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Hello, this is Jason Kendall and welcome to my next intro astronomy lecture. Well, last time we talked about parallax and determining the distances to the stars, and there was one really important caveat, and that caveat was, first, we need the distance between the earth and the sun. And that's a really hard thing. I kind of glommed over it by saying that we look at the distance between the earth and the sun today by doing radar reflection off of Venus and using geometry in order to get that distance.
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But that's kind of a copout because we've known it for a long, longer than that. And in fact, people have made good guesses as to the exact distance between the earth and the sun for a long time. But let's see exactly how we can get there. One of the more important things that we have to think about then is to saying, well, if we want to get the distance between the earth and the sun, perhaps we need to know how big the earth is itself first.
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So let's actually take a diversion and go back and say, well, how do we know how big the earth is? And in fact, we're going to actually find something fascinating along the way. So, again, we're going to be talking about distances and how we get to parallax, how we're going to actually then use the diameter of here to get the distance to the sun using the parallax of Venus during a transit, during a transit across the sun.
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But that's for later. We have to build up a whole bunch of stuff in order to get there. So let's get the size of the earth. All right? So let's think about how we can actually do that. The Earth is extremely large, and if you take a plane flight and you go across country, it's very difficult to even see the curvature of the earth.
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You have to get hundreds of miles above the earth of your above of the earth in order to begin to see curvature. I think you actually start to see around 40 or so miles. But the point is, is that you have to be very high up in order to see the curvature of the earth. All right. So how do we actually know that the earth is curved?
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Let's pretend we never built a space program like the dinosaurs. And you know, that's why they're not around. But let's see, the. But the. But if we look at how far around the earth is all right, we can look at lunar eclipses, which we talked about previously. And we noted that the lunar eclipses only happen at full moon.
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And as the moon goes into the shadow of the earth, as the moon goes into the shadow of the Earth, we find that the shadow is not it is not straight, it's curved. So people have known for thousands of years that the Earth is actually round because of this shadow of the lunar eclipses on the moon. All right.
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So how can we actually translate that into understanding distances? Well, let's actually see how big the earth is. And if we then say, well, there was a wonderful, great we can use actually shadows to do that actual shadows cast by the sun. So, in fact, 200 B.C., a Greek philosopher by the name of Eris Eratosthenes Eratosthenes, it's a very interesting name who lived in Alexandria, Egypt at the time, about 200 B.C. As a Greek philosopher, he determined and learned that in that it right around the first days of summer, there were places specifically inside him, which is like now is now current day Anwar, Anwar Sadat and Anwar in Aswan I'm sorry, Aswan in Egypt,
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but in sign of the time, it was seen that the first days of summer that the light from the sun would go all the way down to the bottom of a deep well and not cast a shadow on either side. In fact, it would totally illuminate the bottom of the well, assuming the well is is completely straight down.
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And also tall poles would cast no shadow and they would actually have zero shadow around them. On this first day of summer at noon. Well, he also learned that in Alexandria, at exactly the same time shadows were cast that that Wells down to the bottom there very deep, did have the sun or did not penetrate all the way down to the bottom, but only made a circle on the side of the well.
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So there was something different in the only way that that could be at the exact same time, on the exact same day is if the Earth is not flat, but rather it's curved. So what Eratosthenes decided to do is he decided to measure the distance between Syene and Alexandria and measure the angle of the shadow in Alexandria when it was had no shadow in sand and he found that the angle of the shadow at that time was about seven degrees.
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And he also found that the distance between Alexandria and Syene was he used a particular particular a particular measuring unit called a stadia and a stadia is about 5.6 kilometers. So it's a it's a little bit less than a kilometer. So what we find is that if the distance between Alexandria and Syene could be measured and of course, back in 200 B.C., there's only one way to do it, you know, to get somebody to walk it.
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And that's how a stadia was measured. So somebody literally put down some poor schmuck, put down thousands upon thousands of these meter sticks and figured out the exact distance between Syene and Alexander Rhea to a pretty good, fair approximation. So it was found to be about 5000 stadia distant, and they're almost directly North-South from each other. And the angle separation that one in one location at zero and the other location had seven degrees.
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So we can use very simple geometry in order to determine the actual size and the circumference of the earth. Well, we know that the circle has 360 degrees, and if the shadow cast is only seven degrees, meaning a tall pillar, had some had some length of some shadow. So how you get this angle, we look at the angle in the shadow and determine it from from that against a plum line and so forth.
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There's a lot of different ways to measure angles, of shadows. And they weren't they weren't alien to people of his time. So but seven degrees divided by 360 degrees. Well, that's the same thing as saying the the length of an arc on the surface of the Earth compared to the entire circumference of the earth. So the length of the arc was 5000 stadia and the circumference of the earth is what we're trying to discover.
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So if we have 7.2 divided by 360 and that's equal to 5000 divided by the number, then that works out to be about 250,000 stadia. Or more specifically, seven degrees is about 1/50 of 360. So 5000 stadia times 550 is about 2500 stadia. Now, since it's a circle, we assume the earth is round so it can be spherical.
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So a circumference would be two pi divided by that. And that gives us, according to his measurements, about 6366 kilometers as a radius of the earth. Now, that's a really good measurement because it's within 1% of the modern value of about 6378 kilometers. So look at this way. Just having some guy pace off the stuff and doing a very accurate measurement across the land between two cities in 200 B.C., well over 2000 years ago was able to actually determine the radius of the earth size to within 1% of the modern value made with extremely accurate measurement systems.
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Well, we used and this diameter of the earth as a baseline, and the baseline can then be used during transit of Venus. When Venus goes between the earth and the sun, very rarely does it simply does across the or it doesn't cross the sun's face as it does so because Venus orbit is tilted slightly with respect to the sun, with respect to Earth's orbit around the sun.
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So true, Venus transits are rare, but when they happen, you can use to people situated across the diameter of the earth, say at the North and South Pole or across very far apart to to time, to cheat, to check the timings of the transits across Venus. And that can give you a parallax of Venus with respect to the sun.
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And that parallax gives you distance. So this is a really interesting thing. But actually, how do we get that? How do we know that that works? Well, that's going to rely on the development of calculus. It's also going to rely on the development of Newton's laws of gravity, Kepler's laws of motion, and utilizing Galileo's relative relativity concept, more specifically, the idea that we can actually that we do actually orbit the sun, that actually the earth does go around the sun and it doesn't feel like that.
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So to think that the Earth is actually round, even though it looks to all of us to be flat, and then to think that if the earth is stationary, then there's the moon and the sun go around, we have these relative sizes. But then to actually make the step to say, how does the earth move? And that is a big story that will come to you very soon.
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See you next time.