 So, to work out, so the order of Earth is not a circle, the mass is not a circle, can you work out the order of Earth and the mass, give it the data that you have. So, this is the data that you have to work with. Now, this looks kind of impossible, because roughly speaking, you're kind of still picturing analysis in one equation. You have one set of data, the definition, you know what, at any given time, you know what direction mass is in the sky, but that depends on both the order of Earth and the order of mass, both of which are unknown. We try to use one equation to solve two unknowns. And also, you're only going to solve half an equation you really want, okay? So, Brahe's data tells you the direction of mass. It doesn't tell you how far it is. You know the distance, you know, polar coordinates is the direction and radius. You only have direction here. So, you kind of solve the two unknowns using half an equation, right? You only have half the data you need, okay, and you want to solve two unknowns. It looks really hard, okay? So, it looks like there's any sufficient information that will solve the problem. In fact, you know, even this, you know, so it looks like there's a curfew problem. This is a Cartesian plot. They can't invent a Cartesian plot about 30, 40 years after. You know, they didn't even have this graph. Here's a big table. You know, it's really, you know, again, they really have really serious limitations in their technology and in their math. But nevertheless, the couple solved this problem. I mean, it's really an ingenious solution. It's really not like a great achievement cycle. So, he made a couple of observations. So, there are two unknowns, okay? Both the of Mars and the Earth. Using that term, maybe if I could work out at least more of the Earth, then this would help me work out a bit with Mars, okay? So, if I knew how Earth would move on the Sun, this would be enough information to tell me. So, how do you use, how do you imagine the Earth? You have to use another celestial body. Okay, that's this chart from the Earth. So, to explain how this works, okay, so let's reduce to, so both the Earth and Mars move. But, of course, Mars didn't move. Okay, Mars is always here. Okay, only Earth moves. If only Earth moves and Mars doesn't move, then you can use Mars as a reference point. Okay, so, we don't know where Earth, but at any given time, whatever Earth is, you can see where in the sky, and you also know which constellation the Sun is in. You know the direction. So, if it was triangle, you have a fixed side and two angles, I don't know, a triangle side. That's the back information to determine the triangle. Okay, so you can triangle it. This is an ancient navigational technique that even ancient Greeks, even ancient Venetians, I think, knew about. As long as you can see two landmarks on the coast, you can work up to these two fixed points where the Earth is. So, triangulation is one of the oldest navigation techniques. We still use it. Well, tetrangulation, you have to use four satellites instead of two points, and you're working four dimensions to other two, but it's the exact time. But it's the same principle. Anyway, if Mars is fixed, then you can use triangulation and you can work on the Earth. Of course, Mars moves. And all these triangles, the side heat change, and you don't know how the side varies. So, this looks really bad. You know, so you have Mars moving in an unknown fashion, and so you don't get a triangulation just until you wear the Earth as anymore. But Kjapa had one crucial additional piece of information. So, you take top-of-the-earth data only at intervals of 687 days apart. And it's just enough data that's like a 10-year data set or something with gaps, you know. In winter, you couldn't measure and so forth. So, Mars was below this data. But there's just enough data that if you only take the data in a series of 687 days, then Mars is now just fixed. And you can reduce the previous question from a previous spot, and this is what I should do. And that's enough information to work out the order of Earth at some points in time. And so using that, it was just enough data to actually work out what the order of Earth was. And once you pick up the order of Earth, you could use that so that then you take a different time series of 687 days. And Mars has a different reference point but around the same orbit. And because now you've computed the orbit, you can compare the relative position of this fixed point of Mars and this fixed point of Mars. And he was able to work out the order of Mars as well. It's an amazing piece of work, especially given, you know, you didn't have, you know, it was really quite interesting. So he worked out the orbit of the planets. Now, because nowadays it's very easy to do this because you just look at Kepler's laws and you're told what the answer is. Strangely enough, you can have Kepler's laws at the time. But once you have this data for Mars and Venus and Jupiter and Saturn, you discover Kepler's laws. You know, the famous one. So he discovered that planets move in ellipses. It's not as one with polka. Evil areas move equal times. And then the hardest one, which actually requires, you know, I think he would do this for six planets and this is just about the most difficult third law that the period of orbit is a power law. Anyway, so he was able to discover some major scientific laws because of his very careful measurements, which, of course, famously led Newton to discover even more than another law, which is basically a unique law that predicts that he would recover Kepler's laws. So what Kepler's method does is it allows you to measure the distance of any planet Mars in terms of the astronomical measurements. So they all vary. They all live in ellipses, but at any point in time you can see exactly how many astronomical measurements. So this is a very precise measurement of other planets in terms of the AU. This is great because, as I said before, the AU is hard to measure. But you can reverse Kepler's measurements. If you can measure the distance of the Venus, and Kepler said that at some point in time Venus is so and so astronomical that it's away, you can work out what astronomical it is. So you can work out