 You're Terry, we're expecting that, okay? Anyway, very pleased to introduce Terry Townsend. Thanks for having me. So, this is, let's talk about this, nothing to do with my research interests unless it helped my amateur astronomy interests as a kid. I always liked astronomy. My parents want me to tell us something. I loved finding all these facts and figures about stars and planets. And only a lot later did I realise that I wanted to share some of it with you. My focus in the subfield of astronomy is called astrometry. So, astrometry is the study of positions and sizes of celestial bodies. So, all the things in the sky, sun, the moon, the planets, so forth. Just where they are, how far away they are, and so forth. So, the type of questions we care about here are things like how far is it from the earth to the moon? How far is it from the earth to the sun? From the sun to Venus? From the sun to Alpha Centauri? To the Adionic Galaxy, so forth. All these numbers. So, of course, nowadays it's very easy to figure these things out. But where do these numbers come from? So, I mean, they're just way too far for any direct measurement to work. You can't just take a ruler or anything to measure any of these distances. There's no direct measurement for virtually any of these. But the way astronomy is, over thousands of years, astronomers have found many, many clever ways to measure distances indirectly. So, for example, you know, here's a galaxy here, and you may not be able to directly measure the distance of this galaxy or this galaxy, but we have ways of comparing the two and finding out the ratio, say, between this distance and this distance. And once you know one of them, you can then work up the other one. And they often rely on both mathematics and on technology, but to lie, they say, just in mathematics. So, for example, for very far galaxies, what you use Hubble's law, that the distance for very distant objects is proportional to the recessional velocity, which you can measure. So, what that does for you is that it lets you control distances to very, very far away objects by distances with slightly less far away objects, which you then control in terms of distances with slightly less far away objects, and so on and so forth. And there are different techniques that work at different ranges. And fortunately, there's enough techniques to cover all the radius which you can get right. But that's not the trivial thing at all. And so, you have this hierarchy of distance measurements which let you get from really far objects all the way down to scales, finally down to scales that you can actually measure directly. And that gives you, and that's called the cosmic distance, so what you're going to do in this talk is just basically climb this ladder. So, you start on the Earth, and you just keep going up and up to higher and higher distance scales, and then each scale requires a different new idea to get further. But, you know, over thousands of years, so the very first scale is just the Earth itself. So, we know the Earth is round. It's basically a sphere, not quite a sphere. At the equator, it has a radius of about 6,338 kilometers, and it's slightly less, slightly more than 6 kilometers. And, of course, nowadays, you know, we can actually measure the sphere directly. We have all these, which you can get satellites, and you can take a whole picture of the whole Earth like this. But now, let's, as I thought at this moment, just subtract all the technology. Suppose we don't have satellites, we don't have space flight, but let's say we don't even have air travel or even much ocean travel. Or even telescopes or sextants. Basically, go back to the technology thing. Can we still compute the radius of the Earth without all that technology? I mean, it's so obvious once you have a picture, but not so obvious if you don't have that. So, yeah, so the ancient Greeks actually worked this out, and pretty much, you know, they had almost zero technology, but they did have geometry. They pretty much invented more than geometry. And that's pretty much all you need, or some measurements, but a lot less than you might think. So, for example, the very first basic question, is the Earth round? And so, you know, it leaks a lot about this, and maybe we've lost it with a sort of aesthetic argument, so it feels most perfect shape or whatever. But the first really convincing scientific proof that the Earth was round suited my Aristotle back in 3rd century BC, 4th century BC. And it was an indirect argument because you could not look directly at all of the Earth at the same time, or not see it as round. So, it's indirect. Every single measurement is indirect. And pretty much every time you want to measure an object in astronomy, you have to compare it with a different object. You have to somehow use a segment of the celestial body. And so, he used the moon. So, he used the moon to show the Earth was round. Okay, so how do you do this? So, can you do it like this? Maybe so often, you know, the moon used to be full, but sometimes during the full moon, the moon was dark, the lunar eclipse. It was observed already by the ancient Greeks that this only happens at certain times. It only happens at the time of full moon. And at the time of full moon, the moon is directly opposite the sun. So, the sun will be here and the moon is over here. If the moon and the sun are over there, and other than 100 degrees, you don't need lunar eclipses. You only need lunar eclipses when the sun and the moon are opposed. And so, as for the reason that the reason why this was happening was because of the Earth class of shadow. So, the sun class of shadow. So, the light of the sun makes the Earth class of shadow. And lunar eclipses happen precisely because the moon falls sometimes into the shadow of the Earth. That only happens when the sun and the moon are opposed. But when eclipses occurs, sometimes you get a partial eclipse. And so, the Earth's shadow is not only an obscure part of the