Exploring Ancient and Modern Astronomy

We're going to start a series of lectures on the history of astronomy. We're going to start with ancient astronomy, and we're going to learn in this lecture about the ancient history of astronomy, the geocentric model, which is the earlier model where the Earth is at the center of the solar system. and the flat earth model, which is an even earlier model where the earth is flat instead of a sphere. And while we learn about all that stuff, we'll also see a lot of examples of how to apply the scientific method. Astronomy has a long history of replacing old theories with new ones based on scientific evidence. Remember in the first lecture I mentioned that this is basically the most important thing about science is when you find out something is wrong you replace it with something else. So learning about astronomy is also a great opportunity to learn about the scientific method and critical thinking and skepticism. All of these tools and skills are extremely important for understanding how the universe really works. You can't understand how the universe works if you're not willing to replace wrong ideas with correct ideas. You can also use these tools in your daily life to tell the difference between what's true and what's not. You'd be surprised how few people actually do this in their daily lives. And of course we can see examples all around us with the anti-vaxxers and the flat earthers and all of those different groups of people that just don't understand science. Today, when we look at the sky, we have a very good understanding of what we see. So we understand the physical laws that govern the movement of the celestial objects, and we also have plenty of details about these objects. Distance, size, composition, how they evolve in time. and so on. We also have today telescopes and other tools to measure properties that cannot be seen with the naked eye. Modern humans evolved around 300 000 years ago And of course that's hard to define exactly, but let's say 300,000 years, and recorded history began around 5,000 years ago. But we learned essentially everything we know about the universe only in the last few hundred years. This is really amazing, I think, because humans have existed for so long. 300,000 years we've been able to see the stars and 5,000 years ago we started being able to write about the stars, collect data, perform mathematical calculations, but we only actually started to understand the universe in the last few hundred years. I would say since the 17th century. In fact, there are some very important things we only learned in the last century, or even in the last decade. So we used to think that the Milky Way was the entire universe. But in 1923, we discovered that there are other galaxies And the Milky Way is actually just a tiny speck of dust compared to the entire universe. I mean, it's just so hard to fathom, you know, living in that time and thinking that what you see around you, all these stars in the sky, that's all there is, that's the entire universe, only to discover that there are actually hundreds of billions of other galaxies, each of which also has this huge collection of its own stars, and there are these vast unimaginable distances between these galaxies. Black holes were theorized more than 100 years ago, but only very recently, in 2019, we were able to obtain the first actual image of a black hole. Until that point, black holes were essentially just a hypothesis. Remember, a hypothesis is a theory that hasn't been proven yet. I think no one really thought black holes don't exist before 2019, because we had a lot of indirect evidence for them, and also because they basically flow immediately from the theory of general relativity, which is the one that we use to describe gravity, but Only in 2019 we were able to get direct evidence that black holes existed. That being said, let's talk about ancient astronomy. So in prehistoric times, for countless years, I mean we're talking about hundreds of thousands of years, Humans had no idea what the true nature of the celestial bodies was. Prehistoric people identified celestial objects with gods, as they did with everything else they didn't understand. The first astronomers were actually priests of ancient religions tens of thousands of years ago. They also believed that the celestial objects influenced their lives. This is the origin of astrology, of course. So astronomy remained closely tied to religion and astrology for thousands of years in essentially every single ancient culture we know of all around the world. If we think about what is the biggest thing that we don't understand unless we have the scientific method and math and everything, It is space, what's going on in the sky. So it makes a lot of sense that all these different cultures independently developed religion and astrology in relation to what they saw in the sky. It's just so hard to explain if you don't have the right tools and the right technology to do it. Because you need the right tools and the right technology to do it, it took a long time before humans finally understood that the celestial objects are governed by mundane natural laws, just like things down here on Earth. So now we know that you can predict where each celestial body is going to be at any point in time using very simple equations. but this was not obvious in prehistoric times where we didn't understand gravity yet. Now proper astronomy involves collecting and analyzing data, therefore it cannot exist without writing and mathematics which were only invented about 5000 years ago. Around that time Ancient civilizations such as the Babylonians and the Egyptians, which we're going to talk about a lot more, noticed that astronomical phenomena are periodic and could be used to keep track of time. So they developed calendars that could be used to predict the change of seasons, which was very helpful for agriculture, for example, to know when to plant and when to harvest. This was, in fact, one of the main catalysts for developing advanced mathematics in the ancient world. Babylonian astronomers measured and recorded the positions of the Moon and the planets for hundreds of years. By around 400 BC, they compiled enough data to be able to find regular patterns. Using these patterns, they could predict not only where the celestial bodies will be at any time, but even when lunar eclipses will happen. However, they couldn't yet predict solar eclipses that came a bit later. Ancient Chinese astronomers also recorded astronomical data, and the oldest written record of a solar eclipse is from around 2000 BC from China. So this was 4,000 years ago. The Chinese astronomical catalogs span 3,000 years and list thousands of eclipses, comets, meteors, exploding stars, and even dark spots of the Sun, which we'll learn about later. The historical data is still being used by modern astronomers even today. So if you want to know certain things about what's happening today, you may need to actually look at data from thousands of years ago to see how things have changed since then. So this is very important even for modern research. So now I want to talk about an important concept called axial precession. The ancient Greek astronomer Hipparchus built an observatory on the Greek island of Rhodes around 150 BC. He used it to measure the accurate positions of objects in the sky and he composed a star catalog with around 850 entries with celestial coordinates for each star specifying its positions in the sky. So these coordinates are kind of like the latitude and longitude we learned about last time, except instead of being on the earth they are on the sky. Hipparchus divided the stars into apparent magnitudes according to their apparent brightness. The brighter the star, as it appears to us, the smaller the magnitude. The stars of the first magnitude are the brightest, and then as you go to higher magnitudes, the stars become less bright. Today, we still use the term magnitude to describe the brightness of stars, but the modern definition is much more precise. So now it's important to understand that the apparent brightness of a star, meaning as it looks to us when we look in the sky, isn't the same as its actual brightness, which we call luminosity. Two stars of the same luminosity, but at different distances from us, will have different apparent magnitudes. So, of course, the farther away a star is, the less bright it will look, because light gets dimmer as it expands towards us. Light expands in a sphere away from the star. There's always the same amount of light, but the surface area of the sphere keeps growing. So that means that the farther away you are, the less light you eventually get, because you get... just a smaller part of the overall sphere of light. By comparing the data that Hipparchus collected with data from older observations, he discovered that the position of the north celestial pole changes over time. Let me remind you, the north celestial pole is the point around which the sky appears to rotate. So if you look at the sky, that point will be a point where nothing rotates and everything will rotate around that point. This phenomenon, that the position of the north celestial pole changes over time, is called axial precession. And here is an illustration. You can imagine that the earth is like a spinning top. and I'll show you a video in a second, and there are two types of rotation. Those first of all spin around the axis. So this is the axis here. You can imagine that it continues through the planet and the planet rotates around that axis just like a spinning top. But also there is the rotation of the axis itself or of where the axis is pointing. And this is called precession. Now the spin around the axis is fast, so it's in fact a full rotation every day by definition, but the precession of the axis is much slower. So in this video you can see a spinning top, and you can see, if you look carefully you'll see, it is indeed rotating very very fast around its axis. And also you can clearly see the axis itself is slowly moving around. So there are two different and independent rotations here. The rotation of the spinning top around the axis, and the rotation of the axis around some imaginary circle. The earth is not a perfect sphere. It actually has a bit of a bulge around the equator. However, the gravitational pull of the Sun and the Moon on this bulge is what causes the axis to precess. It takes the Earth's axis around 25,700 years to complete the full circle. The north and south celestial poles change due to the precession. Today, the north celestial pole is, as we learned last time, near the star Polaris, which is why we call that star the north star. But around 14,000 years ago, the star Vega was the north star. and it will become the North Star again in around 11,700 years. So you can see here again this analogy to a spinning top. So here is the Earth, and here is the circle of this axial precession. So the axis now points towards Polaris. but it will slowly, over thousands of years, rotate until it's actually going to point towards Vega. So in 11,000 years, Vega is going to be the North Star, not Polaris. But then the axis is going to keep rotating and eventually reach Polaris again, after 25,000 years or so. So now let's talk about the spherical earth. So like I said, the earth is a sphere, almost a perfect sphere. But many ancient cultures initially believed that the earth was flat, shaped as a plane or a disc. Of course, if you stand in an open field and you look around you, everything seems flat, right? You don't see anything curve away from you if you just look around you. So it definitely looks like the Earth is flat. But it's actually not hard to prove that it actually is spherical. In fact, it's so easy that the ancient Greeks already knew the Earth was spherical as early as 2500 years ago. in the time of Pythagoras. Many of the proofs that the Earth is spherical were collected by the Greek philosopher Aristotle around 330 BC. And by that time, every Greek scholar accepted the spherical Earth as a fact, and this knowledge gradually spread to the rest of the world. So let's first review some of the evidence, including even some experiments you can do on your own if you're not fully convinced. By doing this, we'll learn a bit about how science works. Some of the following evidence was already known to the ancient Greeks, but