the astronomical unit by taking measurements of the Venus. Now, how far can the Moon's measure depth? They use two eyes, and the slight difference in angle of the brain can convert that to distance. So, you know, if you had two eye-walls, one of them could be in principle, and you could measure angles very, very accurately to measure slightly different. And if you could synchronize your two observations at exactly the same time, then you could obviously work with the Venuses. So, what we're going to do with the Venuses is try to set the sun, because at the moment Venus is across the sun, people on two sides of the planet measure the angle, then they come back to the nose. You could work with the sun in which it can not do because it requires a lot of technology. You need a properly, you need a good timekeeping, a reasonable timekeeping, and you need the ability to travel across the globe. So, this was first done by James Cook, a famous explorer in Australia. My couple was not from Scotland, Australia, but the reason he discovered Australia was that he was trying to do science, and people were trying to, he was racing to the Southern Hemisphere to capture the Kaiser of Venus, at the same time as someone in London who was doing it. He wasn't the only person to do it, but he did something crucial. Accidentally, he discovered Australia, too. It was bonus. But, yeah, so that was the 18th century. That was basically the minimal time that all the technology was necessary to do all this. And he was able to do most of the kinds of Venus, and this actually gave the first accurate measurement of it. Much, much better. Particularly this week, it was called radar. It was just directly radar. Again, every time you make really precise measurements, you discover that your theory doesn't quite have some inaccuracy in it. So, all these measurements eventually revealed that something was going really mercury. Mercury actually was not the biggest source. So, it kept open the checkers with his data but eventually, mercury was wobbling at a funny rate. It was processing. The ellipse was wobbling a little bit. And so, you tell me gravity had to be fixed. And, of course, this was a famous early expert work. So, let me sign it. Okay, the next one, it's not technically a distance, but we need a very important number at the speed of light. Now, because, so you saw these pictures of the telescope, I need a picture at the speed of light. Okay, it's not a distance, but it is something you really need to know to measure. To measure. In fact, it was not clear for a long time that it was even finite. I think Gauss proposed to measure the, we've got a friend to go on. I'm sure this landed. Okay, the moment you see this light, you're much more landed. And I'm going to find how long it will take to reduce this. This didn't work. But the idea was sound. The idea actually was sound. Now, it's just that the distance is needed. Also, the reaction time of this friend was too inadequate. But the same idea actually works. Instead of using two mountains, use two planets, then it works. Now, of course, you can't get your friend to go with the other planet. But, okay, so they used Jupiter. So, yeah, the first measurement was done by Rowe and Williams. And so, use Jupiter. Okay, and so instead of your friend, you can't go to Jupiter. You're someone who really is a Jupiter. It was one of the four big moons of Jupiter. And it has a, probably, it's a sense of Galileo. It's the closest one to Jupiter. So, by Kepler's words, it's the fastest. In fact, it's really fast. Our moon takes 28 days. Jupiter takes 48 or 42 hours. And it's like a clock. In, out. You can look at the telescope and transit Jupiter in and out. Except that it doesn't. Rowe was actually trying to measure it precisely. And he was measuring exactly when Rowe entered Jupiter's schedule. It wasn't quite. Sometimes it was a little bit ahead of schedule. Sometimes it was behind schedule. Sometimes the transit came a little earlier than the period when it came later. And he actually worked out that this happened when Jupiter looked on the same side of the sun. The transit was a little bit advanced. And so, Huygens realized what was going on and it's basically the two mountains going. So the difference is very slight. Okay, so you wait six months and the sun is going on the other side. And it takes only 20 minutes. You need to measure a 20-minute time difference over six months, which by that point they had enough good clocks to get into this. Okay, so Huygens realized what was going on is because light had a finite speed. And when the Earth was on the other side of the sun, the light from Jupiter takes two extra astronomical units to get from Jupiter to the other side of the sun. And so it takes 20 minutes to traverse two astronomical units. And that's enough information to compute the speed of light. So they were the first to get a reasonably accurate estimate of the speed of light. So they got 140,000 miles per second, which is, well, okay. So the truth is 180,000 miles per second, which is okay. So this is not great, but they were the first to do it. Later measurements using similar ideas got better measurements. And they made people close to much later their third time experiments. And this is again, like many other astronomical data points in this talk, the physical science is important now. Because Maxwell, at some point, had Maxwell's laws and he was predicted that electric ways propagated, so to speak, which depends on the permittivity and permittivity of space, and he computed the speed, and it was 180,000 miles per hour. So that number was familiar. And so he looked up the best variable estimate for the speed of light, and it was almost exactly the same. And so he made a very important discovery, which is obvious now, not obvious then. Light is a form of electromagnetic radiation but also developed and hope to work through a spectroscopy, and both of these are needed for astronomy. So astronomy and physics have been in a similar way in relationship before. So we've got as far as the speed of light. Now you can use that to use all this information to get to nearby stars. Okay, well, actually in this particular case you want to use light. Okay, so