moon. And the shadow is always a circular arc. So, whenever you see a partial eclipse, the terminated between light and dark is always a circular arc. So, what it means is that every shadow of the Earth. So, for example, there's a competing theory that the moon has a disk, not a flat disk. And if that wouldn't happen, the flat disk, the shadows are sometimes ellipses. They're not circles. And the sphere is the only shape of the moon. So, that's what's the argument. It used to form a zero measurement. You put an eye-side and you can actually see that the Earth is actually a circle. So, the Earth was round. Now, it could be rounded very small and rounded very big. But the Earth also was new. So, even in the times of the Greeks, the head of this was a travel of a big ocean. So, they could get as far as Egypt. And they knew that in Egypt, there were certain constellations, certain stars, that were visible in Egypt that you couldn't see in this. So, the sphere, you could see why this was happening. It's because of the Earth's curve. And so, if you're in Egypt, you see a different portion of space from Greece to Egypt. There must be some substantial portion of the fraction of the entire sequence of the Earth. So, enough that the set of stars that you see in some of the children. So, the Earth is not a movement sphere. It really is some finite sphere. But this idea, this argument, it really is a good way to measure the radius method. But still, this was a convincing argument, a scientific argument that we have to try. So, the very thing was that the first person to actually compute the radius of the Earth properly, to get it centuries or later, was Eratosthenes. So, he computed the radius of Earth at 40,000 stadia, which in modern terms, the radius of Earth is 6,800 kilometers or 4,200 miles, which is a remarkably good estimate given the zero technology. So, again, it's an indirect argument. So, you need it in that celestial body. In this case, it's the sun. So, you look at the sun. We're not directly at the sun, but you use the sun. Okay. So, it's a famous story, many of you already know it. But I'll tell it anyway. So, Eratosthenes had read somewhere of the Italian edict of Saini. And Saini had as well, and the school had a special property that one day of the year, the summer solstice, the longest day of the year, and you can see the sun reflected directly over his head. He waited until June 21st, but he didn't live any day inside. Because the Earth was trans-Earth, we now know the reason why this is true is because Saini just happens to lie on the top of cancer, and it happens to be basically almost one location on Earth where this happens, that on one day of the year, Eratosthenes tried this. He waited until June 21st. He looked at the world, and he couldn't see the sun reflected over his head. So, at this point, most people would just say, well, that's a story of rubbish, but maybe Eratosthenes knew about Eratosthenes' work. He knew the Earth was trans-Earth. He figured out what was going on. He figured out that basically where he was living in Alexandria, the sun was not quite over his head. So, he assumed the sun was very, very far away. So, this is something to make. The way the sun is parallel, he was a scientist. So, he said, maybe I can do something with this. So, he actually measured the deviation from the vertical. So, he actually had a measuring stick from no one. With geometry, he could actually work out the angle that the sun was making at noon on June 21st. And in modern events, it's seven degrees, or far worse, from Eratosthenes to Saini. So, you know, they both live on an hour. And there were versions going up and down. And the versions had to figure out how many days and how many stay here the day. So, it's not known exactly how he got this number, but this is another which there are some sources that he essentially hired a graduate student to pay a piece from Eratosthenes to Saini. But, it's this is just a story. I don't know to what extent this is actually true, although it's believable. But anyway, he got this one direct notion. And this is actually almost the only direct notion of a user in the photo. Okay, so he knew the distance between Saini and Alexandria at this angle and he knew trigonometry. Not in a modern language, but he knew Greek trigonometry was good enough. And this is enough information to work out assuming the sun is so far away that these two are in parallel. But we'll sort of retroactively work that out. So, that's how you at least measure the Earth. Okay, so now we've come to the next one which is the Moon. Okay, what shape is the Moon? We always see the same face of the Moon. No, maybe it is just a little peep in the sky. Okay, how large is the Moon and how far away will it also figure out these questions too? We're pretty good at this. So, back in Aristotle, when he showed the Earth was round, he also argued that the Moon was round, but it wasn't a disk. Again, he used the shadows. You see, actually, the shadows are pretty much incredibly useful tools from me. So, of course, the Moon has phases which is because the Sun and the Moon is part of the Moon. Again, you know, whenever you have a Moon face, there's this termination, the division between this wall-straight line and this half-moon, but it's always another people's shape. And basically, the reason why it's a sphere, and the Sun and the Moon is exactly half of the sphere, and depending on what angle that makes the Earth, you will see an ellipse. And again, basically, the sphere is pretty much the only shape, the only natural shape at least, which has that property, that the eternities have ellipses. Now, if the Moon was a disk, in fact, there'd be no phases at all. The Sun would always eliminate all the disks or none of the disks. Maybe it didn't detect these, in fact, the right disk or the dark disk, but you never get terminated. Terminated comes from the sphere. So, the Moon also is here, famously computed by Aristarchus, a little