some of it is more modern. So let's start with lunar eclipses. A lunar eclipse happens when the moon moves into the Earth's shadow. Here is the Sun and here is the Earth. The light from the sun shines in this direction, and here is the moon, and you can see that now the moon is in the shadow of the earth. Now what is a shadow? A shadow is where an object like the earth blocks light. Light gets to all these points, but here the earth is in the way, so the light just stops here, it doesn't continue, this causes a shadow. And this is what we call a lunar eclipse. You can actually look at the shape of the shadow of the Earth as seen on the Moon. The shadow of the Earth... moving on the Moon is always round. And here also from another direction. The only kind of object that always produces a round shadow is a sphere. Let me describe to you an experiment that you can do yourself at home to see what I mean. So take objects of different shapes and rotate them in front of a lamp or a flashlight. Now if you do this with a disc-shaped object such as a plate, you will notice that the shadow it creates can be flat, round, or anything in between, depending on its orientation. So certainly the shadow will be round if you shine straight into the plate, but if the plate is on the side, the shadow will just be a line, not a disc. If you do this with a spherical object, such as a ball, you will see the shadow is always round, no matter the orientation. Therefore, the Earth must be a sphere, because if it wasn't a sphere, then we would have seen different shapes during lunar eclipses depending on the relative positions of the Sun and the Earth. We would sometimes see a round shadow, sometimes see a line shadow, and everything in between. Another evidence, travelers who travel a significant distance to the south, see new stars that were not visible from the north. They also see the height of the north star in the sky decrease as they go further south. The reason for that is that the earth is a sphere, and therefore we see different portions of the sky from different points on the sphere. If the earth was flat, then everyone would have seen the same stars, right? So on a flat Earth, everyone stands at the same level, and when you look up, everyone sees the same thing. On a round planet, people who stand on different places on this sphere see a completely different sky. Now, these two proofs were already known to the ancient Greeks, but... they are indirect proofs. Modern technology, that of course did not exist at the time of the Greeks, allows us to provide direct proof that the Earth is a sphere. So there are plenty of photos of the Earth taken by satellites and by astronauts. Since photos taken from different directions always show that the Earth is round, its shape must be spherical. Again, it's the exact same reason that the shadows are all surround if the earth is a sphere. However, in this case, we're not talking about indirect evidence just from looking at the shape of the shadows. We can actually see the shape of the earth itself from images. So now let me demonstrate that using NASA's EPIC Earth Polychromatic Imaging Camera, which takes images of the Earth from space from different angles every day. You can see some information over here, like the distance to Earth, the distance to the Sun, the distance from the Sun to the Earth and so on. And you can choose here different angles from which to see the Earth. Now you see different images of the Earth from different angles around it and of course each image shows different continents like here's South America, here's Australia, And here's Africa. So, of course, taking all these images would not have been possible if the Earth was flat, because then all of these continents, South America and Australia and Africa, would all be in the same direction away from the camera. Now here's... Another kind of experiment you could do on your own You can go to the nearest ocean and you can watch a ship sail into the horizon And you'll see the ship disappear gradually First the bottom part and then the middle and then the top Here is the full ship and then it sails away from us into the horizon And here we only see the ship from the middle and up. And if it continues, we will only see these antennas, I guess if visibility is good enough, and eventually we won't see the ship at all. Now the reason is that the ship sails far enough from you that it actually goes down the slope of the spherical earth. So it's kind of like if you watch an ant walk on an orange. So after a while it's going to disappear because the surface of the orange will block it from view. If you're looking at this side of the orange and the ant is crawling away from you, eventually it's going to be behind the orange and you're not going to see it anymore. Of course, if the Earth was flat, you would have instead seen the entire ship becoming smaller and smaller, but not disappearing, just like if the ant was walking on a flat table. So if the ant was walking on this table, as it moves away from you, it looks smaller and smaller and smaller, but it never actually disappears. Of course, this all depends on visibility, but if there's clear visibility, you would have seen the ship just become smaller and smaller, never disappearing. A related phenomenon is that you can see farther away the higher you go. On a clear day, you climb a mountain and see a city in the distance from the peak. of the mountain. Now you climb back down but you can't see the city anymore even if the terrain is completely flat. Okay, so there's no trees or hills or anything blocking your view but still you will not be able to see the same city that you were able to see from the top of the mountain. And the reason is that the curvature of the earth blocks your view. Again, Basically the same thing as with the ship. So if the earth was flat, you could have still seen the city from the ground if nothing else was blocking your view. Here's another more modern evidence. Between 1519 and 1522, the Magellan and Cano expedition performed the first circumnavigation of the world. They sailed in a complete circle around the world, sailing west and eventually ending up back where they started. Of course, at no point did they find an edge. I could say, well, maybe they just actually sailed in a circle, but since then, many other people have also circumnavigated the Earth, some by boat and some by plane. In particular, the first circumnavigation by plane was done in 1924, and it took 175 days. If the Earth was flat, then a plane going in one direction without turning, right? So you just start your plane, you point it in a direction, and you don't touch any of the controls, you just keep moving straight, then it would have fallen off the edge. Of course, that is impossible. What actually happens if you move in the same direction, in any direction, because the Earth is a sphere, you will just move in a complete circle around the Earth and get back to where you came from. The ancient Greek, Aristotelus, measured the circumference of the Earth around 240 BC. And here's how he did it. So he placed two sticks of the same length in two different Egyptian cities, Syene and Alexandria, separated by about 800 kilometers. Because the Earth is spherical, the two sticks had shadows of different lengths at the same time of day. Light rays from the Sun shine on the sticks at different angles because they're located at different points on the sphere. If the Earth was flat, then the rays from the Sun would have hit every point at the same angle, because if there is something flat, then of course you're always at the same angle to this flat surface, and the shadows would have been of the same length. In Seyen, the sun was at the zenith, so its rays made an angle of zero degrees with the ground. and no shadow was cast. In Alexandria, at the same time, the sun was slightly south of the zenith, and its rays made an angle of about 7.2 degrees with the ground. And of course that did make a shadow. Okay, so if you shine light, let's say you have a stick, you shine light directly above the stick, you're not going to get any shadow. But... If the stick is on a sphere and it's to the side, so there's an angle between the rays and the stick, then it will cast a shadow. Now there are 360 degrees in a circle, and 360 divided by 7.2 is 50. So the circumference of the Earth is 50 times the distance between the two cities. This result... was actually very close to the correct valley we know today, which is around 40,000 kilometers at the equator. Okay, so here's an illustration. Here's the Earth. Here is Egypt. So this is Alexandria and Seine. And there's a distance between them, which is measured as 5,000 stadia. By the way, no one is sure exactly how much one stadia is defined as, but we know the distance between these two cities is 800 kilometers. So now let's look at the Earth. So there are rays coming from the sun. The two rays are parallel. They're in the same direction. In this case, okay, this is the opposite of a stick. It's a well, but it's the same principle. So. the light ray shines directly into the well. So we know that the well is at exactly, it's exactly aligned with the ray. And that's because, like I said, the sun in this city, the sun was at the zenith. And remember, the zenith is the point directly above you. So the sun was directly above the well. The rays of light shone directly down. on the well and just went into the well. There were no shadows cast. Now, here there is Alexandria, 800 kilometers away, and we have a pole, and the ray of light is shining in the same angle from the sun. But now we are in a different place on the sphere, so the angle is now different, and that causes the pole to cast a shadow. So again, if I put this pole over here, there's not going to be any shadow, because the pole is going to be aligned with the ray of light. But since I moved the pole over here, the angle of the pole changed, because the angle of the surface changes as you move to different places on the sphere, and therefore, the same ray from the sun hits the pole at a different angle and causes the shadow. Now, you can calculate the angle from the pole to the shadow, and you can find it's about 7 degrees, or 7.2 degrees. And now, if you use just some simple math, you'll find out that this is also the angle of the sun from the pole. So what we discovered is that Like I said before, this is 1 over 50 of a circle, and we have here 800 kilometers in order to move 1 over 50 of a circle. So all we need to do to find the entire circumference is to take this 800 kilometers and just multiply it by 50. So we do that and we find 40,000 kilometers. I know there's a bit of math, but it's not really the math that's important. It's really just this idea that this experiment measured how much of the full circumference is between these two cities. And once you know that the distance between these two cities is 1 over 50 of the full circumference, then you can easily calculate the full circumference. So let's move on then to the geocentric model. Until the 17th century, almost everyone believed that the Earth is at the center of the universe and everything revolves around it. This is called the geocentric view. Well, geocentric, so geo means Earth. Centric means centered, so this is an earth-centered view. And it was popular for two reasons. One, even though the earth does move around the sun, as we know today, we don't feel that movement. So you stand here on the earth, you look up to the sky, you see the sun and all the planets and the moon move, but you don't feel yourself move. So the natural conclusion from this is that you just don't move, and therefore the earth must be stationary, and everything else must rotate around it. I'll explain in future lectures why it is that we actually don't feel the movement. The second reason, just as important, is that religions usually claim that humans and the Earth have a central role in the universe. And the geocentric view reinforces this claim. So if you believe that you are special, then you want to believe you are at the center of the universe. You don't want to believe you're just some planet around some star, around some galaxy that's just one of those trillions of galaxies. It took a lot of time. for astronomers to realize that the geocentric view is totally wrong. Now we know that the Sun is at the center of the solar