Why does the moon have phases? If you ask children, or even many adults, you might hear the guess that it has something to do with the Earth's shadow. As an initial guess, this does make some sense. It seems like the moon should be a full circle, but something is darkening part of it, and shadows are what usually darken things that should be bright, so it must be a shadow of some kind. And what else could be casting a shadow on the moon, except the Earth?
But let's think more carefully about it. This website is supposed to be "for thinkers", and questioning this hypothesis about the earth's shadow makes a good example of "thinking practice". For children, I think it makes a fun and valuable science lesson. So let's search for clues, and subject this initial hypothesis to a careful scrutiny. This might confirm our initial guess, or it might lead us to a completely different conclusion, but either way, it will strengthen our grasp of the world. Let's think carefully about shadows and the phases of the moon.
The Rules of Shadows
If the darkness on the moon is caused by the earth's shadow, then the moon phases should follow the rules of shadows. They should work the same way shadows work.
Observe shadows, or try to make your own, and you will quickly notice that you need three things:
- LIGHT. You need the sun, or a light, or something bright that lights up the world around it. A shadow is a subtraction, a hole in the light, and you can't have a shadow without light.
- GROUND. You need the ground, or a wall, or a screen, or something to be lit up by object #1. You can't see a shadow until the shadow lands on something...preferably flat but not necessarily.
- SOMETHING THAT BLOCKS THE LIGHT. Some kind of normal "thing", an opaque object, to block part of the light before it gets to object #2. Every shadow is the shadow of something.
The opaque thing casts a shadow onto the ground or the wall, by blocking some of the light from the bright thing. That's how shadows work, in a nutshell.
You should also notice that the shadows always "travel" in straight lines from the thing casting the shadow, to the place where it shows up. Pay attention to flashlight beams in dusty attics, to the shadows of trees in morning mist, or to sunbeams or crepuscular rays in the atmosphere, and you will notice that they always have straight edges. Light—and shadow—travel through space in perfectly straight lines, as rays or beams. Shadows, like flashlight beams, cannot turn in space and go in a different direction.
Now, in the case of the moon phases, the moon could be object #2, the thing that the shadow lands on, and on which we see it. The sun is obviously a light source, and the earth can be the thing casting the shadow. We have the necessary three objects. Perhaps the earth is casting a shadow onto the moon, by blocking the light of the sun, and perhaps this is why the moon sometimes appears to have parts of it missing. Do you have any objections to this idea?
We can argue about what shape the shadow of the earth should be when it hits the moon, and how this should make the moon look. But there is one especially huge, glaring problem with the hypothesis that the earth's shadow causes the moon phases.Where do you see the moon in the sky?
If the earth's shadow causes the phases, then we should see phases only when the moon is on the opposite side of us from the sun. A shaded moon could never be close to the sun in the sky. It could never even be in the sky at the same time as the sun. It could only be up when the sun is down, and it must be down when the sun is up. Wherever the sun is, a moon with phases would have to be exactly opposite. But where do we actually see the moon phases in the sky? (You can scroll through the rest of this article to see a few photos of the moon in the sky.) As any experienced sky-watcher knows, the various phases of the moon often appear in the daytime, sometimes a quarter-turn from the sun, sometimes even closer. We often see crescent moons very near the sun, over sunrise or sunset. The phases of the moon don't have to be on the far side of the sky from the sun. In fact, the only moon phase that appears opposite to the sun, the only moon phase that can never share the sky with the sun, is the full moon, the phase without a dark part.The earth's shadow cannot be causing the moon's phases, because the phases of the moon appear in many different places in the sky, and not always opposite to the sun.
(But then...when the moon does go on the far side of us from the sun, how come we don't see the shadow? Can you explain why we see a full moon, instead of a dark moon or a moon phase? Maybe the earth's shadow is really small, and it is hard for the moon to hit it exactly? Maybe at the time of the full moon, the moon passes pretty close to the opposite side from the sun, but never exactly 180° opposite to the sun? Also, if that's the case, do you suppose the moon could get lucky once in awhile? What if the moon DID hit the "shadow beam"? What if it did pass through the "shadow tail" of the earth on rare occasions? Something very dramatic would happen to the full moon on those special occasions...)
Sometimes widespread errors have no basis in reality, and represent complete make-believe. But often, and especially in science, widespread errors have a reason behind them. There is a seed of truth that grew into the falsehood. The error doesn't come from make-believe, but from real observations ... hastily explained. That is what has happened in this case. There are casual reasons to suppose that maybe the earth's shadow is related to the moon phases, but if we aren't more careful, we fall into error.