bit later. And so, but not directly, you cannot directly measure the distance from the Earth to the Moon, but you can measure the distance in terms of the distance that you can already understand, which was the radius of the Earth. So, he computed the distance from the Earth to the Moon at 60 Earth, really, yeah. Which is actually, and technically, yes, I mean, the Moon actually varies, it's not quite circular, but it varies from between 7 and 6 and 3, so to be honest, exactly. And the size of the Moon, he argued was about a third of the size of the Earth, which is not too bad, it's 0.27 in truth. But, you know, that's also the reason why you need to combine them, and then you start... So, how did Aristarchus do this? So, once again, you directly measure what you need, and that lets you let your body and it's really what you want to be able to use the Sun. Okay, so lunar eclipse is again. Okay, so as we saw already, lunar eclipse happened because the Earth cast a shadow, and the Moon sometimes forces the shadow, and that causes the lunar eclipse. Watch your lunar eclipse, and it starts and stops. And the reason that they are fine at them, because the shadow has a finite size. If the Earth has a radius R, the diagonal is 2R, and so the shadow should basically be 2R, assuming the Sun is far enough away. This is not quite 2R, but roughly speaking the shadow is the size 2R, that's the width of the shadow. And lunar eclipse doesn't last forever. Sometimes it's short, sometimes it won't, but they're never longer than 3 hours. We actually watched it on the once in a while of the eclipse. It's never more than 3 hours. And so basically, it takes 3 hours for the Moon to cross 2R. How long it takes the Moon to complete all the Earth? It's one month, it's friendship enough. One lunar month. So that degrades also the Moon. So in 28 days, you make a full revolution around this circle. And in 3 hours, you could have no problem, that's enough information to work out the relationship between the radius of the Earth. So that's the distance to the Moon. Now how about the size of the Moon? I don't know if you can track this. But you can just watch the Moon set. The Moon sometimes sets. It takes about 2 minutes for the Moon to set. The apparent motion of the Moon traverses 2 Moon radii. But on the other hand, the Moon goes around the Earth once every 24 hours, basically. It traverses the entire circumference of its orbit in 24 hours, and it traverses 2 Moon radii in 2 minutes. And again, that's an example. The word problem, that's enough information to determine the radius of the Moon in terms of the distance to the Moon. And we had a very good distance to the Moon in terms of the radius of the Earth. So you put it together and you find it very impressive. It's given pretty much zero technology. So what long did it have zero technology? They also had very primitive mathematics, I don't understand it. So, for instance, they didn't quite have active power yet. That was approximately 3. The first good approximation of power was after these, which was several decades after Aristarchus. So the level of technology and mathematics we had was only sort of barely sufficient to answer this question. So that's the Moon. So now we keep going up the ladder. So the next natural option to understand is the Sun. So again, the question is how big is the Sun and how far away the Sun is? But at this point, actually, there's a lack of technology started to fit quite badly. But there was no way to get some answers. Only one object available to the Moon. Okay. Actually, it's easy to speculate how much the Sun would be hindered if we didn't actually have a Moon. But anyway. So, okay. So Aristarchus had already computed the distance of the Moon, 60F, 30I, and radius of the Moon 1,3, and 1,4 years. So he knew that the radius of the Moon was 1,180F. And then to our Sun, so we use shadows again, but now we use solar purposes. So there's this amazing coincidence that solar purposes happen when the Moon obscures the Earth. And it happens that the Moon and the Earth happen to be almost exactly the same. So they have the same angle of width. And so, and they use similar triangles to better the concept of the Greece. So they, so he deduced therefore that since the radius of the Moon was 1,180F the distance of the Moon therefore the radius of the Sun was 1,180F the distance of the Sun. So if you know the distance of the Sun, you can also compute the radius. So you have to indirectly need another object. So we use phases again. We're always using shadows. So all right, Moon and Spaces. They have new Moon, full Moon, half Moon and so forth. Okay, so when do new Moons occur? Can new Moons occur when the Moon is directly between the Earth and the Sun? Full Moons occur when the Moon is directly opposite the Sun. Okay, so half Moons, so it sounds like you get half Moons, but exactly half of the Moon is lit. So you think maybe half Moons occur exactly half way between new Moons and full Moons. So what you see therefore is that half Moons are just a little bit closer. So as I was trying to compute this, and it wasn't easy with the technology that they had, but he asserted, I'm not sure how he got this number, but he asserted that half Moons occur a little bit sooner than the midpoint of the new Moon. He asserted that they occur 12 hours sooner. If you take the data back, and so using that computation and the best value of Pi that you have, you can see that the Moon is and the best value of Pi that you have. Using this 12-hour data point to be able to compute that the distance to the Sun is about 20 times the distance to the Sun. Now this is not quite true. So actually, the main problem here was that weak time technology, most accurate clocks had the Sun values, which didn't work at night for some reason, and so there was actually a big problem with the measure. The discrepancy between half Moons and half way between new and full Moons is not 4 hours, it's actually half an hour. And