 Greetings and welcome to the Introduction to Astronomy. In this video we are going to talk about one of the ways of measuring the distances to the stars, and that is through using the method of parallax. So it will be a beginning, a way to start looking at distances, but we are going to find we're going to need other methods, other than just the parallax, to be able to determine distances to other objects in astronomy. So let's go ahead and get started here, and first of all we want to look at some of the ways that we can measure distances in astronomy. And there are some other methods before we get into parallax to look at as well. And one of the big problems is that the distances to these objects are very difficult quantities to determine. When you look out at the night sky, it is not obvious that things are at different distances to you. You can see all of these stars and they look like they are attached to a great celestial sphere. But even the planets when you see them just look like they are all at the same distances just at varying brightnesses. So trying to determine those distances is something that can cause difficulty and has over the centuries. So one of the ways that we can use it, and one of the few direct methods to get distances, is by using radar. Radar measurements will allow you to measure distances within the solar system, and only to very close objects, not even everything within the solar system. But it works by the fact that radar waves, like any electromagnetic radiation, travel at the speed of light. So we know how fast they travel. That means we know that they will be traveling 300,000 kilometers per second. And if we want to know the distance then, we can use that. Use the equation that says distance equals velocity times time. And if we want to find the distance, if we know the velocity, which we do 300,000 kilometers per second right there. And if we measure the time, it takes a signal to say travel from the Earth to Mars. And then return, we can then determine the distance. We know how long it took that radar wave to go from the Earth to Mars. That's the time. And then we can use the velocity, which is known to determine the distance to Mars. Now as I said, this will help within the inner part of the solar system. The distances involved are much too far to use this for any kind of star, or even further in the outer solar system. One key point I wanted to mention here is right here. When we measure this, we're measuring the distance to get there and to get back. And that means we want to divide the time that it took by 2 to actually find the distance to Mars. Because that radar wave had to travel to Mars and back, it traveled twice the distance between Earth and Mars. So that's one way to be able to determine distances. But what we really want to look at here is parallax. Now parallax is a way of being able to look at these, and it is defined as the change in the apparent position of a distant object due to a change in the position of the observer. So what that means is that when you look at something from two different points of view, here from view point A you look at a nearby object, and that nearby object in this case appears to be in front of the blue square. If you move a little bit to view point B, now you look at that same object, nothing else has moved, and now it appears to be in front of the red square. So what you would see from A would be this position, what you would see here is this orientation, and therefore the object, the nearby object has moved, apparently moved. Now the closer the object is, the larger the shift will be. So an object very close to us will undergo a large shift, and a very distant object will appear to undergo a very small shift. If we measure the baseline, which is the distance between these two, if we measure that distance between these two different viewpoints, and we measure this angle, the shift that the object appears to undergo between those two viewpoints, we can then determine the distance to the object itself. So it is a direct method, it is something we can use here on Earth for triangulation, looking at things locally from two different positions, we can measure that, and use that to determine the distance to an object. Now in terms of a little bit of the history of this, as we take a look, the parallax does have a history, this has been known for a long time, the ancient Greeks knew of parallax, they knew this occurred, and they knew that if the Earth was moving, if the Earth was moving around the Sun, that looking at nearby stars here from one position versus the position six months later, that they would appear to shift their position, just as we saw on the previous slide. So they could not detect it, they looked for parallax, they looked for a shifting of the stars, and could not find it, therefore using the scientific method and saying, well, the Earth must be motionless. Well actually it was one of two things, either the Earth was motionless, and that would explain why no parallax occurred, or the distances were just so tremendous that this parallax angle was so tiny that we could not possibly measure it, and that was the case, the Greeks simply did not comprehend the true distances that were involved in space. Now it was not until the 1830s, and in fact 1838, when astronomers measured the first parallax of a star, and that was the star 61 Cygni, and it had a parallax of three tenths of an arc second. Now if we recall an arc second, we divided one arc minute, was equal to 60 arc seconds, and one degree was equal to 60 arc minutes. So essentially one degree equals 3,600 arc seconds. So we were trying to measure a tiny fraction of a