Dear Cecil: I have noticed that the moon (and the sun, for that matter) appears very large just as it rises and sets. When it is overhead, it seems tiny by comparison. The color is also vastly different, but this can be easily explained by the fact that we view the moon through varying ''thicknesses’’ of atmosphere as it makes its way across the sky. But this explanation seems insufficient to account for the change in size. So what’s the straight dope? Frank M., Los Angeles
Believe it or not, Frank, they’ve been arguing about this for two thousand years, and it’s about time I got things straightened out. First of all, let me make it clear that the effect is an optical illusion. If you measure the moon with a ruler held at arm’s length (a paper clip bent into the shape of a calipers will also work), you’ll find it’s always the same size no matter where it happens to be in the sky. If anything, the moon is slightly smaller at the horizon than it is at the zenith, mainly because it’s 4,000 miles (the radius of the earth) farther away. (If you don’t understand why this is so, draw yourself a picture.) Nonetheless, most people are convinced that, area-wise, the moon’s at least twice as big when it’s near the horizon as when it’s overhead.
Numerous theories have been advanced to explain the “”moon illusion.” At one point people thought it had something to do with the angle at which you hold your head and/or eyes while viewing, while others said it was caused by differences in the moon’s brightness when seen at various locations in the sky (a notion first proposed in 1709). Both ideas have long since been discredited. The fact is that the illusion is dependent entirely on the visual cues provided by the terrain when the moon is near the horizon, and the lack of such cues when it’s at the zenith. To prove this, try viewing the moon through a cardboard tube or a hole punched in a sheet of paper to mask out the landscape —the illusion disappears.
What’s now called the “apparent distance” theory was first advanced by the Egyptian astronomer Ptolemy in the second century AD (I told you this goes back a ways). His explanation is a little confusing, but here goes: most people subconsciously perceive the sky to be a flattened bowl —i.e., objects near the horizon seem farther away than objects overhead, due to the abundance of intervening visual cues on the ground. Now, when we see an image of a certain size at what we believe is a great distance, we deduce that it’s bigger than an image of the same size seen at what seems to be a lesser distance. (You might want to let this percolate for a minute.) So when we see the moon at the “distant” horizon, we subconsciously conclude that that it’s “bigger” than when we see it a few hours later overhead, when it’s “close.” To put it another way, perspective —i.e., the march of visual cues to the horizon —makes the the moon look bigger than it does when it’s just hanging in space.
This explanation is OK as far as it goes, but it’s even better if we combine it with one propounded by psychologist Frank Restle. Frank reasons thusly: you judge the size of something by comparing it to the size of things around it. If it’s surrounded by big things, it seems little. If it’s surrounded by little things, it seems big. When the moon is overhead you judge its size against the vast expanse of the night sky (the stars are too small and faint to make any difference). Ergo, it looks small. When the moon is close to the horizon, on the other hand, it’s usually bigger than many nearby objects (trees, houses, waves on the ocean). In addition, just after moonrise (when the illusion is most compelling), the moon’s apparent diameter exceeds the distance from the moon to the horizon. Add in the effect of prespective, and the moon looks huge. That’s all there is to it.
The Teeming Millions aren’t buying it
I know you’re not infallible, but just in case you don’t realize it, let me point out a small bit of misinformation you published recently. The question was, “Why does the moon sometimes appear much larger when it is near the horizon?” or something to that effect. Your answer was that it appeared larger because there were earthly objects such as trees, buildings, etc., “near” the moon, giving a false perspective.
Sorry to disappoint you, but that’s completely wrong. The earth’s atmosphere is, like the planet, curved. And, as anyone who has ever been in a pool knows, water can distort light. The moon appears larger when near the horizon only when there is sufficient water vapor (humidity) in the atmosphere, because the curvature of the earth’s atmosphere combined with the correct vapor density forms what is essentially a gigantic lens. In this case, a magnifying lens. If you proof of this, just watch the moon (or the setting sun) on a humid day. Either celestial body will look somewhat pear-shaped when very close to the horizon, since that’s where the “lens” is thickest. Trees or no trees.
— Tom R., Chicago
Years of dealing with your kind has taught me patience, Tom. Try to pay attention. The “magnifying” effect you refer to is called refraction. It accounts for the fact that the sun, and less often the moon, appears distorted (i.e., vertically elongated, or pear shaped) just at the point of rising or setting. The elongation lasts only a few minutes, and is not what people are talking about when they say the moon looks bigger when it’s low in the sky. The so-called moon illusion persists even when the moon is a couple of degrees of arc above the horizon.
The illusion is entirely psychological in origin. The actual size of the moon’s image doesn’t decrease as it rises in the sky; you only think it does. To prove this yet again, I got up at several points during the night recently and tried the paper-clip caliper test described earlier to measure the size of the moon’s image as it sank toward the horizon. The illusion of great size was compelling toward the end, but it disappeared as soon as I held up the paper clip and confirmed that the size of the lunar image was unchanged. Try it next time you’re tempted to sound off, and save yourself the price of a stamp.
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