Sunshine and Moonshine
So what does cause the phases of the moon, if not the shadow of the earth? Let's look at what we can see.
Pay any attention to the sun, the moon, and the stars in the sky, and you will notice that the moon does not glow like the others. The sun and stars appear as perfect points or perfect circles in the sky, made of some special luminous material, some special glowing stuff. The moon is blotchy, irregular, with dark patches, and shapes. The moon is much more "earth-like" than those perfect heavenly bodies with the special power of shine. (If you look at the moon with a telescope, you might even be able to see mountains and "seas".) The sun and the stars are something like fire, the moon is another world.
Whatever that power that makes the sun and the stars luminous, whatever gives them the rare ability to shine out with their own light, the moon does not have that power. The moon is not like fire. But it does shine. Light comes from it — moonshine can light your way at night, it can allow you to read, it can even cast shadows. If the moon is a dull body like the earth, then where does moonshine come from?
Were we right to think that the moon is glowing in the sunshine? Consider this picture of a quarter moon. Compare the moon at the top with the shadows down below. What do you notice?
They are pointing in the same direction. The moon's face is in line with the sunshine. If you look at many moon phases, in all parts of the sky, at all times of day, you should notice that the bright part of the moon is always facing the sun, and the hidden part is always facing away. Many of us may have noticed this and subconsciously assumed that the moon is lit up by sunshine. It seems almost obvious when you think about it. The principle was stated in writing by the ancient Greeks as early as several hundred years B.C. (They confirmed the assumption by pointing out what happens during lunar eclipses, and there are fascinating things you can learn by thinking about eclipses, but that will have to wait for another article...)
So the moon can shine, but not with its own power. Unlike the sun and stars, the moon shines with borrowed light. To put it in more technical terms, the moon reflects the light of the sun. Moonlight is reflected sunlight.
But this also means that the moon should "look like" anything else in sunshine, anything "normal" here on earth. It should have a bright side and a dark side, and it should look differently when we look at it from different angles. This is what we overlooked when we casually assumed that the moon "should" be a circle. Consider this photograph of a moon just past first-quarter. It was taken facing south, with the sun about to set off to the right. Notice that the tufts of the eucalyptus trees have a vaguely similar appearance to the moon—they are lit up on the right side, and dark on the left side, because they are in the same sunshine, which is coming in sideways from the right.
If the moon is a sphere, then it should look very much like a sphere down here, in the same sunshine. Instead of tree tufts, what if we compare the moon to an actual sphere, in the same sunshine? I tried to set up a photo illustrating this concept by impaling a styrofoam ball on the end of a wayward vine in my school's courtyard. This is one of the photos I managed to obtain of the situation:
Notice how similar the moon and the ball appear. They are both spheres, in the same sunshine, viewed from the same angle, and therefore they both appear gibbous. They appear gibbous, because we are looking at them sideways, but a little more on the side of the bright half. The bright hemispheres are facing sideways, a little up, and a little towards us.
(Setting up photos like this isn't as easy as you might think. I once noticed a gibbous moon over a park, and happened to have my camera nearby, so I tried to talk some unfortunate youngster playing soccer into holding his soccer ball over his head in the sunshine, so I could photograph him with the gibbous moon in the background. He agreed, but the poor fellow didn't seem very happy with the situation. In any case, I decided it was probably better not to post his photo on the internet. But I think the photo of the vine-mounted styrofoam ball turned out just as well.)
Locating a crescent moon in the daytime sky is a challenging task, but it can be done. If you look closely in the center of the following photo, you should be able to find one.
Now look closely at the flagpole finials. They are in the same sunshine, viewed from the same angle, and they display a similar crescent glow along the edge. All spheres in the photo—the earthly ones, and the one in outer space—shine faintly with a crescent shape, because the hemisphere in sunshine is mostly, but not exactly, facing away from us. We are looking at most of the dark side of the sphere, with a little bit of the bright hemisphere showing along one side. (The dark spots are dust on my camera sensor. I didn't realize the sensor was dirty at the time, and I was too lazy to try to remove the spots with post-processing.)The moon is a sphere in sunshine, with a bright hemisphere facing the sun, and a dark hemisphere facing away from the sun. We see a phase whenever the bright hemisphere is not facing directly towards us.