system, and the Earth is just one of several planets revolving around it, and there's nothing really special about it. Except, of course, for the fact that it had the right conditions to develop life. This is called the heliocentric, or Sun-centered view. So helio means sun, centric means centered. So this is a view where the sun is at the center of the solar system. Today, we know that there's nothing special about the Sun and the solar system even. So it's not just that we're moving around the Sun. Even the Sun itself has no special status in the universe. There are trillions of other stars in the observable universe, and trillions of other solar systems. around those stars with trillions of other planets. And some of these planets may be homes to other life forms and even advanced alien civilizations, perhaps even more advanced than our civilization. So the point is that we are not the center of the universe. We are some form of life on some planet in some corner of the universe. But there may be many other planets with life on them and civilizations similar to ours. Or very different from ours, but in any case, civilizations. The Earth and humans turn out to be completely insignificant compared to the universe as a whole. Now, we already saw this. in the first week when we discussed scales in the universe. And we saw these really mind-boggling differences in scale between humans and even the entire Earth, or even the entire solar system, compared to the entire universe, which we saw was many, many orders of magnitude larger. So if a human is one meter, the universe... The observable universe is, as we saw, 10 to the 27 meters, which means it's 27 orders of magnitude larger than a human. The first known heliocentric model was presented by the ancient Greek astronomer Aristarchus of Samos, who lived between 310 and 230 BC. However, most Greek scholars actually rejected this idea. One of the arguments against the heliocentric model, of course, there were other arguments, for example, the two that I mentioned before. First of all, we don't feel the Earth moving, so it's hard to believe that it is actually moving and it's just sand that stays in place. And second of all, humans just... like to think that we are special. One of the other arguments against this model was that if the Earth moved around the Sun, the nearby stars would shift their positions in the sky relative to more distant stars. To see what that means, imagine driving along a road and looking out the window. As you move, objects closer to you, like trees that are right near the road, will appear to move. But objects far away from you, like mountains far away, will stay in the same place. This phenomenon is called parallax. The same thing happens as the Earth moves around the Sun. Over the course of a year, which is a full orbit around the Sun, more distant stars will stay in place, but closer stars will appear to move relative to those distant stars. So there's going to be a kind of a background of distant stars that doesn't move, and then closer stars will be moving across this background. So in this context, this phenomenon is called stellar parallax. Let me demonstrate. So here is the Sun. Here is the Earth's orbit. And we're looking at two different points A and B that are six months apart. Why six months? Because a full orbit is one year or 12 months, so n be separated by half an orbit, so that is six months. I start in point A and I look at the sky. Now here are some distant stars and here is the star that is closer away. As seen from A, I'm looking along this direction. So now I see this star and behind it the background. This is how it will look to me. So here is the background of stars, and here is my red star over here. Now, I wait six months until I am at the other side of the sun. So the Earth and me have completed half a circle around the sun. And now, when we look at the same star, we see it from a different angle. So then we also see the stars behind it from a different angle. And now it's going to look like this. So notice that it looks like the star has moved from this point below this white star to this point below this white star. Now I can calculate the angle called the parallax angle. And using this angle, I can actually, using some math that I'm not going to go into, calculate the distance to that star. And indeed that is one of the ways that we can measure the distance to stars. Okay, so let me show you a nice animation of this. Have you ever traveled down a road in a car and looked at the mountains or hills in the distance? If you have, you've probably noticed that while nearby trees quickly fly past the window, the mountains move much slower, and in the far distance, the moon and the stars don't seem to move at all. As you move, objects closer to you, such as the trees, seems to shift position relative to more distant objects, like the mountains. This effect is called parallax. The size of this shift depends on the distance you travel along the road. and how far away the trees are. The closer they are to the road, the bigger the shift. The same thing happens as the Earth moves around the Sun. Over the course of a year, some stars appear to move a very small amount relative to other stars. Like the trees along the side of the road, these stars are just closer than those that don't seem to move. Actually, all stars are moving through space, but much more slowly than parallax, so we don't notice. Now, if we measure how much a star moves when the Earth does one complete trip around the Sun, we can use this to work out this angle, called the parallax angle. If we observe a star when the Earth is at one spot in its orbit, and then wait six months for the Earth to move around the Sun to the opposite point along its orbit and observe the star again, we can measure the parallax angle. Since we already know the distance from the Earth to the Sun, We can now use this parallax angle and some trigonometry to work out exactly how far away the star is. This is really useful because it allows us to calculate the distance to nearby stars very accurately. This can then be used to check the distance measured by different methods to even more distant objects out in space. The problem... is that even though the ancient Greeks made efforts to observe stellar parallax, they couldn't detect any. They were doing science. There was a hypothesis. They were checking the predictions of this hypothesis, which one of them was stellar parallax, because they wanted to see if this hypothesis is good or not. If there's no stellar parallax, that can mean one of two things. Option one, the Earth doesn't revolve around the Sun. So the geocentric model that was accepted before is the correct model, and that explains the result perfectly, because if the Earth is not moving, we would not expect to see any stellar parallax. The stellar parallax as we saw depends on the movement of the earth around the sun because then we'll see the star in different places. at different points on the orbit. But it won't happen if the Earth is not moving. Option number two is that the stars are just so far away that the parallax angle is just too small to measure. Now, today we know that option two is the correct one. The stars are located many, many light years away. and the parallax angle does exist, it's just too small to measure, at least using the tools that the ancient Greeks had, but the ancient Greeks could calculate those distances and when they found out that the stars would have to be trillions of kilometers away, these just seemed like inconceivable distances. They couldn't really imagine distances like that actually existing. Now, stellar parallax does happen, but it can only be detected using extremely precise modern measurement devices. The first successful measurement of a parallax was only made a couple of millennia after the ancient Greeks. So in 1838, Friedrich Bessel measured the stellar parallax of a binary star called 61 Cygni, which you can see here. And he used this to estimate the distance of the star. So again, if you measure the parallax angle, you can use just simple high school trigonometry to estimate the distance of the star. And he estimated it at about 11.4 light-years. which is close to the actual distance. By the way, this star is a binary star, so as you can see, it's in fact a system of two stars that are also rotating around each other. So we'll learn more about that in the future. So now I want to talk about Ptolemy and his geocentric model. So in the second century, the ancient astronomer Ptolemy wrote a treatise called Almagest. This is the only surviving comprehensive writing on astronomy from ancient times. Ptolemy compiled much of the knowledge about astronomy that existed at the time, including his own work, but also the work of people who came before him. The book also introduced a geocentric model of the solar system. This model predicted the positions of the planets at any date and time. To develop this model, Ptolemy used his own observations. In addition to data collected by Hipparchus, who I talked about last time, this model remained in use for more than 1400 years. Meaning that 1400 years since Ptolemy's time, people still use this model. It was that successful. However, today we know that the apparent motion of each planet in the sky results from a combination of two motions. First of all, the motion of that planet around the Sun, and second, the motion of the Earth around the Sun. The planets always move along the Zodiac, so remember, we have the ecliptic, which is the path where the Sun moves, and it's also the plane where the Earth rotates around the Sun, and there's this narrow belt around the ecliptic in the sky. And that is where all the planets are. The Sun, the Moon and the planets. That's because, as I remind you, all the planets move along very very similar planes of rotation. Over a year, the Sun continuously drifts eastward relative to the constellations. So, Remember, the constellations are fixed in the sky, or at least we treat them as being fixed, even though they do change over thousands of years. So we measure something moving in the sky with respect to these constellations because the constellations don't move. Planets mostly move eastward. which is called prograde motion. But sometimes they seem to stop and go westward for a bit, which is called retrograde motion. Of course, things aren't actually rotating around the Earth. There is this complex rotation of all the planets around the Sun, and what we see... is a consequence of that complex rotation. So the planets don't actually move back in their orbits. Instead, retrograde motion happens whenever Earth catches up to the planet and moves past it. Because the Earth at that time is momentarily moving faster relative to the planet, It looks like the planet is moving backwards. Planets never actually move backwards. They keep rotating in the same direction forever and ever. They never just stop and go back in their orbit. But it looks like that to us, because we don't see the full picture. Now this is similar to what you see when you drive on a road. and you pass a slower car. So imagine that from your point of view, it looks like the other car is moving backwards, even though both of you are going forward. Okay, so you're both going in the same direction. Neither of you is stopping or moving back at any point. But if you move faster than this other car, as you're passing next to it, It looks to you like it is moving backwards with respect to you. So here is an illustration. I'm also going to show you a simulation in a bit. So here is the Sun. Here is the Earth's orbit. And here is the orbit of another planet. Let's say Mars. and they both move without stopping. But now, let's see how this looks like to someone that is on Earth. So here, we are on Earth at the point A, let's say in January, and we look... to the direction of this planet. Now here, these stars are the background stars. These stars are not moving. I mean, again, they are actually moving, they're just moving very, very slowly. So as far as we're concerned, they don't move. So we look in the direction of this planet, and right now we are seeing it at this position in the sky. because this is the direction where it is respect to us. Now we continue moving and now we are at point B and now the other planet is also at point B. Now we look in the direction of the