parallax, as you said, you could use two different points on the Earth and try to do the same thing to measure distances of the stars. You can take measurements like both Australia and England of the same star and try to measure parallax. But it doesn't work. If you try, even closest to Alpha Centauri, the difference in angle between for Jupiter and Venus is 10,000 arc second. Arc second is 60th of a minute to the mid 60th of a degree. Okay, I think even modern telescope sun's not a two or three-act AUA. It's 270,000 AUA. So the distance between two ends of the Earth is not good enough. So rather than traveling to the other side of the Earth, we just sit in one place on the Earth and just wait six months. The sun will move you very hopefully two AU of over to the right AU. And then you use these to do two idols. Okay, and using and now we have much way of parallax. And if you mentioned and so if you have a good photography you can take photographs and see the constellation six months apart and some of the stars will move slightly because of parallax. And with enough good photography, you can actually use this to measure distance of stars. But again, you need pretty good parallax. If you just use the Earth-bound telescope you can get about as far as 100 light years. Which is good enough to get a fair bunch of stars. Nowadays you can use satellites and you can take you a lot better. But initially you can go 100 light years. There's about 10,000 stars which are close enough for parallax to work. So that's a tiny fraction of all the stars in the galaxy. But that's a huge set of data points that you can use to climb the next one. And this was first time in the episode one of the first things you need is an actual telescope. And this was first time at Bessel. So I mentioned earlier that when Aristarchus proposed the head ascension model the other reason this can't be true because if the Earth would not have a sun and if the sun was so far away from the Earth you would see parallax effects. And you would see that every six months the constellation is slightly different because it's usually open. And they saw the constellations they didn't change. And the only way they couldn't change is that the stars were enormously far away. And so far when the universe was like hundreds and hundreds of thousands of times bigger than they thought. And this was clearly absurd. So therefore the Earth-type model but of course they're completely correct the stars are incredibly far away. So you have to wrap your heads around it that's such a distance. So sometimes it's a bit trust in mathematics. So the next thing is the movie way. So parallax only gives you a tiny fraction. But once you have the partures of the stars you can get the rest. So this is another famous story to open high school sometimes. So once you have really good once you have some spectroscopy which we talked about earlier not only can you measure stars you can also measure the colour, the red or green. And once you have good photography you can measure how bright the star is. At least how bright the star looks. So sometimes they're bright because they really are bright. But sometimes they're bright because they're close to us. So they're bright, they're absolute bright because they're far away, as small as the parent brightness. So if you measure the parent brightness it's either square or the further away you get from a star they're different in looks. And so for 10,000 stars you get the brightness and you know the distance for parallax. And so we cannot have absolute brightness of 10,000 stars in my view. So that's a lot of work that somebody did it. First from the muscle if you're a astronomers took all the stars which parallax was known they computed absolute brightness of these stars also with their colour. And when they followed it they got the first from muscle diagram but most stars the main secret stars have a relationship with absolute brightness and colour. Red stars are not as bright blue stars are not as bright. So they currently found this curve that the astronomers have curve. Which I give a curve like this you can use it in reverse. So once you have this curve now you can measure distance to other stars that shift too far from parallax to reach. Take another star in the galaxy you can still work as colour directly but you can work as a parent brightness. Once you have this curve this is a wonderful curve once you have the colour you also have the absolute brightness. And once you have the parent brightness and absolute brightness you solve the square law and that gives you the distance. So you can use the first from muscle diagram to work out the distance to all the stars in the galaxy. So it works quite far out about 30,000 to 300,000 light-years which is pretty much in the entire galaxy. Beyond that you run into serious problems the stars that you faint that the stars you can see outside the galaxy live next to all the other stars in the same galaxy. And it's really hard to work out the power part of that one star. So it doesn't quite work beyond the galaxy but it works everywhere within the galaxy. So now you need to look at the other galaxies. So first person to do this so she was measuring a certain type of star called a secret star. So these stars are funny they must have been in brightness. So sometimes they were bright because they were small but they didn't know why at that time but they didn't oscillate in these variable stars. Now some of them were in the galaxy in our galaxy, some of them were distant galaxies. So the ones in our galaxy she could actually compute the distance to. So the secret don't actually live on those cluster diagram but they often live in clusters or the clusters not clusters but the cluster of other stars for which she can use. So she could measure the distance to see if it's within the Milky Way and she could measure the brightness and she could measure the period. So some secret took a long time to oscillate in a short time and so she could measure absolute brightness and so she got another curve. So it turns out that there's two types of circuits type one and type two but these types there's a relative period of curve and the brightness curve. And this is again something that he was