The moon is just an ordinary object in sunshine, like anything down here on earth. But there is still a noteworthy difference. With objects here on earth, we can normally see the shadow side. It is a bit darker than the side in the sun, but it still contrasts with the things around it, and we can clearly grasp the size and shape of the whole thing. We don't look at a ball in sunshine and think "that's gibbous", we think "that's a ball". But with the moon phases, we can't see the shadow side at all. It is as if the side away from the sun has been erased from existence, or washed with invisible paint or something. The crescent moon was so nearly invisible we had to struggle to find it. Why the difference? Why is the shadow side of the moon invisible, when we can clearly see the shadow sides of things here on earth?
The Old Moon in the New Moon's Arms
Sometimes we actually can see the other side—and it's beautiful. If you pay attention to sunsets, once in awhile you will notice something like this:
In this case, you can actually see the shadow side of the moon, just like the shadow side of things in sunshine here on earth. But why now, and not at other times? Can you think of possible reasons?
Part of the answer is that this photo was taken at night, or a little while after sunset. The sky is darker. The other photos above were taken in the daytime. The faint glow on the shadow side can stand out better when it isn't overpowered by the sun in the sky. Just as the daytime ocean of blue sky drowns out the stars, so it can apparently drown out the shadow side of the moon.
But there is another reason. You can find quarter moons and gibbous moons in a black nighttime sky, and you will not see the shadow side of the moon. It will be as black as the sky. The other side will be invisible, even at night. Something else besides the blue daytime sky is keeping the dark side of the moon hidden during non-crescent phases.
See if you can see anything special about the crescent moon, from how things are arranged at the time. For us to see a crescent moon, we have to be looking at the dark side of the moon from a slight angle, and the bright side of the moon must be facing the sun, and thus we can draw what the arrangement must look like. It must be something like this:
Someone watching the sunset just after the sun goes down (meaning he is just inside of the dark side of the earth) will see the moon a little above his horizon, over the sunset, with the sun hidden just a little below the horizon. What if there were an observer on the dark side of the moon, looking up into the lunar night sky, at the same time? What would he see? Just as earth-dwellers see the moon in the sky, moon-dwellers would see the earth in the sky. In the late 1960s and early 1970s, astronauts visited the moon and got to see this marvelous sight for themselves. Some of them took pictures. One of the most famous pictures got its own name: "Earthrise". (This was actually taken from orbit, rather than the surface, but the view would be much the same.)
Notice in the photo that the earth in the lunar sky has a phase. In this photo, the earth is slightly gibbous. Do you suppose that people on the moon could see a whole range of earth phases in their sky, just as we see a whole range of moon phases in our sky? If so, can you tell what phase the earth would be at the same time the moon is a crescent? Look back at the Earth-Sun-Moon triangle, and see if you can work it out. When earthly observers see a crescent moon, lunar observers would see a gibbous earth. The bright side of the earth is facing them, and the earth would be nearly full in the lunar sky. And the thinner the moon's crescent is in earth's sky, the fuller earth is in the lunar sky.
Do you see what this means? What happens down here, on earth, on nights when the moon is full? The moon lights up the night. It casts shadows, allows us to nagivate, makes the night brighter. What about lunar observers under a full earth? Just as moonshine from a full moon lights up the earth's night, wouldn't earthshine from a full-phase earth light up the moon's night?
When we see both halves of that beautiful moon over the sunset, we call that glow on the night side of the moon "earthshine", because it is exactly the same thing as moonshine, in reverse. That is the glow of a full earth shining on the moon, and lighting up the lunar night. But why do we only see it during a crescent moon? Why don't we see earthshine on the shadow side of the moon during quarter or gibbous phases? Maybe you can answer that now.
Part of the reason is that the larger and brighter the bright side of the moon phase, the darker the dark part will appear by contrast. You can hardly expect to see a faint glow coming from a thin crescent-shaped shadow-side, when the bright side is gibbous. But do you see another important reason? The larger the moon phase is in earth's sky, the smaller the earth's phase is in the lunar sky. When the moon is a quarter phase, so is the earth. When the moon is gibbous over the earth, the earth is crescent over the moon. Just as a quarter moon fails to make the earth's nights very bright, so a quarter earth fails to light up the moon very much. The bright side is facing the wrong direction.We only see earthshine when the moon is near new, because that's the only time the earth is near full in the lunar sky.