planet. it's going to look to us like it is at this point in the sky. So again, this background of stars is always the same. When we look in this direction, we always see the same stars, no matter what time of the year. But we see this planet at a different point. But until now, it has moved in the same direction. Okay, so now we keep rotating around the Sun. Now we are at point C. We look out to the planet. And now it looks like the planet moved backwards in the sky. Of course, as you can see from the illustration, the planet actually kept moving forward. It didn't actually go back. But it looks to us, because we are now over here, then we see it as going back. If it were still here, we would see it as being at this point. So we would see it as if it kept going. forward. But since we are now here, we see it as if it went backwards. Now we are at point D, and this planet has also made some progress, so now it's at point D over here. We look from Earth to the direction of that planet, and now on the sky it is going to be here. So again it was moving, it looks like it was moving backwards. Now we are at point E, and the other planet is at this point. We look in the direction of the planet, and now we see it moving forward instead of backwards. So we would see the planet moving forwards in the sky most of the time, but at the time when we are basically overtaking this planet, we're passing next to it, it will look to us as if it is moving backwards in its path. So now I want to show you a simulation so you can see this in real time. So this program, which you can all access at this URL, simulates the motion of a planet in the Earth's sky compared to the Sun and the constellations. So here we can see Earth over here, and here we see another planet, and here we see the sky. So these are all the constellations of the zodiac. Remember, the planets always move along the zodiac. Here is the sun right now, and here is the other planet right now. Now here, this assumes that the observer planet is at one astronomical unit, which is the distance of the Earth from the Sun, and the other planet is assumed to be 2.4 astronomical units. We can actually choose any planet we want, for example Jupiter or Mars. Let's choose Mars, because usually, you know, when Mars is in retrograde, then interesting things happen, apparently. So let's play this and see what happens. Maybe I'll do it a bit slower. Okay, so here we see both planets just moving forward along their orbits. And we always see... You see this line? This line is between our planet and Mars. So this is the direction in which we look to see Mars. And now here is where Mars is in the sky. So right now it's moving to the east. But now let's wait until we pass next to Mars. right about now, and you see the planet moving backwards for a bit, and then it's back to moving forwards. Let's roast this again. So the planet throughout the year keeps moving to the east, in the same direction as the sun. However, eventually, when we pass next to that planet right now, it's actually moving a bit to the west. and then moving back to the east. So this is the phenomenon that is responsible for the retrograde motion of the planets, as we understand it today. Here's the problem. Today we know how this works, but our understanding is based on the sun being in the middle, because both the Earth and the other planets have to be moving in separate orbits. So explaining retrograde motion in Ptolemy's model required some assumptions. So, each planet orbits in a small circle called an epicycle. So here is the Earth, which is at the center in this model, and here is the other planet, let's say Mars, and it's not actually orbiting around this circle. It is orbiting around a smaller circle called an epicycle. And this epicycle is orbiting in a circle. The larger circle that the epicycle is orbiting along is called the deferent. Also, the Earth is not at the center of the deferent. It's a bit to the side. So this is the big circle. This is the center of the circle, but the Earth actually has to be a bit to the side. On the opposite side of the Earth, there is the equant, the point with respect to which the epicycles move at a constant speed. So let's see a simulation of this to understand how this model works. Right, so here we can see a simulation of the Ptolemaic system. And so here is this big circle and this small circle, the epicycle. And here is the earth that is kind of off-center. Right, so now it's kind of exaggerated now, but you can see clearly that there is a circle, a big circle, and there's this point at the center. And then the Earth is over here, not at the center. And now this other planet is rotating on this epicycle. Let's make it smaller. Yeah, so here, let's now start the animation and see. Okay, so you can see that there is kind of this weird motion for this other star. in space, it's not moving along a circular orbit, because it's moving along a circle that's moving around another circle. So it creates this weird shape. However, this weird shape actually can explain the retrograde motion. So if we assume that this is really how things work, which, to be clear, it's not, Then here is the Sun, here is the planet, and now we can look over here and we can see the Sun and the planet moving along the zodiac as before. And you can see, oh, here's the planet moving just momentarily back in its orbit. Maybe let me make this a bit slower. Okay, so here is The motion of the Sun, the Sun always moves east. Here is the other planet, let's say Mars. It is now moving east. But then, due to this weird motion, at some point it's going to stop and look for a second like it might be moving backwards. And now it will keep moving forwards. This is interesting because this is clearly not how the solar system actually works as we understand it today. However, you can still see from the simulation it does predict this retrograde motion. Today, we know that the Sun is at the center of the solar system, not the Earth. We also know... that the planets move in ellipses around the Sun, not in circles, and certainly not in epicycles. This is definitely something that doesn't happen. Therefore, the epicycle model has nothing to do with how the orbits of the planets actually work. But somehow it did manage to accurately predict the motion of the planets in the sky. including even the retrograde motion. So how is that possible? So using some advanced math, It can be proven that any shape can be approximated using enough epicycles. This includes ellipses. So the epicycles were able to approximate the elliptical orbits of these planets. So the point is essentially that if you add enough epicycles, you can really make the planets moving any shape you want. And what Ptolemy actually did is he was creating this mathematical approximation of the heliocentric model with the Sun at the center and with elliptic orbits. He just didn't realize it. He was using circles to approximate ellipses, and that is mathematically possible. He just didn't know what he was doing. But that is why it was so successful for more than a thousand years. Ptolemy's model is a great example of a model that gives correct predictions, but has no real explanatory power. A scientific model is only useful for explaining how things work, if it provides a simple mechanism that can explain complicated results. So Ptolemy described the complicated motion of the planets using a model that is just as complicated. He just basically moved the complexity around without providing a real explanation. In other words, there was this complicated motion in the sky with this retrograde motion, and all kinds of other different things happening. That's very complicated. So he made a model that is basically just as complicated to explain that complicated motion. That means that his model, it doesn't explain what's happening. It just kind of reproduces what's happening without giving any explanation. The modern heliocentric model with elliptic orbits plus the laws of gravity that we'll learn about soon is a very simple model with only a few simple rules. And yet it can predict the complicated motion of the planets very accurately. And this makes the heliocentric model much more useful in providing a true explanation for the motion of the planets. In other words, in this model there's only a few simple assumptions. Planets move in elliptical orbits and there's gravity, and gravity also works in a very simple way as you'll see soon. So these two simple assumptions essentially explain all this complicated movement. So we're getting more than we put in. That's what we want from a scientific theory. So the geocentric model, you put in complex and you get complex. But in the heliocentric model, you put something simple and that simple thing explains the complex thing. So the simple rules are complex. Explain the complex movement of the planets that you see in the sky. Occam's Razor is a very important scientific principle. What it says is that simple theories should be preferred over complex ones. The reason is not that simpler theories are easier to understand. That's actually a common misconception. There's no reason to expect that the laws of nature are simple enough that humans can understand them. Maybe the laws of nature are extremely complicated, maybe we'll never fully understand them. So that's not why we prefer simple theories. The reason we prefer simple theories is that the simpler the theory is, the more predictive value it has. We want a scientific theory to generate plenty of output based on as little input as possible. The modern heliocentric model gives you a lot of output for just a bit of input. But Ptolemy's geocentric model requires as much input as it gives output. And by that I mean that you have to look at the motion of the planets in the sky and use that to decide where exactly all the epicycles are and how many there are and what is the radius of each epicycle and so on. You're basically just converting one form of data to a different form of data. So although you can use this to predict the motions of the planets, you cannot use this geocentric model to explain the motion of the planets. It's just kind of a different way to write the data about the motion of the planets. Okay, so in this lecture... We saw concrete examples of how science works and how the scientific method allows us to tell truth from fiction. We've seen that geocentrism and flat Earth are two hypotheses that were accepted by ancient people, but discarded once we learned how to use science to study the universe. Despite all the very conclusive evidence against these hypotheses, some people still believe in one or both of them, even today. Like many other anti-scientific beliefs, the main motivation for modern geocentric or flat earth beliefs is a literal interpretation of religious scriptures. These scriptures, of course, were written in ancient times, so they reflect the way humans thought the universe worked. Back then, when they were written, that was before modern math, science and astronomy were developed. So today we know that religious scriptures are not a reliable source of knowledge. In fact, almost everything written in them turned out to be incorrect upon further investigation. Another major reason for belief in flat Earth specifically is conspiracy theories which spread misinformation. And most of this happens online, for example via YouTube videos. In these videos, conspiracy theorists claim that the Earth is actually flat. This fact is being hidden from the public. in an elaborate conspiracy, and every one of the millions of scientists around the world is somehow able to keep this huge secret. They never explain why hiding this information would benefit any scientist. Now, believers in geocentrism or flat Earth are relatively few, but there are other beliefs which are just as irrational. and yet are believed by millions or even billions of people around the world. One of these is astrology, and it will be the focus of my next lecture. In conclusion, in this lecture we'll learn about some important concepts in ancient astronomy such as axial precession and parallax which are still used today. We also learned about some ancient ideas that are no longer used, because modern theories match our observations much better. For reading, you can read section 2.2 of the textbook, and I will post practice questions about this lecture on TIMSS.