degree on the sky, and to get an example of that, the full moon is one half of a degree. So the full moon is just one half of a degree, or 1,800 arc seconds. So we're trying to measure a tiny fraction of the size of the full moon. Certainly not something that you could notice with the naked eye, way too small, and it took telescopes into the 1830s before we were actually able to determine this. Alpha Centauri, the nearest star, does have the largest parallax of a little over an arc second. So let's go ahead and take a look at what we've been able to measure here, and what we find is that we have looked and we have to define a different term here, which is the parsec, and the parsec is another measure of distance. We use the light year as well, but it is the distance at which a star would have a parallax of one arc second. Now, that means that anything with a parallax of one arc second would be at a distance of one parsec, or about 3.26 light years. So what that means is the angles that we use. Another way to measure distances. So sometimes you'll hear parsecs used, sometimes you'll hear light years. It's about three light years per parsec if you're trying to convert them quickly. There are no stars within, except for the sun, within one parsec of the earth within 3.26 light years, which means there are no stars that have a parallax of greater than one arc second. Now, that seems to conflict with what I told you on the previous page with Alpha Centauri, having a parallax of one and a half arc seconds. That was actually, it is how astronomers measure the angle. The angle is measured by, is actually half of that full parallax angle. So if you're looking from one location and another location at this nearby star, this for Alpha Centauri, this would be 1.5 arc seconds. But astronomers actually only measure half of that parallax angle, which would be a little less than one arc second. So it can be a little bit of a confusion there in terms of the definitions. But when we define the parsec there, that gives us the name comes from parallax and arc second. And it is the distance at which a star will have that parallax of one arc second. However, there are dozens of stars that we can find within 15 light years of the Earth, and here they are shown as well. There are a whole bunch of these, and if you take a look at many of these names, then we see that they're not very familiar probably. We do notice a few things like Alpha Centauri here is one you may have heard of, but many of the others are just catalog names. They are not among the brightest stars in the sky, and in fact the nearest stars to us are all very small red dwarf stars for the most part and are not really visible to the naked eye. But as you get further and further away those angles get smaller and smaller and it gets harder to be able to measure the distances. So what can we do to improve on this? Well one thing we can do to improve is to make measurements from space. So as we go out we've actually put satellites up in orbit, and Hipparchos in 1989 was able to measure distances for 300 light years or 100 parsecs. A big improvement over what we could do here on Earth, but still a tiny fraction of what we could see in the galaxy. More recently Gaia in 2013 put up is working on measuring distances to 10,000 parsecs or 30,000 light years. That is still just a fraction of our galaxy, our galaxy being 100,000 light years across, we're getting stars out to about a third of our galaxy. So it still is not helping us a lot, it does help us a lot but it's not getting everything that we want and it's not going to help us with determining distances to other galaxies or anything else. But it is important because parallax is really the only direct measurement of distances that we have. It is the only way to directly determine distances to the stars and it will be our base for using other methods that we will look at later to determine distances not only to other stars but to the distant galaxies. And we need this one to be as accurate as possible. So being able to get accurate maps for seven and a half million stars is really a big jump from what could have been done just decades before. And you can actually go to the website I mentioned here for Gaia. It will, Gaia Sky you can download and it will actually do, you can actually make three dimensional maps of the galaxy. Again, something that was very hard to do before we had a good number of distances accurately determined. So let's finish up here with our summary. And what we find is, first of all, the radar measurements work within our solar system and that's about it. So radar works but it's not a very good one for determining distances further away because we cannot send radar signals to the nearest stars and expect to get any kind of return signal. Parallax is used a lot more and that is defined as the apparent shift of an object when measured from two different viewpoints. So a star would be an example of that. We can measure a star from two different viewpoints and the biggest baseline we can get would be the Earth six months apart when the Earth is on one side of the sun as compared to when it is on the other side of the sun. So that can be used to measure the distances to nearby stars and now going out to millions of stars. And more recently, as I've said, space observatories have allowed us to measure distances to many millions of stars beginning to give us a real good three dimensional view of our galaxy. So that concludes this lecture on determining distances in astronomy using parallax. We'll be back again next time for another topic in astronomy. So until then, have a great day everyone and I will see you in class.