By the way, can you explain why it is that we see the shadow side of things here on earth? Why is it that most of the world, including the space under tables, under trees, inside boxes, and behind buildings, is not in direct sunshine, yet we can still see it without any trouble? Maybe for the same reason we can see things at night, under a full moon? If the dull moon can reflect light, maybe everything else can, too. Maybe all the things in the world that cannot glow can still reflect light from things that can. Maybe this is where "ambient light" comes from—it's just sunshine reflected from things all around? Seeing the shadow side of the moon by earthshine is no different than seeing things in shadows here on earth by ambient light. Sunlight missed it directly, but got reflected onto it by something else nearby.
Finally we can answer: why is the shadow side of the moon invisible in our sky most of the time, even at night? Because there is nothing to shine on it, and make it any brighter than the night sky. We see the shadow sides of things here on earth due to ambient light shining from all directions, but there is no ambient light in space, so the shadow-side of the moon is usually invisible.Why does the moon have phases? Because we see the sunlit hemisphere from different angles, and the hemisphere facing away from the sun is (usually) invisible.
A Simple Classroom Project
You can make a model that illustrates the phases of the moon very simply. Purchase a styrofoam ball from the craft store and dunk it halfway into a can of black matte paint. You will then have a very simple model of the sunlit moon. It has a bright hemisphere and a dark hemisphere, and by looking at the hemispheres from different angles, you can clearly see why the shapes appear the way they do. You see them as full circles, gibbous shapes, quarter circles, or crescents, depending on which way they are facing, compared to your line of sight. And the dark side is always the inverse of the bright side, because you are looking at complementary hemispheres.
You can buy styrofoam balls in bulk fairly cheaply, and I have had success turning this into a mass-production classroom project in which each youngster can make his or her own moon to take home. I find that even fairly young children can usually hold a styrofoam ball gently in their fingertips while they dunk it in the paint. Most styrofoam balls have evidence of a seam remaining from the manufacturing process, and you can use this as an "equator" showing you when to stop dunking the ball, and pull it out again. (Although, to be exact, this circle would not correspond to the equator of the moon, but to the terminator dividing the illuminated side from the dark side.)
The biggest problem will be catching drips and allowing the paint to dry. I had my kids stick their styrofoam balls onto toothpicks, and then we stuck all of the children's toothpicks into another large chunk of foam, so we had what looked like a block of white-and-black lollipops sitting on a shelf in the back of the room while the paint dried. You obviously want to have the painted side facing down, otherwise you risk having the paint run from the black side to the white side before it is completely dry.
You might also want to test your procedure before you use it in the classroom. One year, it worked beautifully for me, but the next time I tried it, the paint didn't adhere very well to the styrofoam, and some of the children were disappointed in the final appearance. I'm not sure what made the difference—perhaps I used a different brand of styrofoam or paint, or maybe finger oils contaminated the surface of the spheres. If the same thing happens to you, you can probably touch up blemishes on the dark side with a black Sharpie, and blemishes on the white side with Wite-Out. That's what I did.
How You Can See That The Sun Is Very Far Away
You don't have to trust priests of astronomy to know that the sun is much farther away than the moon. You can see it for yourself in the phases of the moon. Easily. You just have to think a little more about the moon phases.
What if the sun were closer to us than the moon? What moon phases would we see? (When teaching science, it is often helpful to play "What if...") Try drawing a sketch, with the sun close by and the moon going around, and see if you can deduce what the moon would look like. Could we ever see a quarter moon, or a crescent, or any of the "dark" phases? If the sun were closer to us than the moon, the bright side of the moon would always be turned in our direction, and we would only ever see full and gibbous phases. Just the fact that we see a "normal" moon cycle, with crescent and new moons, tells us that the moon must be closer to us than the sun. It is only when the moon is between us and the sun that we get to see the shadow side.
(Incidentally, whenever I would go through this discussion with children, they would often say: "Another reason we know that the sun isn't close to us is that we would burn up." Good thinking. But like the idea that the earth's shadow causes the moon phases, this is a casual thought that requires more chewing. If we imagine a huge sun far away, and then bring it close, it would indeed probably cook us. But wouldn't a huge sun up close look huge in the sky? Couldn't that thing in the sky be a small campfire up close, instead of a huge bonfire far away? That's what the ancient Greeks thought. At first, many of them thought that the sun was probably as big as the Mediterranean Sea, somewhere up in the sky a little beyond the moon. Let's talk more about how big the sun is in a little while.
What if the sun were farther away than the moon, but only a little farther? What would the phase cycle look like then?
