Templates for Moon Dials

The Motion of the Sun

Can you predict where the sun will be in the sky at any given time? Can you tell approximately what time it is from the position of the sun in the sky? The sun is the most obvious thing in the sky, not only in its presence, but also in the regularity of its motion. If you spend any time observing it, you quickly grasp that it follows the same path, regularly, once a day. It rises in the morning in that direction (we call it east), passes through the sky in an arc, reaching a peak in that direction (south) at mid-day, and it sets in the evening in that direction (we call it west), in a smooth and regular repetition (we call each cycle a day.) The sun moves in an arc from east to west, tilted towards the south, once a day. (In my experience, children often assume that the sun passes straight overhead, but you can demonstrate fairly easily that this is not the case by marking the shadows of a vertical stick or pole through the course of a day, thus making a crude sundial.) If we wanted to record the timing and the path of the sun moving through the sky in a little cartoon picture, we could draw something like this:

Sun Path Cartoon

What happens to the sun when it goes down? It goes down in the west, somewhere beyond the horizon, it spends about as long down as it spends up, and it comes up again in the east, somewhere beyond the horizon. It is as if the sun is stuck on a tilted wheel, larger than the land we stand on, and it circles steadily around us. If we wanted to be a little more elaborate with our sun-path-map, we could make a sort of movable sun-sky-clock, with the sun drawn on a wheel, something like this:

The top of the cover piece would represent the horizon, the wheel behind would represent the “sunwheel”, and spinning the wheel to the right would represent the passage of the sun through the sky and below the horizon each day. We could also write the times of day somewhere on the wheel, so that the appropriate time of day is revealed in a window or something.

The Motion of the Moon

After the sun, the next most obvious thing in the sky, and the only other celestial object that appears as more than just a pinprick of light, is the moon. The moon is less obvious than the sun, both in its presence and it its motion, and it is more difficult to say where it will be in the sky at any given time. However, if you spend a day or even a few hours observing it, you see that it, too, follows a simple and regular path–more or less the same path as the sun, in fact. It travels in the same direction along pretty much the same path as the sun at pretty much the same rate. They both rise in the east, pass across the sky in an arc tilted towards the south, and set in the west, about once a day. Neither of them is ever in the northern sky, neither one ever rises or sets in the south, and neither of them ever go backwards from west to east. It is as if they are both stuck onto huge wheels tilted towards the south, and they race each other around us, following more or less the same circular racetrack.

The Loser of the Race

The complication is that the moon is in different places along the racetrack at different times on different days. Sometimes the moon is just a little bit ahead of or behind the sun and is up in the daytime, sometimes it is a quarter-lap behind or a quarter-lap head and is easily visible at sunset or sunrise, sometimes it is directly on the opposite side of us from the sun and is only up when the sun is down. Why? If you find the moon at the same time each day for several days, you will see the moon gradually but steadily creep backwards, westwards. (Actually, whenever the moon is near a bright star for comparison, you only need a couple of hours to notice that the moon moves compared to the star.) The moon is not going around completely each day, it is a little bit slower than that. It is losing the race and falling behind the sun a little bit each day (or the sun is catching up to the moon, depending on which one is leading at the time). And this falling behind of the moon is closely connected to another obvious change in the moon every few days–the appearance. Sometimes–when the moon is directly opposite to the sun and it rises at sunset–the moon is a complete disk, it is “full”. Sometimes–when the moon is close to the sun–it is a thin “crescent” shape. When the moon is a quarter-turn from the sun, it has the shape of a half-disk, it is a “quarter moon”. The moon displays different shapes on different days, but it always has the same shape whenever it is the same distance behind or ahead of the sun in the race. The moon’s shape goes with the position along the racetrack in front of or behind the sun. If we wanted to make a map of the moon relative to the sun, showing which “phase” goes with which position around the racetrack, we could draw something like this:

Phase Ring

In a sketch or a “map” like this, the ring represents the “racetrack” that the sun and moon follow across the sky and below the horizon, and the sequence of phases represents the gradual losing of the race by the moon to the sun. The moon gradually creeps counterclockwise through the sequence of phases. How long does it take for the moon to move from one phase to the next? How much faster is the sun than the moon in the race? If you watch the moon for a month or two, you will find that it takes about a week for the moon to go from each unique quarter phase (by which I mean each quarter-turn: new, first quarter, full, third quarter) to the next one, and it takes about a month for the moon to go through the whole sequence. It takes about a month for the sun to “lap” the moon and pass it in the race, and for the whole cycle to repeat itself. (The length of our calendar month is actually derived from the moon-cycle, and the word “month” is related to the word “moon”.)

