 Let's talk a little about how we came to know what we know today. Now, to begin the story of astronomy, we could easily take it as far back as the earliest cavemen who looked up to the sky and wondered what was up there. But for the sake of brevity, we're going to just limit our discussion for the time being to the ancient Greeks. Turns out that there's a lot of ideas that the ancient Greeks popularized that still hold to this day, and many, of course, that have been since discarded. We begin our story with Aristotle, who was a major proponent of the idea of the so-called geocentric universe. That is, the moon, Mercury, Sun, and all the planets all were revolving around the Earth, with the Earth at the center of the universe. This was a very easy idea to come to. After all, everything in the sky appears to be moving around us. It just seemed to make sense that so did the planets, and perhaps fixed upon the sky where the stars themselves. Now one thing that Aristotle, and indeed most of the ancient Greeks believed, was that the Earth was, in fact, round, and the reason why is because they observed lunar eclipses. If you notice the way the Earth's shadow passes along the face of the moon, you'll notice that the shadow is curved, and it turns out that the only object capable of casting a circular shadow is a spherical object. So for this reason, as well as some other lines of evidence, the Greeks well understood that the Earth was round. And today, thanks to the Internet, more people believe that the Earth is flat than at any time since the 1400s. Yay, progress. Anyway, it turns out, though, that the idea that the Earth was at the center of the universe wasn't 100% shared among all Greek thinkers. Aristarchus of Samos, for example, gave us the first known heliocentric model. In other words, he proposed that the Sun was at the center of the cosmos and everything revolved around the Sun. He published his ideas in something called On the Size and Distances, and he used lunar eclipses to work out the relative distances and sizes of the Earth, Sun, and Moon. He also proposed that the stars were distant suns and that the universe was vast. However, his idea that the Sun might be at the center of the universe was largely rejected. The reasoning went something like this. If the stars were at varying distances from the Sun, and if the Sun were at the center of, well, what we now know today to be our solar system, and Earth were to be traveling around in an orbit, from one location we should be able to look at a relatively nearby star and see its apparent image projected onto the background stars. That means that six months later, we should be able to make a similar observation and see that same star this time with its position shifted with respect to the background stars. This phenomena is the phenomena of parallax, and it's a phenomenon that you and I are familiar with all the time. We have two eyes and our brains work constantly to take the information from each eye and infer a distance to some object, and it's a useful thing for, well, not running into everything all the time. Well, what happened was that the Greeks decided to test this idea by enlisting their very best visually acute individuals. They even pulled soldiers from their ranks who specialized in scouting, and they looked at the brightest stars hoping to detect a parallax. Unfortunately, no parallax could be detected, and therefore, the Greeks largely just gave up on the idea of heliocentrism in favor of geocentrism. Another Greek thinker was Arisatsanes of Cyrene. He actually made the first calculation of the Earth's circumference, and his calculation went something like this. There was a column in the city of Alexandria in what is now modern-day Egypt. There was also a well at Cyene, and it turned out that the distance between the two was something about 5,000 stadia. Arisatanes learned that the incoming sunlight on the day of the summer solstice, the sun would be directly overhead Cyene, and that means that from the bottom of the well, the sun would be directly visible. At the same time, Arisatanes learned that there was a shadow being cast at the column of Alexandria. So, invoking a little bit of simple geometry, Arisatanes reasoned that, well, the shadow makes a seven-degree angle. That means the sunlight is seven degrees tilted from the vertical at Alexandria. And therefore, the opposite angle must also be seven degrees. So if we were to draw an imaginary line from both of these locations to the center of the earth, that means that the angle should be there seven degrees as well. Now, seven degrees is equal to about a 50th of a circle. And since the distance between the two, or 5,000 stadia, then 50 times 5,000 stadia gives you 250,000 stadia. Now, depending upon what the actual value of the stadia was relative to today's units, it turns out that Arisatanes may have come very close to measuring the actual circumference. At worst, within about 20%. But he may have done as well as 1%. So it's a remarkably accurate result using just some simple geometry and reasoning. This brings us to Hipparchus of Nicaea. His work involved making a detailed catalog of stars and also measuring the first brightness system. Something that we call the apparent magnitude. And it's a system that we still use today, albeit with some modification. Hipparchus's magnitude system works something like this. As we see the sunset toward the late afternoon and early evening, the first stars come out. And he assigned these stars magnitude one. They were, after all, the brightest stars. And therefore, they would be the first magnitude, the first stars seen after sunset. A little while later, more stars would come out. And so, he assigned these magnitude two for the second brightest stars. As more stars emerged, they would be designated third magnitude, fourth, fifth, and so on, until reaching about magnitude six. Hipparchus not only cataloged the stars by their brightness, but he was very careful to measure their positions in the sky. And he did something else. He compared his measurements of the positions of stars to the ancient Babylonians and Mesopotamians. And he discovered something rather remarkable. Now, to explain this, I'd like to take a different perspective. Instead of viewing things from the Earth, let's go ahead and view things from an imaginary viewpoint south of the Earth's south pole. We're looking at a very wide-angle view of the sky. We have the north celestial pole up to our top. And we have modern-day Ursa Minor and the bright star on the very end of the handle would be Polaris, our present-day