In this case, we would see a full moon cycle, with all the phases, but they wouldn't be evenly spread out. We would see a full moon ... then gibbous ... gibbous, quarter, crescentnewcrescent, quarter ... gibbous ... gibbous ... full, and so on. It would go very quickly through the "darker" half of the cycle (assuming the moon circles around at a fairly steady speed), and take a long time to complete the "fuller" half of the cycle. Also, the quarter moons would be close to the sun in the sky.
Finally, what if the sun is not just a little farther away than the moon, but much, much farther than the moon? In this case, we would see a full cycle, and they would be evenly spread out in the sky, and in time. The moon would march steadily around the circle from new to crescent, quarter, gibbous, and so on. And quarter moons would appear almost a quarter-turn from the sun in the sky.
Now, which of these three cases do we actually see? What does the phase cycle that we see tell us about how far away the sun is?The sun must be very much farther away than the moon, because that's the only way we can see the phase cycle that we see. That's the only way we can see a quarter moon a quarter-turn from the sun in the sky.
(If you are a teacher, you may like to design your own handouts, but if you have any interest in seeing the handout I used for this lesson, click here. There is a blank version, and a filled-in version, with a few miscellaneous comments.)
If we want to practice our geometry, we can even try to figure out how many times farther the sun is than the moon. We can try to measure the ratio of distances. We just have to measure how far the sun is from a quarter moon in the sky, and use our ability to think about triangles.
The sun, the moon, and the earth always form a triangle in space. The angle at our corner of the triangle, the earth's corner, is obvious to our eyes—that's just the angle between the sun and the moon in the sky. And the angle at the moon's corner of the triangle is the angle between the direction of sunshine, and our line of sight. The phase of the moon tells us the angle at the moon's corner of the triangle. And once we know two angles, we know the shape of the triangle. We can draw a toy triangle with the exact shape of the real triangle in space. In particular, if we see a quarter-moon, this means that the sunlight must be coming in exactly sideways to our line of sight. Then we have a right triangle, like this:
With such a triangle, we can easily figure out how many times farther away the sun is than the moon, because it is drawn right there in the ratios of the sides of the triangle. We just have to get the shape of the triangle right. For example, suppose we wait until a quarter moon, and measure how far apart the sun and moon are in the sky. Perhaps we find that they are 60° apart. In that case, we would draw a 30-60-90 right triangle, and the ratio of the hypotenuse to the short side would be 2, meaning that the sun is twice as far from us as the moon. What if the sun is not twice as far as the moon, but many times farther? The farther away the sun is, the larger the angle at the earth's corner of the triangle has to be. Or, if you look at it the other way around, the farther the sun is from the moon in the sky, the farther away it must be from us in space. What if they are 80° apart? In that case we would have to draw a 10-80-90 right triangle, and we would discover that the ratio of sides is around 6, meaning that the sun is about 6 times farther from us than the moon.
So, when you see a quarter moon, how far away from the sun is it in the sky really? How many degrees of angle? Pay close attention next time ... and you'll see that it's a right angle! Well, it can't be exactly a right angle, or we'd have a rectangle. But it's really, really close to a right angle, and we have a really long, really skinny triangle. The sun is many, many times farther away from us than the moon.
The ancient Greeks tried to measure this angle, so they could figure out how far away the sun is. They found out that this angle was so close to a right angle, they couldn't tell the difference. In the 3rd century B.C., the astronomer Aristarchus figured that if the difference was more than 3°, he would be able to tell the difference, so he said that the angle was at least 87°, and therefore the sun was at least 20 times farther away. As we now know, the sun is almost 400 times farther away from us than the moon. But you can still see without measuring that the sun is many times farther than the moon, just by observing the sun and the moon at the time of a quarter moon. The next time you see a quarter moon, imagine the bright side of the moon pointing towards the sun ... way over there.Because the sun and moon are almost a right angle from each other in the sky at the time of a quarter moon, we can see that the sun is many dozens of times farther away than the moon.
Incidentally, can you say something else about the sizes of the sun and the moon? If the sun is so much farther than the moon, but they look the same size in the sky, then whan can you deduce? If the sun is dozens (or hundreds) of times as far away as the moon, then it must also be dozens (or hundreds) of times as large as the moon. That's huge! Aristarchus was perhaps the first person in history to realize how incredibly far, and how incredibly huge, the sun is, and he did it by thinking about the phases of the moon. Aristarchus was also one of the first people to propose that maybe the sun should be the center of the universe instead of the earth. Shouldn't the biggest thing be in the middle?
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