Adjunct faculty in Astronomy at CUNY Hunter (2015-2018) and William Paterson University (2011-2020)
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How Big are the Sun and Moon?
In this video, I further discuss the nature of distances and sizes in astronomy, and its measurement just positions in the sky.
I alos discuss how we know the relative sizes and distances of the Sun and Moon to the Earth.
00:00:00:00 - 00:00:23:20
Hello, everyone. My name is Jason Kendall and welcome to another one of my introductory astronomy lectures. Well, today we're continuing the concept of distances and sizes. Last time we looked at the nature of the size of the size of the year or the size of the earth, using piecing it out, using using stadia and shadows and various places on the equator.
00:00:23:22 - 00:00:45:11
But if I want to actually then say, fine, that's how big the earth is. But we can also use simple geometry to make extraordinarily good guesses as to the relative distances between the earth and the sun. Not the exact distances, but getting very, very, very close. In fact, this method would work if it were more if it were easier to do.
00:00:45:13 - 00:01:13:06
All right. So let's describe yet another ancient Greek philosopher. This one, Aristarchus of Samos. Aristarchus lived from about 310 B.C. to about 230 B.C. so that's over 2200 years ago. And what he found was that he was able to deduce the distances, the relative distances, and in fact get a good estimate for the exact distance to the sun and the exact distance to the moon and their relative sizes as well.
00:01:13:09 - 00:01:30:29
So how did he do this? He did this all by eye and with by hand. Remember his contemporary actually knew the size of the earth. So we can actually use that and plug that in later in order to get the to get the actual sizes of the sun of the moon, according to Aristarchus. So how did he do it?
00:01:31:01 - 00:01:56:28
So let's go back and remember our phases of the moon. So we look at all of the phases of the moon that we see going around. And one of the phases is, of course, first quarter. So when the moon is at first quarter phase, we know that the geometry in space, if we look down from above, we see that the moon is in is in one part of a triangle between the moon, the moon, the earth and the sun.
00:01:57:00 - 00:02:19:20
But the moon in that triangle makes a 90 is at the 90 degree point. So we have a 90 degree triangle with the moon at the 90 degree point, and that's when it's a quarter phase. Remember, it's half illuminated. That means it's quarter phase. That means that's 90%. That means you have a 90 degree angle between the Terminator, meaning the day and night boundary and the edge of the moon that we can see.
00:02:19:26 - 00:02:43:09
So that is a quarter phase or 90 degrees around a circle. So we've got our 90 degree area. So when aristarchus then looked at and hey, that's a 90 degree angle, which means that all I need to do is get some sort of rough distance or in fact actually I can get their relative distances pretty easily because using simple geometry, we can get their relative distances because of the size of a triangle.
00:02:43:14 - 00:03:05:25
And all we have to do is measure angles. And so what he did is he endeavored like crazy to measure the angle in the sky between the moon and the sun. Remember the 90 degree angle of the triangle is where the moon is. But then the angle that we when we look at the moon and we look at the sun, that is less than 90 degrees.
00:03:06:01 - 00:03:34:06
And so we can use trigonometry or specifically the, the, the, the cosine of the angle to get the the relative distances between the earth and the sun. So what he measured in the sun, in the sky was he measured, roughly speaking, about 87 degrees. That's a pretty good measurement. It's not 90 degrees. It's about 87 degrees. So he was able to roughly get about one degree.
00:03:34:12 - 00:03:58:24
Remember that your thumb held at arm's length is about a degree. So he used a similar method or something more accurate than that. But he got about 87 degrees between the moon and the sun in the sky. Well, at Quadrature or when the moon is at first quarter, the real angle is about 89 degrees and 51 minutes. So it's a little bit closer to 90 than aristarchus actually measured.
00:03:59:01 - 00:04:25:03
But let's go with his measurement. If the angle of measurement is 87 degrees, then the ratio of the earth-moon distance compared to the Earth's sun distance is about 1 to 20. And specifically the sun's distance is about 19 times that of the earth, the moon's distance. So Aristarchus found out something very important. He found out that the sun is much, much, much further than the moon.
