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The Moon looks bigger on the horizon because the air acts like a lens, magnifying it (excerpts)
When on the horizon, the Moon appears
huge and flat from space, too.
Almost everyone has seen the Moon, red and swollen, looming hugely as it rises over the horizon. A few hours later, when it's high in the sky, it has shrunk considerably, looking more "normal." Most people are also aware the Sun exhibits this behavior, and even constellations do, too.
It's true that the Earth's air is thicker near the horizon. When you look up, you are looking through the thinnest part of the atmosphere, and the closer you look toward the horizon, the more air you look through.
However, the air actually compresses the Moon's image, instead of magnifying it. Have you noticed that the Moon looks noticeably squashed when it's right on the horizon? That's because the varying thickness of the air near the horizon distorts the Moon's shape, making it smaller top-to-bottom.
It turns out this effect of the Moon looking larger near the horizon, called the Moon Illusion, really is an illusion. You can see this for yourself, by comparing the rising Moon's size with some household object (say, the tip of a pencil eraser held at arm's length), and then wait a few hours and do it again. You'll find the size hasn't changed appreciably.
This illusion is convincing, but it's not real.
What's going on here is that your brain is interpreting the sky as being farther away near the horizon, and closer near the zenith (directly overhead). This isn't surprising; look at the sky on a cloudy day and the clouds overhead may be a few kilometers above you, but near the horizon they might be hundreds of kilometers away. The Moon, when it's on the horizon, is interpreted by your brain as being farther away. Since it's the same apparent size as when it's high up, your brain figures it must be physically bigger. Otherwise, the distance would make it look smaller.
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