Remember in the first lecture I mentioned that this is basically the most important thing about science is when you find out something is wrong you replace it with something else. So learning about astronomy is also a great opportunity to learn about the scientific method and critical thinking and skepticism. All of these tools and skills are extremely important for understanding how the universe really works. You can't understand how the universe works if you're not willing to replace wrong ideas with correct ideas.

You can also use these tools in your daily life to tell the difference between what's true and what's not. You'd be surprised how few people actually do this in their daily lives. And of course we can see examples all around us with the anti-vaxxers and the flat earthers and all of those different groups of people that just don't understand science. Today, when we look at the sky, we have a very good understanding of what we see.

So we understand the physical laws that govern the movement of the celestial objects, and we also have plenty of details about these objects. Distance, size, composition, how they evolve in time. and so on.

We also have today telescopes and other tools to measure properties that cannot be seen with the naked eye. Modern humans evolved around 300 000 years ago And of course that's hard to define exactly, but let's say 300,000 years, and recorded history began around 5,000 years ago. But we learned essentially everything we know about the universe only in the last few hundred years.

This is really amazing, I think, because humans have existed for so long. 300,000 years we've been able to see the stars and 5,000 years ago we started being able to write about the stars, collect data, perform mathematical calculations, but we only actually started to understand the universe in the last few hundred years. I would say since the 17th century.

In fact, there are some very important things we only learned in the last century, or even in the last decade. So we used to think that the Milky Way was the entire universe. But in 1923, we discovered that there are other galaxies And the Milky Way is actually just a tiny speck of dust compared to the entire universe. I mean, it's just so hard to fathom, you know, living in that time and thinking that what you see around you, all these stars in the sky, that's all there is, that's the entire universe, only to discover that there are actually hundreds of billions of other galaxies, each of which also has this huge collection of its own stars, and there are these vast unimaginable distances between these galaxies.

Black holes were theorized more than 100 years ago, but only very recently, in 2019, we were able to obtain the first actual image of a black hole. Until that point, black holes were essentially just a hypothesis. Remember, a hypothesis is a theory that hasn't been proven yet. I think no one really thought black holes don't exist before 2019, because we had a lot of indirect evidence for them, and also because they basically flow immediately from the theory of general relativity, which is the one that we use to describe gravity, but Only in 2019 we were able to get direct evidence that black holes existed. That being said, let's talk about ancient astronomy.

So in prehistoric times, for countless years, I mean we're talking about hundreds of thousands of years, Humans had no idea what the true nature of the celestial bodies was. Prehistoric people identified celestial objects with gods, as they did with everything else they didn't understand. The first astronomers were actually priests of ancient religions tens of thousands of years ago. They also believed that the celestial objects influenced their lives. This is the origin of astrology, of course.

So astronomy remained closely tied to religion and astrology for thousands of years in essentially every single ancient culture we know of all around the world. If we think about what is the biggest thing that we don't understand unless we have the scientific method and math and everything, It is space, what's going on in the sky. So it makes a lot of sense that all these different cultures independently developed religion and astrology in relation to what they saw in the sky.

It's just so hard to explain if you don't have the right tools and the right technology to do it. Because you need the right tools and the right technology to do it, it took a long time before humans finally understood that the celestial objects are governed by mundane natural laws, just like things down here on Earth. So now we know that you can predict where each celestial body is going to be at any point in time using very simple equations.

but this was not obvious in prehistoric times where we didn't understand gravity yet. Now proper astronomy involves collecting and analyzing data, therefore it cannot exist without writing and mathematics which were only invented about 5000 years ago. Around that time Ancient civilizations such as the Babylonians and the Egyptians, which we're going to talk about a lot more, noticed that astronomical phenomena are periodic and could be used to keep track of time.

So they developed calendars that could be used to predict the change of seasons, which was very helpful for agriculture, for example, to know when to plant and when to harvest. This was, in fact, one of the main catalysts for developing advanced mathematics in the ancient world. Babylonian astronomers measured and recorded the positions of the Moon and the planets for hundreds of years.

By around 400 BC, they compiled enough data to be able to find regular patterns. Using these patterns, they could predict not only where the celestial bodies will be at any time, but even when lunar eclipses will happen. However, they couldn't yet predict solar eclipses that came a bit later.

Ancient Chinese astronomers also recorded astronomical data, and the oldest written record of a solar eclipse is from around 2000 BC from China. So this was 4,000 years ago. The Chinese astronomical catalogs span 3,000 years and list thousands of eclipses, comets, meteors, exploding stars, and even dark spots of the Sun, which we'll learn about later. The historical data is still being used by modern astronomers even today.

So if you want to know certain things about what's happening today, you may need to actually look at data from thousands of years ago to see how things have changed since then. So this is very important even for modern research. So now I want to talk about an important concept called axial precession. The ancient Greek astronomer Hipparchus built an observatory on the Greek island of Rhodes around 150 BC. He used it to measure the accurate positions of objects in the sky and he composed a star catalog with around 850 entries with celestial coordinates for each star specifying its positions in the sky.

So these coordinates are kind of like the latitude and longitude we learned about last time, except instead of being on the earth they are on the sky. Hipparchus divided the stars into apparent magnitudes according to their apparent brightness. The brighter the star, as it appears to us, the smaller the magnitude. The stars of the first magnitude are the brightest, and then as you go to higher magnitudes, the stars become less bright.

Today, we still use the term magnitude to describe the brightness of stars, but the modern definition is much more precise. So now it's important to understand that the apparent brightness of a star, meaning as it looks to us when we look in the sky, isn't the same as its actual brightness, which we call luminosity. Two stars of the same luminosity, but at different distances from us, will have different apparent magnitudes.

So, of course, the farther away a star is, the less bright it will look, because light gets dimmer as it expands towards us. Light expands in a sphere away from the star. There's always the same amount of light, but the surface area of the sphere keeps growing.

So that means that the farther away you are, the less light you eventually get, because you get... just a smaller part of the overall sphere of light. By comparing the data that Hipparchus collected with data from older observations, he discovered that the position of the north celestial pole changes over time. Let me remind you, the north celestial pole is the point around which the sky appears to rotate. So if you look at the sky, that point will be a point where nothing rotates and everything will rotate around that point.

This phenomenon, that the position of the north celestial pole changes over time, is called axial precession. And here is an illustration. You can imagine that the earth is like a spinning top. and I'll show you a video in a second, and there are two types of rotation.

Those first of all spin around the axis. So this is the axis here. You can imagine that it continues through the planet and the planet rotates around that axis just like a spinning top.

But also there is the rotation of the axis itself or of where the axis is pointing. And this is called precession. Now the spin around the axis is fast, so it's in fact a full rotation every day by definition, but the precession of the axis is much slower.

So in this video you can see a spinning top, and you can see, if you look carefully you'll see, it is indeed rotating very very fast around its axis. And also you can clearly see the axis itself is slowly moving around. So there are two different and independent rotations here. The rotation of the spinning top around the axis, and the rotation of the axis around some imaginary circle.

The earth is not a perfect sphere. It actually has a bit of a bulge around the equator. However, the gravitational pull of the Sun and the Moon on this bulge is what causes the axis to precess. It takes the Earth's axis around 25,700 years to complete the full circle.

The north and south celestial poles change due to the precession. Today, the north celestial pole is, as we learned last time, near the star Polaris, which is why we call that star the north star. But around 14,000 years ago, the star Vega was the north star.

and it will become the North Star again in around 11,700 years. So you can see here again this analogy to a spinning top. So here is the Earth, and here is the circle of this axial precession.

So the axis now points towards Polaris. but it will slowly, over thousands of years, rotate until it's actually going to point towards Vega. So in 11,000 years, Vega is going to be the North Star, not Polaris. But then the axis is going to keep rotating and eventually reach Polaris again, after 25,000 years or so. So now let's talk about the spherical earth.

So like I said, the earth is a sphere, almost a perfect sphere. But many ancient cultures initially believed that the earth was flat, shaped as a plane or a disc. Of course, if you stand in an open field and you look around you, everything seems flat, right? You don't see anything curve away from you if you just look around you. So it definitely looks like the Earth is flat.

But it's actually not hard to prove that it actually is spherical. In fact, it's so easy that the ancient Greeks already knew the Earth was spherical as early as 2500 years ago. in the time of Pythagoras. Many of the proofs that the Earth is spherical were collected by the Greek philosopher Aristotle around 330 BC.

And by that time, every Greek scholar accepted the spherical Earth as a fact, and this knowledge gradually spread to the rest of the world. So let's first review some of the evidence, including even some experiments you can do on your own if you're not fully convinced. By doing this, we'll learn a bit about how science works.

Some of the following evidence was already known to the ancient Greeks, but some of it is more modern. So let's start with lunar eclipses. A lunar eclipse happens when the moon moves into the Earth's shadow.

Here is the Sun and here is the Earth. The light from the sun shines in this direction, and here is the moon, and you can see that now the moon is in the shadow of the earth. Now what is a shadow? A shadow is where an object like the earth blocks light.

Light gets to all these points, but here the earth is in the way, so the light just stops here, it doesn't continue, this causes a shadow. And this is what we call a lunar eclipse. You can actually look at the shape of the shadow of the Earth as seen on the Moon.