A Moon-Position Calculator

If we return to our movable sky-map-clock, our toy “sunwheel” spinning behind a “horizon”, and we replace the “sunwheel” with the “moon phase ring”, we can show the race of both the sun and moon through the sky. We can show not only where the sun is at any time of day, but also where the moon is at each time of day, as long as we know what phase it is in on that day. With a dial like this, if we know what phase the moon is currently in, all we have to do is turn the dial to the appropriate time of day, and find where in the sky (or below the horizon) the corresponding phase of the moon is.

Moon Dial

With a dial like this, spinning the dial to the right corresponds to the daily motion of sun and moon through the sky, and following the moon counter-clockwise relative to the sun corresponds to the gradual loss of ground, so to speak, of the moon in its race with the sun, i.e. the monthly progression of the moon through the phases.

My Templates

I have two templates for Moon Dials, one simple one intended for Elementary or Junior High students, and a larger more mathematical version with numberlines for Junior High or High School students.

Template for a Simple Moon Dial

Template for a Simple Moon Dial

A Large Moon Dial with Numberlines, Phase Ring

A Large Moon Dial with Numberlines, Phase Ring

A Large Moon Dial with Numberlines, Cover Plate

A Large Moon Dial with Numberlines, Cover Plate

The assembled large version looks like this:

Mathematical Moon Dial

To assemble them, print them onto cardstock, and cut out the pieces along the outermost borders. Use a hole punch to make a hole at the center of the cover piece, between the words “horizon” and “south”. Pass a brass fastener through this hole, then press it through the center of the dial, fold the legs of the fastener flat against the back of the dial and tape them in place against the back of the dial.

The simple version is designed for students to draw and label the phases of the moon themselves. When shading, remember that the side of the moon facing the sun is always bright, and the side facing away is always dark. Starting with the phase of the moon immediately adjacent to the sun and working counter-clockwise, the names of the phases are:

  • New Moon
  • Waxing Crescent (or New Crescent)
  • First Quarter
  • Waxing Gibbous
  • Full Moon
  • Waning Gibbous
  • Third Quarter (or Last Quarter)
  • Waning Crescent (or Old Crescent)
  • New Moon

Note that the first half of the cycle, with the moon dropping behind the sun, is the waxing half, with the moon growing from nothing to full, and the second half, with the sun catching up to the moon from behind, is the waning half, with the moon shrinking from full to nothing again.

Unlike the simple version, I didn’t make a special “time window” for the mathematical dial–you just read the time of day from the top of the dial. Technically, the time numbers indicate “mean local solar time”, which means you mark the peak of the sun as “midday”, and halfway between sunset and sunrise as “midnight”, and you divide the intervals into twelve equal portions, with numbered hours from 1-12 Ante Meridiem (before midday), and 1-12 Post Meridiem (after midday). Modern Universal Time, shown on clocks, is still based on this idea, but incorporates some fine-tuning. It differs a little from solar time depending on where your city is within your time zone, varies a little from month to month, and is an hour ahead of solar time during Daylight Savings Time. If you are not too finicky, just treat “solar time” as being the same thing as normal clock “time”. For detailed time offsets, consult a book on sundials.

In the mathematical version, the “age in days” of each moon phase is a way of expressing in numbers exactly where the moon is in its cycle. You start counting the number of days from the exact moment of a new moon, and the resulting number is the “age of the moon”. We say that a first quarter moon is about 7 1/2 days old, about 18 days after a new moon the moon will be a waning gibbous, etc.

Random Comments:

I didn’t intend this post to include an explanation of the reason for the phases of the moon, in part because I think it is a good idea to connect the explanation with the subject of eclipses. However, you can illustrate it fairly simply by painting two halves of a ball different colors and looking at it from different angles–the colored hemispheres will take on various “phases” when viewed from different angles. Another step would be to notice that the bright half of the moon always faces the sun, and the dark half is always away from the sun–if the moon is a sphere in the sunshine, that would naturally give it two hemispheres, a bright one illuminated by the sun and a dark one opposite to the sun, which would appear differently to us depending on the angle, just as the two colored hemispheres of the ball.

If you pay very close attention through the course of a year, you may notice some discrepancies from the simple behavior of the sun and moon described here. For example, you may notice that the arcs of both the sun and moon wobble a bit–sometimes they pass through their arcs a little higher or a little lower. When the moon does this, we say it “rides high” or “rides low”. When the sun “rides high”, of course, we have summer, and when it “rides low”, it is wintertime. These are details that we don’t need to worry about here, however. The essential thing to observe here, especially for elementary students, is the constancy of the arc–the sun and moon always follow pretty much the same path every day, and it is basically a circle around us.

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