How Eclipses Revealed Our Solar System (Script) (Patreon)

A little later today a ball of rock the size of Australia will drift directly between the Earth and theSun. That ball—our Moon—will cast a shadow that will pass across the North American continent, carving a narrow line from Mexico to Newfoundland. For anyone lucky enough to be on that line the sky will go twilight-dark for up to four and a half minutes, and the Sun will be transformed into a black disk crowned with the ghostly filaments of its corona. will witness a total solar eclipse. Of all the astronomical phenomena you can witness, the total solar eclipse has to be the most visceral--the most in-your-face reminder that our reality consists of giant balls of rock spinning around stars. It's also the eclipse and phenomena like it that set us on the path to understanding that reality in the first place. 

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On this show we tend to speak from a position of already knowing stuff. We know that space is big and that moons orbit planets orbit stars, and we go from there to some pretty crazy places. . But imagine what it must have been like to know nothing. I mean, nothing about the scale of the cosmos or the nature of the solar system. Imagine how terrifying and mysterious a total solar eclipse would be. But also inspiring--you might feel inspired to figure out what in the world--or out of it--was going on. And in fact the eclipse and phenomena like it were the very first tools used by the ancients on our path from that place of mystery and not-knowing to our modern understanding of the universe.  So, today, as a celebration of the impending eclipse I want to retrace some of that cognitive journey so that when the eclipse happens we can appreciate a bit better how we know what we know about what we're seeing.

This particular telling of how we figured out the universe starts with the ancient greeks. Many other peoples contributed different things to our modern story, but it was the Greeks who kickstarted the whole science thing. So what did they figure out? Well, despite the common notion that we all thought the world was flat until Christopher Columbus sailed around it, the ancient Greeks were well aware of the roundness of the planet. 

They knew that boats disappear ‘hull’ first as they head out to sea with their large sails disappearing last. They knew that, when moving north or sound, the altitude of stars change in the way you’d expect for moving on the surface of a sphere. And they knew the Earth was round because of eclipses. Lunar eclipses in this case. As long as you know that these are caused by the Moon moving through Earth’s shadow, it’s hard to imagine a non-round object causing that distinctly round shadow. 

And, as it happens, the ancient Greeks were fully aware of the cause of both lunar and solar eclipses. That was first worked out by Anaxagoras in the fifth century BCE. He realized that only one configuration made consistent sense of our observations. For it to all make sense the Moon must travel around the earth, must be spherical, and must be closer to us than the sun. That gives us a changing partial view of the illuminated side of the Moon—hence phases—and a lunar shadow for solar eclipses and Earth shadow for lunar eclipses. 

But the subtle details of the eclipses revealed so much more than their basic nature. As I mentioned, the shape of Earth’s shadow pointed to our planet’s roundness. There’s also the fact that eclipses don’t happen every lunar orbit, but rather can only happen twice per year. That fact was a clue that Earth orbits the Sun. See, there’s a slight misalignment between the Earth’s orbit around the Sun and the Moon’s around the Earth. That means the Moon usually ducks under or over Earth’s shadow, and its own shadow usually misses the Earth.

But twice a year the Moon’s orbital tilt is perpendicular to a line connecting Sun and Earth. At those times the Moon has to pass through Earth’s orbital plane while it’s on the Sun-Earth line On this “line of nodes” we’ll typically get a solar and a lunar eclipses, and sometimes more than one depending on the Moon’s orbital position. This periodicity to the eclipses tells us that the positions of the Sun and Earth change in a regular manner, and we now understand this to be due to Earth’s orbit.

OK, great, so eclipses gave us the basic shape of the Moon-Earth-Sun system. But they also give us the relative size scales for our growing model solar system. Those details are hidden in deeper subtleties of the eclipses, and it took our next ancient Greek—Aristarchus of Samos—to figure them out in the 3rd century BCE. Aristarchus figured out three clever ways to use the shadows cast by celestial bodies to map the solar system. The shadows of eclipses, but also the shadow that the Moon casts on itself causing lunar phases. 

The amount of time the moon spent in its different phases tells us the relative distances between Earth, Moon and Sun. You might think that the moon spends equal time in its different phases. For example, the time spent as a crescent should be the same as the time spent gibbous. For simplicity, by “crescent” I’m going to mean anything less than half full—including a new moon—that’s when the Moons is closer to the Sun. I’ll use gibbous for anything more than half full, including actually full—when the Moon is further from the Sun. Oh, and confusingly those half-full points are technically called quarter moons. Don’t ask me why. So surely the Moon should be in the crescent and gibbous phases for the same amount of time. After all, the Moon does spend the same amount of time on each side of its orbit, on average at least.

But, oddly, the Moon is gibbous for a little bit longer than it’s a crescent. The reason for this is that the distance to the Sun also matters. If the Sun were infinitely far away, then indeed we’d expect equal time in gibbous and crescent phases. We see a half moon when the Sun’s light illuminate the Moon at 90-degrees to our view of the moon. If the Sun was extremely far away compared to the size of the Moon’s orbit then its rays arrive nearly parallel across that orbit, and so the half-moon points would be on opposite sides of the Earth.

But if the Sun isn’t “infinitely” far compared to the Moon then its rays reach the Moon at a different angle on either side of the Earth. The half-moon points end up being a little closer to the Sun, which means the crescent phase between these points is shorter than the gibbous phase beyond these points. By measuring the difference in the length of the gibbous versus crescent phases it’s potentially possible to get the distance of the Sun relative to the distance to the moon.