The shadow of the Earth... moving on the Moon is always round. And here also from another direction. The only kind of object that always produces a round shadow is a sphere. Let me describe to you an experiment that you can do yourself at home to see what I mean.

So take objects of different shapes and rotate them in front of a lamp or a flashlight. Now if you do this with a disc-shaped object such as a plate, you will notice that the shadow it creates can be flat, round, or anything in between, depending on its orientation. So certainly the shadow will be round if you shine straight into the plate, but if the plate is on the side, the shadow will just be a line, not a disc.

If you do this with a spherical object, such as a ball, you will see the shadow is always round, no matter the orientation. Therefore, the Earth must be a sphere, because if it wasn't a sphere, then we would have seen different shapes during lunar eclipses depending on the relative positions of the Sun and the Earth. We would sometimes see a round shadow, sometimes see a line shadow, and everything in between.

Another evidence, travelers who travel a significant distance to the south, see new stars that were not visible from the north. They also see the height of the north star in the sky decrease as they go further south. The reason for that is that the earth is a sphere, and therefore we see different portions of the sky from different points on the sphere.

If the earth was flat, then everyone would have seen the same stars, right? So on a flat Earth, everyone stands at the same level, and when you look up, everyone sees the same thing. On a round planet, people who stand on different places on this sphere see a completely different sky. Now, these two proofs were already known to the ancient Greeks, but...

they are indirect proofs. Modern technology, that of course did not exist at the time of the Greeks, allows us to provide direct proof that the Earth is a sphere. So there are plenty of photos of the Earth taken by satellites and by astronauts. Since photos taken from different directions always show that the Earth is round, its shape must be spherical.

Again, it's the exact same reason that the shadows are all surround if the earth is a sphere. However, in this case, we're not talking about indirect evidence just from looking at the shape of the shadows. We can actually see the shape of the earth itself from images.

So now let me demonstrate that using NASA's EPIC Earth Polychromatic Imaging Camera, which takes images of the Earth from space from different angles every day. You can see some information over here, like the distance to Earth, the distance to the Sun, the distance from the Sun to the Earth and so on. And you can choose here different angles from which to see the Earth.

Now you see different images of the Earth from different angles around it and of course each image shows different continents like here's South America, here's Australia, And here's Africa. So, of course, taking all these images would not have been possible if the Earth was flat, because then all of these continents, South America and Australia and Africa, would all be in the same direction away from the camera. Now here's... Another kind of experiment you could do on your own You can go to the nearest ocean and you can watch a ship sail into the horizon And you'll see the ship disappear gradually First the bottom part and then the middle and then the top Here is the full ship and then it sails away from us into the horizon And here we only see the ship from the middle and up.

And if it continues, we will only see these antennas, I guess if visibility is good enough, and eventually we won't see the ship at all. Now the reason is that the ship sails far enough from you that it actually goes down the slope of the spherical earth. So it's kind of like if you watch an ant walk on an orange.

So after a while it's going to disappear because the surface of the orange will block it from view. If you're looking at this side of the orange and the ant is crawling away from you, eventually it's going to be behind the orange and you're not going to see it anymore. Of course, if the Earth was flat, you would have instead seen the entire ship becoming smaller and smaller, but not disappearing, just like if the ant was walking on a flat table. So if the ant was walking on this table, as it moves away from you, it looks smaller and smaller and smaller, but it never actually disappears.

Of course, this all depends on visibility, but if there's clear visibility, you would have seen the ship just become smaller and smaller, never disappearing. A related phenomenon is that you can see farther away the higher you go. On a clear day, you climb a mountain and see a city in the distance from the peak.

of the mountain. Now you climb back down but you can't see the city anymore even if the terrain is completely flat. Okay, so there's no trees or hills or anything blocking your view but still you will not be able to see the same city that you were able to see from the top of the mountain.

And the reason is that the curvature of the earth blocks your view. Again, Basically the same thing as with the ship. So if the earth was flat, you could have still seen the city from the ground if nothing else was blocking your view. Here's another more modern evidence. Between 1519 and 1522, the Magellan and Cano expedition performed the first circumnavigation of the world.

They sailed in a complete circle around the world, sailing west and eventually ending up back where they started. Of course, at no point did they find an edge. I could say, well, maybe they just actually sailed in a circle, but since then, many other people have also circumnavigated the Earth, some by boat and some by plane.

In particular, the first circumnavigation by plane was done in 1924, and it took 175 days. If the Earth was flat, then a plane going in one direction without turning, right? So you just start your plane, you point it in a direction, and you don't touch any of the controls, you just keep moving straight, then it would have fallen off the edge.

Of course, that is impossible. What actually happens if you move in the same direction, in any direction, because the Earth is a sphere, you will just move in a complete circle around the Earth and get back to where you came from. The ancient Greek, Aristotelus, measured the circumference of the Earth around 240 BC. And here's how he did it.

So he placed two sticks of the same length in two different Egyptian cities, Syene and Alexandria, separated by about 800 kilometers. Because the Earth is spherical, the two sticks had shadows of different lengths at the same time of day. Light rays from the Sun shine on the sticks at different angles because they're located at different points on the sphere. If the Earth was flat, then the rays from the Sun would have hit every point at the same angle, because if there is something flat, then of course you're always at the same angle to this flat surface, and the shadows would have been of the same length.

In Seyen, the sun was at the zenith, so its rays made an angle of zero degrees with the ground. and no shadow was cast. In Alexandria, at the same time, the sun was slightly south of the zenith, and its rays made an angle of about 7.2 degrees with the ground. And of course that did make a shadow.

Okay, so if you shine light, let's say you have a stick, you shine light directly above the stick, you're not going to get any shadow. But... If the stick is on a sphere and it's to the side, so there's an angle between the rays and the stick, then it will cast a shadow. Now there are 360 degrees in a circle, and 360 divided by 7.2 is 50. So the circumference of the Earth is 50 times the distance between the two cities. This result...

was actually very close to the correct valley we know today, which is around 40,000 kilometers at the equator. Okay, so here's an illustration. Here's the Earth.

Here is Egypt. So this is Alexandria and Seine. And there's a distance between them, which is measured as 5,000 stadia.

By the way, no one is sure exactly how much one stadia is defined as, but we know the distance between these two cities is 800 kilometers. So now let's look at the Earth. So there are rays coming from the sun. The two rays are parallel. They're in the same direction.

In this case, okay, this is the opposite of a stick. It's a well, but it's the same principle. So. the light ray shines directly into the well.

So we know that the well is at exactly, it's exactly aligned with the ray. And that's because, like I said, the sun in this city, the sun was at the zenith. And remember, the zenith is the point directly above you. So the sun was directly above the well. The rays of light shone directly down.

on the well and just went into the well. There were no shadows cast. Now, here there is Alexandria, 800 kilometers away, and we have a pole, and the ray of light is shining in the same angle from the sun.

But now we are in a different place on the sphere, so the angle is now different, and that causes the pole to cast a shadow. So again, if I put this pole over here, there's not going to be any shadow, because the pole is going to be aligned with the ray of light. But since I moved the pole over here, the angle of the pole changed, because the angle of the surface changes as you move to different places on the sphere, and therefore, the same ray from the sun hits the pole at a different angle and causes the shadow.

Now, you can calculate the angle from the pole to the shadow, and you can find it's about 7 degrees, or 7.2 degrees. And now, if you use just some simple math, you'll find out that this is also the angle of the sun from the pole. So what we discovered is that Like I said before, this is 1 over 50 of a circle, and we have here 800 kilometers in order to move 1 over 50 of a circle.

So all we need to do to find the entire circumference is to take this 800 kilometers and just multiply it by 50. So we do that and we find 40,000 kilometers. I know there's a bit of math, but it's not really the math that's important. It's really just this idea that this experiment measured how much of the full circumference is between these two cities.

And once you know that the distance between these two cities is 1 over 50 of the full circumference, then you can easily calculate the full circumference. So let's move on then to the geocentric model. Until the 17th century, almost everyone believed that the Earth is at the center of the universe and everything revolves around it. This is called the geocentric view. Well, geocentric, so geo means Earth.

Centric means centered, so this is an earth-centered view. And it was popular for two reasons. One, even though the earth does move around the sun, as we know today, we don't feel that movement. So you stand here on the earth, you look up to the sky, you see the sun and all the planets and the moon move, but you don't feel yourself move. So the natural conclusion from this is that you just don't move, and therefore the earth must be stationary, and everything else must rotate around it.

I'll explain in future lectures why it is that we actually don't feel the movement. The second reason, just as important, is that religions usually claim that humans and the Earth have a central role in the universe. And the geocentric view reinforces this claim.

So if you believe that you are special, then you want to believe you are at the center of the universe. You don't want to believe you're just some planet around some star, around some galaxy that's just one of those trillions of galaxies. It took a lot of time.

for astronomers to realize that the geocentric view is totally wrong. Now we know that the Sun is at the center of the solar system, and the Earth is just one of several planets revolving around it, and there's nothing really special about it. Except, of course, for the fact that it had the right conditions to develop life.

This is called the heliocentric, or Sun-centered view. So helio means sun, centric means centered. So this is a view where the sun is at the center of the solar system.