north star. Now, in the lower left, we see the intersection of the celestial equator in red and the sun's path through the sky, the ecliptic in green. And to make things a little bit more visible for us, I chose a date when the sun happened to be located at the vernal equinox. So it looks like it's close to Pisces, but believe it or not, in Abarcus' era, the vernal equinox was considered to be in Aries. Now, the reason why I show you this is because Hipparchus made very careful measurements of the positions of these stars. And when he compared his measurements to the measurements of the ancient Babylonians and Mesopotamians, he determined that their positions were a little bit different. In fact, every star in the sky was systematically shifted by a few degrees. And what Hipparchus was able to do was intuit that it wasn't that the sky was moving around, but rather that the Earth itself must be wobbling like a top. And this wobbling is called precession. It turns out, we now know today that the Earth has a 26,000-year precession cycle. The Earth's axis is pointing to different locations in the sky over time. This has some interesting implications because if we could wind the clock backward to, say, 3,000 BC, you'll notice that the North Celestial Pole is nowhere near Polaris. It is instead rather close to the star Thuban in the constellation Draco the Dragon. Likewise, the vernal equinox is also located in the constellation of Taurus. Fast forward 1,000 years, the North Celestial Pole now precesses away from Thuban, and the vernal equinox makes its way toward Aries. By 1,000 BC, we're getting farther from Draco at the North and farther from Taurus at the vernal equinox. We are certainly in the constellation of Aries. And it is for this reason that to this day, the vernal equinox is still sometimes known as the first point of Aries. In other words, it represents the location of the vernal equinox when Hipparchus was doing his work. At around the turn of the millennium, the vernal equinox had moved firmly toward Pisces. And if we continue to just move forward in time, you'll see that by 2,000 or so, the North Celestial Pole was right almost exactly where Polaris is today. So if we continue to let things move along and let the earth continue to wobble along its precession, you'll see that over 26,000 years, we will no longer have a North Pole star of Polaris. We'll instead have Vega in a few thousand years, maybe four eventually coming around back again toward Thuban. So we'll be returning to a orientation of the North Celestial Pole that was very similar to the orientation of the earth when the ancient Egyptians built their pyramids. So at the center of the pyramid are the king's burial chambers. And there are two air vents that are directed one on the left facing to the south and one on the right facing to the north. And the position and the angle of this air vent was carefully chosen such that looking through the air vent from inside the burial chamber would reveal the star Thuban. This was the North Star of the time that the pyramids were built. This way the king could gaze upon the circumpolar stars and watch them revolve around the North Star Thuban for all of eternity. This was a very sacred idea to the ancient Egyptians. So what would that look like? Well, there's Thuban circled for us. This was the North Star of its day. And here we are in about 3000 before the common era. And we can see that the stars are circumpolar surrounding Thuban, which was almost at the time at the location of the North celestial pole. It turns out that most of the works of the ancient Greeks, Babylonians and Mesopotamians were lost in the great fire of the library at Alexandria. However, Claudius Ptolemy was careful to compile much of that work and published his ideas in something called the Almagest, the greatest. In other words, he was paying tribute to the greats that had come before him. So he was able to popularize the idea of the geocentric model. Again, this was the prevailing idea of the ancient Greeks. It seemed to make the most sense despite a few dissenters. And it was also Ptolemy who gave the first explanation for something called retrograde motion. And this idea would dominate for over 1500 years, well into the next millennium. Let's talk a little bit about retrograde motion for a moment. Retrograde motion is simply the apparent shift in the position of the planets. So given a planet's normal tendency, it will seem to go eastward or prograde. But then once in a while, the planet will appear to backtrack. This is the retrograde motion before resuming its prograde motion once again. Now, for everything to rise in the east and set in the west, it would be perfectly reasonable to conclude that the earth was at the center of the cosmos. But this retrograde motion was an anomaly. It did not make sense. So in order to make the retrograde motion work, rather than having Mars in this example and all the planets directly revolving around the earth, Ptolemy introduced a new concept called the epicycle. The epicycle was an invisible circle that carried Mars and the epicycle itself revolved around something called a deferent. And it would be this epicycle moving about the deferent that would create the apparent retrograde motion. So you can imagine yourself on earth looking at Mars and it appears to be going in prograde motion before executing a slight zigzag back and forth in the sky, giving us retrograde motion. Now, this was a good first order approximation. But the problem though is that the epicycle that we see here just would not be accurate enough to predict when the next retrograde motions would be. To solve this problem, Ptolemy introduced a modification to his ideas. He introduced a equant. That is, the earth is still very much at the center of the cosmos. But the epicycle, the deferent and so forth, now we're centered on an offset point called an equant. And this is what helped to make the retrograde motion of Mars and all the planets be a little bit more on time to a slightly better job of predicting exactly when these retrogrades would occur. Even then, sometimes additional modifications would be required. Not the least of which was adding an additional epicycle to the epicycle. Things got a little bit complex over time. And this was a major problem because while the epicycle model did an extremely good job of predicting retrograde motions for about 1500 years, it was at the same time a little bit messy. And it allowed some people to begin to think maybe there were alternatives and maybe some of these ideas to the geocentric model should be revisited.