The quarter moon points are only about 0.5 degrees off the locations expected for an infinitely distant sun. That tells us that the Sun is nearly 400 times more distant than the Moon. Aristarchus measured a bit high—he got 3 degrees, which told him that the Sun is at 20 times the lunar distance. But remember that he was working without clocks and without telescopes, so we’ll cut him some slack. 

Aristarchus’s second calculation is simpler. It uses the fact that the Moon exactly blocks the Sun during a total solar eclipse—as many people will witness today. That told him that the ratio of the size of the Moon to the size of the Sun has to be the same as the ratio of the distance to the moon to the distance to the Sun. That sure would be helpful if he knew either of those distances.

But that brings us to the third thing that Aristarchus figured out, this time using lunar eclipses. The Moon takes some time to pass through Earth’s shadow during such an eclipse. The width of that shadow depends on the size of the Earth, the distance between the Earth and the Moon, but also on the size to and distance of the Sun. Aristarchus used simple geometry to write down some equations that related the ratios of sizes and distances. The ratio of sizes of the Earth to both the Sun and Moon and the ratio of distances between Earth and both the Sun and Moon, all in terms of the ratio of the width of Earth’s shadow to the Moon’s size—how many moons fit across that shadow. And that last one could be measured just by watching a lunar eclipse. It’s 2.6 moons, FYI.

Aristachus concluded correctly that the Moon is approximately a third the diameter of the Earth. You might remember that he had already gotten the ratio of Earth-Sun to Earth-Moon distances from the phases of the Moon—and he got a number that was too small. This error propagated to his estimate of the Sun’s size, and so he found a ratio between the Earth and Sun’s diameter that was also about a factor of 20 too small.

This was nonetheless all very impressive. Aristarchus, using little more than shadows and geometry, was the first to seriously present evidence for our modern picture of the solar system. But you might have noticed that all these distances and sizes are relative—for example, it’s the size of the Moon or Sun compared to the size of the Earth. In order to pin down the actual scale of the solar system, we needed just one real physical value. 

This came from the chief librarian of the great library of Alexandria, Eratosthenes, also in the 3rd century BCE. Erastonthenes realized that, on a curved world, the Sun could be directly overhead at noon at one latitude, but at another latitude might be lower in the sky. He had heard that at noon on the summer solstice the Sun illuminated the bottom of a deep well in the city of Syene, far to the south of Alexandria—he concluded that it must be directly overhead at that time and place. 

But he also knew that at the same time in Alexandria, the Sun wasn’t quite overhead. A vertical pole would still cast a shadow. Again with simple geometry, and by measuring the length of shadows cast on that day in Alexandria as well as the distance to Syene, Eratosthenes was able to calculate the radius of the Earth. And he got it right, to within less than 2% of the true value. 

Adding Aristachus’s measurement for the size of the Earth to Erastothenes’ measurements of the relative sizes of Earth, Moon and Sun, we got our first real physical values for the sizes of these bodies. At the very least the size and distance of the Moon was now pretty solid.

But there was still the uncertainty in the distance to the Sun. And we found new motivation to get that distance right when we finally figured out the motion of the planets. We’ll breeze past Copernicus who verified the suspicion of some of the ancient Greeks that the Sun really is in the center of the solar system, and go straight to Johanne Kepler. His laws of planetary motion told us that the relative speed of planets through space depends on their distance from the Sun. Finding the distance between the Earth and Sun—what we call the Astronomical Unit—would lock into place our first ever precise model of the solar system. 

And again, it was an eclipse of sorts that gave us that number. It was the observation of another world passing in front of the Sun—in this case a planet rather than the moon, so not really an eclipse, but a transit.

If you look at the Sun through a pinhole camera when Mercury or Venus transit the Sun, you’ll see a tiny black dot moving slowly across a bright disk. The line traveled by the planet depends on the relative positions of all three bodies—but also on your own position on the Earth. A transit observed from New York might cross near the edge of that disk, but might cross deep into the disk if observed in Puerto Rico. This is due to parallax—the same effect as when your finger appears to move side to side relative to the background when you blink your eyes back and forth. In this case it’s called solar parallax.

Measuring the difference in position of the transit at two different locations tells you the distance to the transiting planet and to the Sun. There was an early attempt to measure a transit of Mercury back in the 1660s—but Mercury’s tiny size made the observation difficult and this effort failed. A century  later the astronomer Edmund Halley realized that Venus- being closer to the earth, would make the measurement easier. The only problem was that it transited much less often - only twice per century, eight years apart. 

So, when the regularly scheduled transits of Venus arrived in 1761 and 1769, the astronomy world was prepared, scattering themselves across the world to observe the 1769 transit from as many places as possible. In 1769, observations were made everywhere from Philadelphia to St Petersburg to Tahiti that, when combined, provided the first accurate measurement of the size of the solar system. It’s a really cool moment in the history of science- a massive international collaboration, requiring large government grants to fund expeditions to the far side of the planet. It’s almost like a precursor to modern ‘big science.’ 

Okay, drumroll, put all their measurements together, and you get the distance to the sun to be 153 million km. That’s only 2% above the modern accepted value. With the earth’s orbital radius and orbital period known, and with the help of Kepler’s laws, the orbital radii of every planet in the solar system could be calculated immediately. Not bad for watching a dot move across the face of the Sun. But this achievement was really the crystallization of two thousand years of astronomy, a final synthesis of the revelations brought by asymmetric lunar phases and of measuring ancient lunar and solar eclipses. Ultimately, though, the credit goes to those clever humans who witnessed these mystical-seeming phenomena and, rather than credit gods and myths, resolved to make sense of our once-mysterious space time.