the line between the Moon and the center of the Earth and roughly the same distance away. But when you look at the Moon when it’s overhead, you are
The second incorrect explanation — Earth’s air distorts the Moon’s image, making it look bigger — is also wrong. A ray of light will bend when it enters a new medium, say, as it travels from air to water. This effect is what makes a spoon look bent when it sticks out of a glass of water.
Light will also bend when it goes from the vacuum of space to the relatively dense medium of our atmosphere. As you look to the sky, atmospheric thickness changes very rapidly with height near the horizon. This is because the atmosphere curves along with the Earth (see chapter 4, “Blue Skies Smiling at Me,” for an explanation). This change causes light to bend by different amounts depending on the angle of the light source off the horizon. When the Moon sits on the horizon, the top part is about a half a degree higher than the lower part, which means that light from the bottom half gets bent more. The air bends the light up, making it look as if the bottom part of the Moon is being squashed up into the top half. That’s why the Moon (and the Sun too, of course) looks flattened when it sits directly on the horizon.
The vertical dimension is squashed but not the horizontal one. That’s because as you go around the horizon, side to side, the thickness of the air is constant. It’s only when the light comes from different heights that you see this effect.
Like the distance explanation, we see that near the horizon the Moon’s disk is actually physically a little smaller than when it is high in the sky, so again this explanation must be wrong. Even so, this belief is commonly held by a diverse and widespread group of people. It’s taught in high school and even in college, and I have heard that it is even used in textbooks, although I have never seen it in print.
Despite what your eyes and brain are telling you, if you go out and measure the size of the Moon when it is near the horizon and again when it is near the zenith, you will see that it is almost exactly the same size. You need not measure it accurately; you can simply hold a pencil eraser at arm’s length to give yourself a comparison. If you do this, you’ll see that even though the Moon
The big Moon on the horizon effect is amazingly powerful. But the change in size is an illusion. So if this isn’t a physical effect, it must be psychological.
The third explanation relies on psychology and doesn’t need the Moon to be physically bigger; the Moon just has to be near other objects on the horizon. Mentally, we compare the Moon to these objects and it looks bigger. When it’s near the zenith, we cannot make the same comparison, so it looks farther away.
But this can’t be right. The illusion persists even when the horizon is clear, as when the Moon is viewed from ships at sea or out airplane windows. Also, you can position yourself so that you can see the zenith Moon between tall buildings, and it still doesn’t look any bigger.
For further proof, try this: The next time you see the huge, full Moon on the horizon, bend over and look at the Moon upsidedown from between your legs (you may want to wait until no one else is around). Most people claim that when they do this the effect vanishes. If the illusion were due to comparison with foreground objects, it would still persist while you were contorted like this, because even upside-down you could still see the foreground objects. But the illusion vanishes, so this cannot be the correct explanation either. Note, too, that this is further proof that the effect is not due to a measurable size change in the Moon’s diameter.
So what
This doesn’t mean we don’t understand it at least partially. There are several factors involved. Probably the two most important are how we judge the size of distant objects and how we perceive the shape of the sky itself.
When you look at a crowded street scene, the people standing near you appear to be larger than the ones farther away. If you measured how big they looked by holding a ruler up near your eye and gauging the apparent size of the people around you, someone standing 5 meters (16 feet) away might look to be 30 centimeters (12 inches) tall, but someone twice as far away would look only 15 centimeters (6 inches) tall. The physical sizes of the images of these people on your retina are different, but you
This effect is called size constancy. It has clear advantages; if you actually perceived the more-distant people as being smaller, you would have a messed-up sense of depth perception. A species like that wouldn’t survive long against a predator that knows very well just how far away (and how big) you are. In that sense, size constancy is a survival factor, and it’s not surprising that it’s a very strong effect.
However, we can be fooled. In the diagram you see two lines converging to a point at the top. There are two horizontal lines drawn across them — one near the top where the lines converge, and the other near the bottom where they are farther apart. Which horizontal line is longer? Most people report the top one to be longer. However, if you measure them (and feel free to do so) you will see they are the same length.
This is called the Ponzo Illusion, after the researcher who characterized it. What’s happening is that your brain is interpreting the converging lines to be parallel, like railroad tracks. Where they converge is actually perceived as being in the distance, just like railroad tracks appear to converge near the horizon. So your brain perceives the top of the diagram to be farther away than the bottom.
The Ponzo illusion is one of the most famous of all optical illusions. The horizontal lines are actually the same length, but the upper one appears longer because of the converging vertical lines.
Now remember size constancy. Your brain wants to think that the top line is farther away. But since the length of the line is the same, your brain interprets this as meaning the top line is longer than the bottom line. Size constancy works in coordination with the perspective effect to trick your brain into thinking the upper line is longer when in fact it isn’t.
What does this have to do with the Moon Illusion? For that we have to turn to the shape of the sky.
The sky is usually depicted in diagrams as a hemisphere, which is literally half a sphere. Of course, it isn’t really; there is no surface above the Earth. The sky goes on forever. However, we do perceive the sky as a surface over us, and so it does appear to have a shape. In a sphere all points are equally distant from the center. The point on the sky directly overhead is called the zenith, and if the sky were indeed a sphere it would be just as far away as a point on the horizon.
But that’s not really the case. Most people, myself included, actually see the sky as flattened near the top, more like a soup bowl than half a ball. Don’t believe me? Try this: Go outside to level ground where you have a clear view of the sky from horizon to zenith. Imagine there is a line drawn from the zenith straight down across the sky to the horizon. Extend your arm, and point your finger to where you think the halfway point is between the ground and the zenith, 45 degrees up from the horizon.
We don’t see the sky as a hemisphere, but actually as a bowl inverted over our heads. When the Moon is on the horizon, it appears farther away than when it is overhead. Our brains are tricked into thinking the Moon is bigger than it really is when it’s on the horizon.
Now have a friend measure the angle of your arm relative to the ground. I will almost guarantee that your arm is at an angle of roughly 30 degrees and not 45 degrees, which is truly halfway up to the zenith. I have tried this myself with many friends (some of whom were astronomers), and no one has