00:04:25:06 - 00:04:42:16
Now, he could also turn this around and say, Wait a second. If we look in the sky and we look at the moon in the sun, the earth and the moon and the sun, will they look to be the same size in the sky? So therefore, if the sun is 19 times further than the moon, it has to be 19 times bigger.
00:04:42:18 - 00:05:10:29
So that's the nature of Angular, angular things. It's a ten angles across the sky. So he knew that the earth, that the sun was really big. He said, Well, wait a second, how big's the moon? And we thought, Hey, let's go back and look at those lunar eclipses again. And if we look at the lunar eclipse, he actually timed how long it traveled through the shadow and specifically from the first contact of the of the pin of the umbrella of the earth shot in the darkest portion, the first contact until it went completely into the shadow.
00:05:11:04 - 00:05:34:27
And then time the duration of the eclipse and aristarchus determined it was roughly about twice. So he thought that because of the time, the length of totality of the lunar eclipse was about twice that of the of the time it takes to go from first contact to second contact. Then he determined that roughly that the site that the moon is about half the size of the earth.
00:05:35:00 - 00:05:53:19
Well, this assumes something and assumes that the shadow of the earth is linear and goes out for a very long way and doesn't taper. We know it tapers. So as the moon's shadow tapers, because the sun is big and so there's a place far behind the earth where it does not cast a shadow. Anyway, but that wasn't what Aristarchus thought.
00:05:53:22 - 00:06:14:28
Aristarchus said, Well, wait a second. The moon is about half the size of the earth. That's interesting. And if he determined that was about half the size of the earth, then he could turn that around and determine that about twice times, times 19, he determined that that sun was at least about 40 times the size of the earth.
00:06:15:00 - 00:06:41:02
That's a really interesting discovery. So he found something really fascinating with that and that that helped him. But he only did this with totally by eyeball with very rudimentary measurements and actually determined some very important parameters. But today, we know that the Earth's actual size is about four times that of the size of the moon. So when the moon is in the shadow, it's actually it's actually a smaller object.
00:06:41:02 - 00:06:58:29
And the shadow of the moon of the earth actually tapers to a point. So that's why it can travel so quickly through it. All right. So what Aristarchus did is he used angles between the moon and the sun, and he determined they were the same angular size. So he determined that they were that the sun was much further than the moon.
00:06:59:05 - 00:07:20:14
He also determined the size of the sun based upon the size that he thought the moon was based on its how long it took to go through a lunar eclipse. And you could even use Eris, Eris Eratosthenes as the description of the size of the earth in order to get the relative sizes of all of them. So that's really interesting.
00:07:20:22 - 00:07:43:11
Well, before 200 B.C., it was understood, at least to a pretty good estimation. Now, Aristarchus measurements were off by pretty considerably, but that's okay. We have to give him props for trying because who else does this kind of thing? And basically, the true earth, sun distance, about 400 times that is the earth moon. So he's off by a factor of say, I don't know, 20.
00:07:43:18 - 00:08:03:19
But that's okay. Let's let's let him live with that. He did great. But what we did learn is that the moon is closer than the sun to the earth and the sun. We also learned that the sun is much, much, much larger than the Earth, and it's much larger than the moon. So this brings up some very interesting questions and points.
00:08:03:21 - 00:08:24:08
And one of them that came about later, or at least in the contemporary moment, is the great debate about whether or not the Earth should be at the center of the cosmos. And we're going to discuss that shortly. But we can look at this and say, well, the sun is really a lot bigger than the Earth, so shouldn't it be at the center of everything?
00:08:24:10 - 00:08:50:29
And that makes kind of sense, I guess. But that doesn't actually prove anything. It says it should be, but that doesn't necessarily mean it is. B And there should and is are very, very different objects. So what's actually discussed that next time when we start to get go down the rabbit hole of how big how we know that the earth actually moves in the sky?
00:08:51:02 - 00:09:20:00
Because I know that you don't feel it. And occasionally people say, well, did the earth move? And that's an interesting question. If you happen to live in an earthquake zone, yes, it moves occasionally. But we can also think that how do we know that the earth is actually moving around the sun? And that was one of the great questions of all of astronomy, in fact, that led to the development of the calculus and it led to the development of modern day science just by asking these simple questions.
00:09:20:02 - 00:09:22:12
Okay. So we'll see you next time.