 Greetings and welcome to the Introduction to Astronomy. In this lecture, we are going to start talking about measuring distances of the stars, and this time we will look at mainly the method of parallax. And that is really the direct method that we have to be able to measure distances to the stars. So, how do we determine distances? Well, this is something very difficult and one of the more difficult quantities to be able to determine, when we talk about stars and galaxies. It is tough to determine those. Now, one method we can use before we get to parallax is radar. This works to measure some distances within the solar system. So, what we use is the fact that radar waves or radio waves are light. So, they travel at the speed of light or 300,000 kilometers per second. So, if for example we send radar waves to Venus and bounce them off, and measure the time it takes for the return signal, then we can determine the distance. Distance is velocity multiplied by the time. We know what the velocity is because it is 300,000 kilometers per second. We measure the time, we have to divide it by two because it took time to get there and to get back. And that would give us the distance. However, this only works within the inner portion of our solar system. You need to have a strong enough signal for it to be detected. And you also need a solid surface off which to bounce something. So, it would not work for something like the sun either. So, let's take a look at the method of parallax. Parallax is the change in the apparent position of a distant object because of a change in the position of the observer. So, you can observe from position A here and observe again from position B and you will see that you will have to turn your device to slightly different angles to mark the position of the tree. If we measure the baseline, which is the distance between the two measurements and measure the angular shift of the object between these two viewpoints, we can determine distance. The closer an object is, the larger the shift we will get and the bigger the angle. So, the easier it is then to measure the distance. Now, we can use this on the ground, we can also use this on the sky. And here we see the same kind of thing, except now our baseline is Earth's orbit from one side to the other. So, we have a baseline of two astronomical units. So, we're letting the Earth move giving us our very large baseline. And we see the position of the nearby star has shifted at point A it's in one position and in point B it's in a slightly different position relative to the distant background stars. We can use the shift and the determination of that parallax angle to be able to measure the distance. Now, what we can do with that, we can look at that and the parallax has been known for a long time, the Greeks knew of parallax. In fact, that's one of the reasons they assumed Earth was not moving is because they could not detect a parallax in the stars. The problem was they did not comprehend the true distances that were involved. In 1838, we finally measured the first parallax of the star 61 Cygni. That was the first star to have its parallax measured at point three arc seconds. Alpha Centauri has the largest parallax being the nearest star at three-quarters of an arc second. And let's go ahead and take a little bit of an aside and look at what these angles mean. So the distance is an arc second. Let's split ahead here and look at arc seconds. If we divide a circle into 360 degrees, then as we divide time, we divide each of those degrees into 60 arc minutes, and we divide each of those minutes into 60 arc seconds. So one degree is equal to 3,600 arc seconds. Our moon is about half a degree in the sky. So we're measuring really, really tiny angles. Our moon would be 1,800 arc seconds across, and we're measuring tiny fractions of these arc seconds. But once we can measure them, the distance of the star is given by one divided by the parallax angle. P is the parallax angle in arc seconds. D is the distance in parsecs, where one parsec is a little over three and a quarter light years. So if we measure a parallax angle of 0.75 arc seconds, it means the distance is 1.33 parsecs or 4.35 light years. The parsec is specifically the distance at which the parallax is equal to one arc second. So let's look a little bit about the nearby stars then. There are no stars, other than our Sun, of course, that are within one parsec of Earth. No star has a parallax of greater than one arc second. However, there are dozens of stars within about 15 light years of Earth, and if you take a look at these, you probably don't recognize most of the names. Some of the primary stars you hear of things like Alpha Centauri, and you might hear of some of the others. There's the bright star Sirius, and a couple of others, maybe a couple of other stars, Procy and one of the bright stars in the sky. But only a handful of these are visible to the naked eye. Remember, most stars are very small in faint, and even though they're very close, they're essentially invisible to us. Now, how can we measure parallax accurately? Some of the problems is that the parallax angle is so tiny and it's difficult to measure. So we've had satellites such as the Hipparco satellite in 1989, which was working to measure distances of stars out to 300 light years, about 100 parsecs. And that would mean parallax angles of .01 arc seconds, one one hundredth of an arc second. Very small, but a great improvement to what we could do on Earth, but a tiny fraction of our galaxy, which is 100,000 light years across. Gaia in 2013 is measuring distance out to 30,000 light years, nearly a third of the size of our galaxy. And we can now start to make three-dimensional maps of our galaxy from these measurements, and you see the link here where you can actually go look at this data. It will be able to map seven and a half million stars with accurately determined positions. We will see that this is very important. Parallax is our first step in the distance ladder to determine distances to other stars and eventually to galaxies. So it needs to be accurate because other methods will build upon this. So let's go ahead and finish up with our summary, and we mentioned radar measurements, which work within our solar system but not beyond. And we looked at parallax, which is the shift of an object measured from two different viewpoints that allows us to determine the distance. And space observatories are now allowing us to accurately measure distances to millions of stars, giving us a three-dimensional view of the galaxy. So that concludes this lecture on distances to the stars 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.