Today, we know that there's nothing special about the Sun and the solar system even. So it's not just that we're moving around the Sun. Even the Sun itself has no special status in the universe.

There are trillions of other stars in the observable universe, and trillions of other solar systems. around those stars with trillions of other planets. And some of these planets may be homes to other life forms and even advanced alien civilizations, perhaps even more advanced than our civilization. So the point is that we are not the center of the universe.

We are some form of life on some planet in some corner of the universe. But there may be many other planets with life on them and civilizations similar to ours. Or very different from ours, but in any case, civilizations. The Earth and humans turn out to be completely insignificant compared to the universe as a whole.

Now, we already saw this. in the first week when we discussed scales in the universe. And we saw these really mind-boggling differences in scale between humans and even the entire Earth, or even the entire solar system, compared to the entire universe, which we saw was many, many orders of magnitude larger. So if a human is one meter, the universe... The observable universe is, as we saw, 10 to the 27 meters, which means it's 27 orders of magnitude larger than a human.

The first known heliocentric model was presented by the ancient Greek astronomer Aristarchus of Samos, who lived between 310 and 230 BC. However, most Greek scholars actually rejected this idea. One of the arguments against the heliocentric model, of course, there were other arguments, for example, the two that I mentioned before. First of all, we don't feel the Earth moving, so it's hard to believe that it is actually moving and it's just sand that stays in place. And second of all, humans just...

like to think that we are special. One of the other arguments against this model was that if the Earth moved around the Sun, the nearby stars would shift their positions in the sky relative to more distant stars. To see what that means, imagine driving along a road and looking out the window.

As you move, objects closer to you, like trees that are right near the road, will appear to move. But objects far away from you, like mountains far away, will stay in the same place. This phenomenon is called parallax.

The same thing happens as the Earth moves around the Sun. Over the course of a year, which is a full orbit around the Sun, more distant stars will stay in place, but closer stars will appear to move relative to those distant stars. So there's going to be a kind of a background of distant stars that doesn't move, and then closer stars will be moving across this background.

So in this context, this phenomenon is called stellar parallax. Let me demonstrate. So here is the Sun.

Here is the Earth's orbit. And we're looking at two different points A and B that are six months apart. Why six months? Because a full orbit is one year or 12 months, so n be separated by half an orbit, so that is six months. I start in point A and I look at the sky.

Now here are some distant stars and here is the star that is closer away. As seen from A, I'm looking along this direction. So now I see this star and behind it the background. This is how it will look to me.

So here is the background of stars, and here is my red star over here. Now, I wait six months until I am at the other side of the sun. So the Earth and me have completed half a circle around the sun.

And now, when we look at the same star, we see it from a different angle. So then we also see the stars behind it from a different angle. And now it's going to look like this. So notice that it looks like the star has moved from this point below this white star to this point below this white star. Now I can calculate the angle called the parallax angle.

And using this angle, I can actually, using some math that I'm not going to go into, calculate the distance to that star. And indeed that is one of the ways that we can measure the distance to stars. Okay, so let me show you a nice animation of this. Have you ever traveled down a road in a car and looked at the mountains or hills in the distance? If you have, you've probably noticed that while nearby trees quickly fly past the window, the mountains move much slower, and in the far distance, the moon and the stars don't seem to move at all.

As you move, objects closer to you, such as the trees, seems to shift position relative to more distant objects, like the mountains. This effect is called parallax. The size of this shift depends on the distance you travel along the road.

and how far away the trees are. The closer they are to the road, the bigger the shift. The same thing happens as the Earth moves around the Sun.

Over the course of a year, some stars appear to move a very small amount relative to other stars. Like the trees along the side of the road, these stars are just closer than those that don't seem to move. Actually, all stars are moving through space, but much more slowly than parallax, so we don't notice. Now, if we measure how much a star moves when the Earth does one complete trip around the Sun, we can use this to work out this angle, called the parallax angle. If we observe a star when the Earth is at one spot in its orbit, and then wait six months for the Earth to move around the Sun to the opposite point along its orbit and observe the star again, we can measure the parallax angle.

Since we already know the distance from the Earth to the Sun, We can now use this parallax angle and some trigonometry to work out exactly how far away the star is. This is really useful because it allows us to calculate the distance to nearby stars very accurately. This can then be used to check the distance measured by different methods to even more distant objects out in space.

The problem... is that even though the ancient Greeks made efforts to observe stellar parallax, they couldn't detect any. They were doing science.

There was a hypothesis. They were checking the predictions of this hypothesis, which one of them was stellar parallax, because they wanted to see if this hypothesis is good or not. If there's no stellar parallax, that can mean one of two things.

Option one, the Earth doesn't revolve around the Sun. So the geocentric model that was accepted before is the correct model, and that explains the result perfectly, because if the Earth is not moving, we would not expect to see any stellar parallax. The stellar parallax as we saw depends on the movement of the earth around the sun because then we'll see the star in different places. at different points on the orbit. But it won't happen if the Earth is not moving.

Option number two is that the stars are just so far away that the parallax angle is just too small to measure. Now, today we know that option two is the correct one. The stars are located many, many light years away. and the parallax angle does exist, it's just too small to measure, at least using the tools that the ancient Greeks had, but the ancient Greeks could calculate those distances and when they found out that the stars would have to be trillions of kilometers away, these just seemed like inconceivable distances.

They couldn't really imagine distances like that actually existing. Now, stellar parallax does happen, but it can only be detected using extremely precise modern measurement devices. The first successful measurement of a parallax was only made a couple of millennia after the ancient Greeks.

So in 1838, Friedrich Bessel measured the stellar parallax of a binary star called 61 Cygni, which you can see here. And he used this to estimate the distance of the star. So again, if you measure the parallax angle, you can use just simple high school trigonometry to estimate the distance of the star.

And he estimated it at about 11.4 light-years. which is close to the actual distance. By the way, this star is a binary star, so as you can see, it's in fact a system of two stars that are also rotating around each other.

So we'll learn more about that in the future. So now I want to talk about Ptolemy and his geocentric model. So in the second century, the ancient astronomer Ptolemy wrote a treatise called Almagest.

This is the only surviving comprehensive writing on astronomy from ancient times. Ptolemy compiled much of the knowledge about astronomy that existed at the time, including his own work, but also the work of people who came before him. The book also introduced a geocentric model of the solar system.

This model predicted the positions of the planets at any date and time. To develop this model, Ptolemy used his own observations. In addition to data collected by Hipparchus, who I talked about last time, this model remained in use for more than 1400 years.

Meaning that 1400 years since Ptolemy's time, people still use this model. It was that successful. However, today we know that the apparent motion of each planet in the sky results from a combination of two motions.

First of all, the motion of that planet around the Sun, and second, the motion of the Earth around the Sun. The planets always move along the Zodiac, so remember, we have the ecliptic, which is the path where the Sun moves, and it's also the plane where the Earth rotates around the Sun, and there's this narrow belt around the ecliptic in the sky. And that is where all the planets are.

The Sun, the Moon and the planets. That's because, as I remind you, all the planets move along very very similar planes of rotation. Over a year, the Sun continuously drifts eastward relative to the constellations.

So, Remember, the constellations are fixed in the sky, or at least we treat them as being fixed, even though they do change over thousands of years. So we measure something moving in the sky with respect to these constellations because the constellations don't move. Planets mostly move eastward. which is called prograde motion.

But sometimes they seem to stop and go westward for a bit, which is called retrograde motion. Of course, things aren't actually rotating around the Earth. There is this complex rotation of all the planets around the Sun, and what we see...

is a consequence of that complex rotation. So the planets don't actually move back in their orbits. Instead, retrograde motion happens whenever Earth catches up to the planet and moves past it. Because the Earth at that time is momentarily moving faster relative to the planet, It looks like the planet is moving backwards.

Planets never actually move backwards. They keep rotating in the same direction forever and ever. They never just stop and go back in their orbit. But it looks like that to us, because we don't see the full picture.

Now this is similar to what you see when you drive on a road. and you pass a slower car. So imagine that from your point of view, it looks like the other car is moving backwards, even though both of you are going forward.

Okay, so you're both going in the same direction. Neither of you is stopping or moving back at any point. But if you move faster than this other car, as you're passing next to it, It looks to you like it is moving backwards with respect to you.

So here is an illustration. I'm also going to show you a simulation in a bit. So here is the Sun.

Here is the Earth's orbit. And here is the orbit of another planet. Let's say Mars. and they both move without stopping. But now, let's see how this looks like to someone that is on Earth.

So here, we are on Earth at the point A, let's say in January, and we look... to the direction of this planet. Now here, these stars are the background stars.

These stars are not moving. I mean, again, they are actually moving, they're just moving very, very slowly. So as far as we're concerned, they don't move. So we look in the direction of this planet, and right now we are seeing it at this position in the sky.

because this is the direction where it is respect to us. Now we continue moving and now we are at point B and now the other planet is also at point B. Now we look in the direction of the planet.

it's going to look to us like it is at this point in the sky. So again, this background of stars is always the same. When we look in this direction, we always see the same stars, no matter what time of the year.

