dial. The two most important constellations here 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.

The southern constellations.

Filling out the northern cover:

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.

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.

The North side of the cover sleeve.

Filling out the southern cover:

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 (for viewers in the northern hemisphere). 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.

The southern side of the cover sleeve.

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 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 or a hole punch, and tape them 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 (concave) 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 (convex) 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. (As we know now, the true cause is the rotation of the earth, but that’s beside the point here.) To make the planisphere represent the sky at a specific date and time, spin 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 all of the stars above the northern horizon at that month and time above the “N” on the cover plate, all of the stars above the eastern horizon above the “E”s on the cover plate, etc. 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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5 Responses to Printable Double-Sided Planispheres

  1. Julie says:

    Hi,
    I love your well worked out planispheres what a lot of work and thought you put into them! I live in Kerry ireland lat 51 degree N by 10 degree W – how can I adapt the planisphere sleeve to reflect the the difference? …Julie

    • jrkrieger says:

      The short answer is to pretend that the southern cover rises a bit higher, and the northern cover dips a bit lower. You live at a higher latitude than I do, so you will see more of the northern stars and fewer of the southern stars. If you want a precisely modified cover, check back here in a few months. I may actually be able to get back to this project this coming summer, and I’m planning to make a range of covers for various latitudes.

      Thanks for your positive feedback,
      John

    • jrkrieger says:

      I finally got around to creating a series of planispheres for various latitudes, in 10 degree increments from the Equator up to 60 Degrees latitude. Here they are:

      Equator
      Latitude 10 degrees
      Latitude 20 degrees
      Latitude 30 degrees
      Latitude 40 degrees
      Latitude 50 degrees
      Latitude 60 degrees

      The two sides of the star disk should be aligned well enough this time so that you can use a double-sided printer to print them automatically on opposite sides of one piece of paper, instead of having to cut them out separately and align them and glue them back to back.

      If you live in the Southern Hemisphere, you just 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.

      • Andy Puckett says:

        I wonder if you could revisit the idea of a planisphere designed for 60 degrees north latitude? I know you’ve said above that there are problems with this layout, but I’d be interested to know specifically what they are.

        I’m an astronomy professor and planetarium director in Anchorage, Alaska (61.2 deg N), and I get requests from time to time for a planisphere that would actually work up here, without having to fudge it. I often have to translate the national news about “what’s up in the night sky” for my audience; sometimes the view is better up here, but sometimes it’s worse. I also like your design because it would allow us to label the times correctly for Anchorage, which is 15 degrees west of Juneau but observing the same time zone. So all our times are off 1 hour in winter, 2 hours in summer!

      • jrkrieger says:

        I’ve added a planisphere for a latitude of 60 degrees to the list above.

        The problem with the covers at high latitudes is mainly one of convenience. At the equator, both sides of the cover should be perfect half-circles, and as you get farther away from the equator, the two sides become more different, one side becoming more and more humped, and the other becoming more deeply concave. As you approach the poles, one side becomes almost completely covered, and the other becomes almost completely exposed. This leads to some practical problems with the paper shapes, such as the floppy “pinchers” that stick out on the exposed side. I’ve never actually tried to cut out and use a model like this, and I’ll be really curious to know how well it works.

        Someday, I intend to make a webpage on which users can design their own planisphere for any latitude from the south pole to the north pole, but that’s still a couple of years away, I think.

        John

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