just like he can use for the first cluster diagram that now if you take a circuit which is far away in a different galaxy there's period, brightness which is hard because all the other stars in the galaxy can measure the period you use this actually brightness but you still need to measure the brightness but the studies are really bright. This works, so the Milky Way is about 100,000 light years across and the studies are really really bright and this method actually works so this gets you a reasonable track in the universe but not everything so it gets you about 100,000,000 light years away the universe is about 76,000,000 light years so and most galaxies happen to be at least 1,700 so we can actually do quite a lot of galaxies so we need to go up we don't just use satellites there's some other things that so you get something so bright that you can actually work with an inactive galaxy so I know you use this super but what we know of is the entire universe so this is the thing that said at the very beginning so the shape, to measure galaxies which are too far away it's never used to work, it's not very Hubble and so this story is quite famous of course so he measures all these galaxies and he noticed that some galaxies were redder than they should so there's a certain color that was predicted by stellar evolution and so forth but some galaxies are spectrum of shifted from what should happen and he computed this redshift and there are thousands of galaxies for which it was close enough that this method would have a distance so he plotted the redshift against the distance and he got a curve but he had a line in this case not a great line but later later he considered it so he discovered Hubble's law that the further away and so again, once you have a curve and you get a line, you can use it in reverse but if you take any galaxy you don't want it to be far away if you know it's redshift so now every galaxy in the universe you can measure how far away it is so one thing he discovered was that everybody is redshifted everyone's moving away from the rest and this was of course now he's going to explain that but astronomy could only measure directions for centuries but now just the galaxies you cannot stop drawing the entire universe so you can start making maps for the universe every galaxy you see so this is I think it's called a 2 degree field you can just start with an arc of 2 degrees look at all the galaxies in that arc and you can watch the distance and you can talk to the coordinates and here are those galaxies and you start finding that they're not uniformly distributed they're not spread out evenly on the space they're clocked into the strings so there will be massive superstructures and the entire galaxy is the means of the strings so again that was simply the Great Wall it wasn't the Great Wall of China it was a much, much bigger wall the wall of galaxies but these are structures that you cannot see unless you can measure distances so in some way you have to find the entire ladder and so we are now beginning to understand what the entire universe is shaped like and there's other data that they're going for and so for example we can start measuring the current best assessment because I mean this is about 70 or 80 people doing that is 4 more initially we were using ancient Greek mathematics in ancient Greek technology at this point we are no longer using ancient Greek so you really need pretty much 21st century mathematics and 21st century astronomy you need general agility in particular at the universal cosmological scales and you need really good telescopes in particular it's happening in space next year there will be the James Webb Telescope which you will see through it so that's going to be another huge and so we're still going we haven't completed enough of the universe yet and so astronomy is extremely active now it is still so I want to close where we are so here are 4 pictures we cannot even wait for describing the state of astronomy today ok so this map here is the famous map of Tongli so Tongli we talked about earlier the century AD decided to try to make a map of the world to make Asia here and Europe here Tongli did not actually travel to all these places so the way he got this map first of all he bought every single map to get his hands on and try to station together but he also talked to merchants so even in ancient Greek times there were merchants who managed to get as far as Asia or at least maybe get as far as Persia and Persia to get from so he could start using it to be a very crude plot of mafia and so you know this is what he got now it's not bad this is what they actually started and you know really given the limited technology this is an incredibly good the analog of Tongli's map this is like one of the best maps of the universe we have right now and it's a very similar thing you measure all the now over here should be a picture I don't have that picture but what you can do is you can sit in a big bang this could be any kind of galaxy you use gravity you can't buy this class of gravity you can also use class of gravity and you will find that as you evolve these galaxies by just gravity they will walk as the strings and you see the same stream structures so that's very new we haven't screwed up much of it as you can find in this lab but the experiment is still filling with things that we have we would like to have the analog of this picture we would like to have the true map of the universe but maybe you know all these new telescopes eventually we will actually so we are in time for a couple of questions nowadays we don't actually use the AU as much it was important before we had once you have satellite forwarding I guess AU is really a very public thought works and so there is a sort of survivorship bias and so there are other intermediaries who also let it go at these problems and they got lousy answers and they didn't talk about those so there are many other ingenious attempts to make it I'll just show you one example of it so I think there was a lot of trauma here but also these were very bright people if I had many things in it there are historians of science and chronicles of science I had some other there were some there were some ways to