the distance to the Sun actually is not 20 times the distance to the Moon. So there are quite a bit because now of limitations in technology. But the method is correct. If they had more technology, the perfect conclusion data that they had, Avestar has still created so here all the information you knew the distance from the Moon in terms of the Sun, and you knew the radius of the Sun in terms of the particle. So you put all that together. If you're the first person to realize something very important, the Sun is bigger than the Earth. You put all that together, you compute the Sun was 703. Now at the time, this is so obvious nowadays, but it was not obvious. The Sun is about this big. It is not obvious if the Sun is bigger than the Earth. Now this was an incorrect data. The Sun is actually 109 times bigger. But still, the basic conclusion is correct. The Sun is much, much bigger than the Earth. And so, of course, at the time that the dominant cosmological theory was the geocentric theory that the Sun was going on the Earth, but now he realizes that the Sun is 7 ounces bigger than the Earth, so that this cannot possibly be correct. And Avestar just was the first to know if it actually proposed the heliocentric model. But actually he proposed that the Earth was bigger. The Sun was this much bigger than the Earth. He would definitely have. One reason why we don't know why it's worked as well is because the other 18 weeks distributed this conclusion. And there's a good reason for that, and I'll come back to that later. But anyway, Avestar just was able to compute a very important unit in astronomy. The distance from the Earth to the Sun. And so, this unit is sometimes the name of the astronomical unit, AU. And pretty much, it's AU. So much of the planets and other stars sort of have an urgent basis in terms of the AU. So this turns out to be extremely crucial. And so, it's actually a serious problem that Avestar has had a really lousy estimate of AU that people did work out better ways to compute it. So that's the Earth and the Moon and the Sun. The next one is the planets. So the ancient Greeks also studied the planets. They knew that the planets were either playing because they only went through a certain ring of constellations, like the Zodiac cancels the Earth and so forth. So they all had a plane and it's got the ecliptic. But in this plane, what happens? So again, basic questions, how far away are the planets? Like how far away is Mars? What are the orbits? What do they actually do? And how long does it take for Mars to go around the orbit? So it's so obvious that the Moon takes 20 to 20 days, but Mars isn't there. So this was, again, attempted by the Greeks. Tom Lee was the first, I think, to have had to sort of try it. Tom Lee was the first to seriously attempt these questions. But his answers were really, really much worse than our stock is. Basically, because he was using the wrong model. He was trying to do was using the geocentric model. And very hard to fit the data of the geocentric model. So he had to invent these epicycles to even get sort of close. So the Greeks actually did not succeed in... The first person to actually was Copernicus, who did have access to the vectors of ancient Avalonians. So they measured the centuries. Mars does do a funny thing, though. It goes backwards and forwards and so forth. But it turns out that every 708 days the position of movement of the Marsans in the sky returns to where it's at. So the apparent period, the symbolic period of Mars is 708 days. Now, under the geocentric model this means that Mars takes 708 days to go around the Earth. But Copernicus was working the helicentric model and he knew that the Earth was going around the Sun and Mars was also going around the Sun. And so 708 days is not a... It's not the rotation of what we say, one rotation for 708 days. It's not the angle of velocity of Mars. In fact, the angle of velocity of Mars minus the angle of velocity of Earth. The Earth took one year to go around the Sun and so the angle of velocity of Earth was one rotation per year. And it implied that the differential between the angle of velocity of Mars and the angle of 708 days was able to work out the truth. So Mars actually went around the Sun once in 16, 7 days. So he knew that Mars went around the Sun while he was in the geocentric model and how often. So at this point he assumed circular orbits. So he assumed that Mars went around in a symmetric circle and he only unknown that this is the relative ratio between the radius of the Earth orbit and the Mars orbit and he had enough mathematics at the time to compute to then solve for that radius using various rational data. At any given time, you can see where the Sun was rising, maybe it was rising in Libra and Mars was maybe in Capricorn. And so this gives you some information about the directions that Mars is assuming circular orbits and he computed that the distance from Mars to the Sun is one and a half miles from the Sun is about 50% further away from the Sun. Some serious calculations, this is not so obvious but the calculations that he did are quite accurate to do this in places. So a little bit later, Taku Rahi, astronomer, made very detailed measurements over many years of the position when they set what constellation they were in and so forth. In fact, he basically puts an enormous government graph with a village of peasants to go to an astronomer. But I tried to fit this data that he had. So the type of data he had is in a way where Mars is completely different. But you try to fit this to the model of circular orbits and it doesn't quite work because by 10% off you see the discovery that it wasn't the measurement data, it was actually the model data. And so Kepler managed to get his hands on the data. There's some storage, I think he basically stole the data. But anyway, but somehow he got his hands on the data and the reason that what was going on was that the orbits on the moon this is the only reason why