The coincidental geometry of a total solar eclipse

A total solar eclipse is both chance and certainty—and there's something kind of beautiful about that.

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According to Smith’s Illustrated Astronomy (publication date 1855), the effects of a total eclipse of the sun are as follows:

That gloom is the feeling of insignificance, because in the darkness, you have to acknowledge you live on a planet orbiting a sun, and that sun is one star of billions, among the billions of galaxies in our universe. That gloom is awe.

That “awe,” to be precise, is the when the Moon perfectly blocks out the sun, casting its shadow on Earth, and leaving only the wispy, ephemeral aura of the Sun’s corona ghosting into the darkness. It happens only because of math and coincidence. A total solar eclipse is both chance and certainty.

Take this for example: If the radius of the Sun is 695,700 km, how can the moon, radius 1,737 km, block it out? No, it’s not an optical illusion. By chance, two cosmic equations add up.

Here’s the first one: The radius of the Sun is about 400 times larger than that of the Moon. And the second? The Sun is about 400 times further away from the Earth than the Moon.

So, if you’re an Earthling looking to the celestial heavens, the Sun and the Moon usually appear the same size in the sky. If you were a Martian, though, your moons would appear much smaller than the Sun, and you’d never be lucky enough to see a total solar eclipse. The fact that we can experience one on Earth is a matter of distance and size being coincidentally relative—chance.

What’s certain is the Moon and the Earth’s orbit around the Sun. When those heavenly bodies align—Earth, Moon, Sun (in that order)—you get a solar eclipse.

Think of the Earthling looking to the celestial heavens. Recall that the Sun and the Moon usually appear the same size in the sky—usually.

The moon’s path around Earth is an ellipse, not a perfect circle, which means the distance between us and the Moon changes all the time. When the Moon is farther away, it looks smaller from our earthly vantage point. So it blocks most, but not all of the Sun. We call that an annular eclipse. “Annular” because it leaves a fiery ring, or “annulus,” around the Moon. In a total eclipse, the Moon is nearer to Earth in its orbital path, and completely covers the Sun in the sky. Chance and certainty are at play again.

The Moon’s plane of orbit isn’t aligned with Earth’s—it’s tilted 5.1 degrees. So, when the Moon falls in-between the Sun and Earth, which happens once every 29.5-day lunar cycle, the sun is obscured. But rarely does the Moon’s shadow actually fall on Earth. Instead, it is usually lost in space.

In the end, the moon’s shadowy echo only appears on Earth when the moon’s tilted orbit meets the sun-Earth plane at two celestial points called “nodes.” But it won’t happen forever. Every year, the Moon moves about 3.8 cm away from us. Six hundred million years from now, Earthlings will see their final total solar eclipse.

Think of yourself six hundred million years from now, looking up at that final total eclipse. We’re a planet suspended in math. Not numbers; numbers are just symbols, after all, but math—geometry that’s built into the fabric of our universe.

The Earth sits in the heavens amidst angles and radii, ellipses and cones—fundamental shapes that appear throughout nature and help us explain not only motion and gravity, but things like electricity and the genome. And woven through all of it is the unlikely coincidence that any of this is happening at all.

Chance and certainty: a total solar eclipse.

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