But we see this planet at a different point. But until now, it has moved in the same direction. Okay, so now we keep rotating around the Sun. Now we are at point C. We look out to the planet.

And now it looks like the planet moved backwards in the sky. Of course, as you can see from the illustration, the planet actually kept moving forward. It didn't actually go back. But it looks to us, because we are now over here, then we see it as going back.

If it were still here, we would see it as being at this point. So we would see it as if it kept going. forward. But since we are now here, we see it as if it went backwards.

Now we are at point D, and this planet has also made some progress, so now it's at point D over here. We look from Earth to the direction of that planet, and now on the sky it is going to be here. So again it was moving, it looks like it was moving backwards.

Now we are at point E, and the other planet is at this point. We look in the direction of the planet, and now we see it moving forward instead of backwards. So we would see the planet moving forwards in the sky most of the time, but at the time when we are basically overtaking this planet, we're passing next to it, it will look to us as if it is moving backwards in its path.

So now I want to show you a simulation so you can see this in real time. So this program, which you can all access at this URL, simulates the motion of a planet in the Earth's sky compared to the Sun and the constellations. So here we can see Earth over here, and here we see another planet, and here we see the sky. So these are all the constellations of the zodiac. Remember, the planets always move along the zodiac.

Here is the sun right now, and here is the other planet right now. Now here, this assumes that the observer planet is at one astronomical unit, which is the distance of the Earth from the Sun, and the other planet is assumed to be 2.4 astronomical units. We can actually choose any planet we want, for example Jupiter or Mars. Let's choose Mars, because usually, you know, when Mars is in retrograde, then interesting things happen, apparently. So let's play this and see what happens.

Maybe I'll do it a bit slower. Okay, so here we see both planets just moving forward along their orbits. And we always see... You see this line? This line is between our planet and Mars.

So this is the direction in which we look to see Mars. And now here is where Mars is in the sky. So right now it's moving to the east. But now let's wait until we pass next to Mars. right about now, and you see the planet moving backwards for a bit, and then it's back to moving forwards.

Let's roast this again. So the planet throughout the year keeps moving to the east, in the same direction as the sun. However, eventually, when we pass next to that planet right now, it's actually moving a bit to the west. and then moving back to the east. So this is the phenomenon that is responsible for the retrograde motion of the planets, as we understand it today.

Here's the problem. Today we know how this works, but our understanding is based on the sun being in the middle, because both the Earth and the other planets have to be moving in separate orbits. So explaining retrograde motion in Ptolemy's model required some assumptions. So, each planet orbits in a small circle called an epicycle.

So here is the Earth, which is at the center in this model, and here is the other planet, let's say Mars, and it's not actually orbiting around this circle. It is orbiting around a smaller circle called an epicycle. And this epicycle is orbiting in a circle.

The larger circle that the epicycle is orbiting along is called the deferent. Also, the Earth is not at the center of the deferent. It's a bit to the side. So this is the big circle.

This is the center of the circle, but the Earth actually has to be a bit to the side. On the opposite side of the Earth, there is the equant, the point with respect to which the epicycles move at a constant speed. So let's see a simulation of this to understand how this model works. Right, so here we can see a simulation of the Ptolemaic system. And so here is this big circle and this small circle, the epicycle.

And here is the earth that is kind of off-center. Right, so now it's kind of exaggerated now, but you can see clearly that there is a circle, a big circle, and there's this point at the center. And then the Earth is over here, not at the center.

And now this other planet is rotating on this epicycle. Let's make it smaller. Yeah, so here, let's now start the animation and see.

Okay, so you can see that there is kind of this weird motion for this other star. in space, it's not moving along a circular orbit, because it's moving along a circle that's moving around another circle. So it creates this weird shape. However, this weird shape actually can explain the retrograde motion. So if we assume that this is really how things work, which, to be clear, it's not, Then here is the Sun, here is the planet, and now we can look over here and we can see the Sun and the planet moving along the zodiac as before.

And you can see, oh, here's the planet moving just momentarily back in its orbit. Maybe let me make this a bit slower. Okay, so here is The motion of the Sun, the Sun always moves east. Here is the other planet, let's say Mars.

It is now moving east. But then, due to this weird motion, at some point it's going to stop and look for a second like it might be moving backwards. And now it will keep moving forwards.

This is interesting because this is clearly not how the solar system actually works as we understand it today. However, you can still see from the simulation it does predict this retrograde motion. Today, we know that the Sun is at the center of the solar system, not the Earth. We also know...

that the planets move in ellipses around the Sun, not in circles, and certainly not in epicycles. This is definitely something that doesn't happen. Therefore, the epicycle model has nothing to do with how the orbits of the planets actually work.

But somehow it did manage to accurately predict the motion of the planets in the sky. including even the retrograde motion. So how is that possible? So using some advanced math, It can be proven that any shape can be approximated using enough epicycles. This includes ellipses.

So the epicycles were able to approximate the elliptical orbits of these planets. So the point is essentially that if you add enough epicycles, you can really make the planets moving any shape you want. And what Ptolemy actually did is he was creating this mathematical approximation of the heliocentric model with the Sun at the center and with elliptic orbits. He just didn't realize it.

He was using circles to approximate ellipses, and that is mathematically possible. He just didn't know what he was doing. But that is why it was so successful for more than a thousand years. Ptolemy's model is a great example of a model that gives correct predictions, but has no real explanatory power. A scientific model is only useful for explaining how things work, if it provides a simple mechanism that can explain complicated results.

So Ptolemy described the complicated motion of the planets using a model that is just as complicated. He just basically moved the complexity around without providing a real explanation. In other words, there was this complicated motion in the sky with this retrograde motion, and all kinds of other different things happening.

That's very complicated. So he made a model that is basically just as complicated to explain that complicated motion. That means that his model, it doesn't explain what's happening.

It just kind of reproduces what's happening without giving any explanation. The modern heliocentric model with elliptic orbits plus the laws of gravity that we'll learn about soon is a very simple model with only a few simple rules. And yet it can predict the complicated motion of the planets very accurately. And this makes the heliocentric model much more useful in providing a true explanation for the motion of the planets.

In other words, in this model there's only a few simple assumptions. Planets move in elliptical orbits and there's gravity, and gravity also works in a very simple way as you'll see soon. So these two simple assumptions essentially explain all this complicated movement. So we're getting more than we put in.

That's what we want from a scientific theory. So the geocentric model, you put in complex and you get complex. But in the heliocentric model, you put something simple and that simple thing explains the complex thing.

So the simple rules are complex. Explain the complex movement of the planets that you see in the sky. Occam's Razor is a very important scientific principle.

What it says is that simple theories should be preferred over complex ones. The reason is not that simpler theories are easier to understand. That's actually a common misconception. There's no reason to expect that the laws of nature are simple enough that humans can understand them.

Maybe the laws of nature are extremely complicated, maybe we'll never fully understand them. So that's not why we prefer simple theories. The reason we prefer simple theories is that the simpler the theory is, the more predictive value it has.

We want a scientific theory to generate plenty of output based on as little input as possible. The modern heliocentric model gives you a lot of output for just a bit of input. But Ptolemy's geocentric model requires as much input as it gives output.

And by that I mean that you have to look at the motion of the planets in the sky and use that to decide where exactly all the epicycles are and how many there are and what is the radius of each epicycle and so on. You're basically just converting one form of data to a different form of data. So although you can use this to predict the motions of the planets, you cannot use this geocentric model to explain the motion of the planets.

It's just kind of a different way to write the data about the motion of the planets. Okay, so in this lecture... We saw concrete examples of how science works and how the scientific method allows us to tell truth from fiction. We've seen that geocentrism and flat Earth are two hypotheses that were accepted by ancient people, but discarded once we learned how to use science to study the universe.

Despite all the very conclusive evidence against these hypotheses, some people still believe in one or both of them, even today. Like many other anti-scientific beliefs, the main motivation for modern geocentric or flat earth beliefs is a literal interpretation of religious scriptures. These scriptures, of course, were written in ancient times, so they reflect the way humans thought the universe worked. Back then, when they were written, that was before modern math, science and astronomy were developed.

So today we know that religious scriptures are not a reliable source of knowledge. In fact, almost everything written in them turned out to be incorrect upon further investigation. Another major reason for belief in flat Earth specifically is conspiracy theories which spread misinformation. And most of this happens online, for example via YouTube videos.

In these videos, conspiracy theorists claim that the Earth is actually flat. This fact is being hidden from the public. in an elaborate conspiracy, and every one of the millions of scientists around the world is somehow able to keep this huge secret. They never explain why hiding this information would benefit any scientist. Now, believers in geocentrism or flat Earth are relatively few, but there are other beliefs which are just as irrational.

and yet are believed by millions or even billions of people around the world. One of these is astrology, and it will be the focus of my next lecture. In conclusion, in this lecture we'll learn about some important concepts in ancient astronomy such as axial precession and parallax which are still used today. We also learned about some ancient ideas that are no longer used, because modern theories match our observations much better. For reading, you can read section 2.2 of the textbook, and I will post practice questions about this lecture on TIMSS.

Transcript for:Exploring Ancient and Modern Astronomy

Transcript for:
Exploring Ancient and Modern Astronomy