 Greetings and welcome to the Introduction to Astronomy. In this lecture we are going to talk about distances of the stars and the method to determine them used known as spectroscopic parallax. So we'll look at various methods to be able to determine the distances to stars in the universe. So let's start off looking at this, and what we mean by spectroscopic parallax is using the HR diagram to determine distances. Can we use the spectral class of a star to determine distance? Remember the spectral class only depends on the spectrum. So as long as the star is bright enough that we can see a spectrum, this is good because it is then easy to measure. However, the different thing we have to consider is that stars of a spectral class can have various luminosities and that you can have a star such as a type, say, right here, and it can be a main sequence star, luminosity class 5, it could be a giant star, luminosity class 3, or it could be a super-giant star of luminosity class 1. So we need to be able to determine the two-dimensional spectral class, not only the OBAFGKM class, but also the Roman numeral 1 through 5 class to be able to determine. So for example, our sun is a G25 star. Another G2 star could be a giant, class 3. It would be much brighter, and that could cause our distance measurements to be off if we are not careful. So we need to look at both of these when we are measuring distances. So what do we do with spectroscopic parallax? So first of all, nothing to do with parallax at all, except that it's used to measure distance. What we do is measure the spectral class and the luminosity class of a star. That allows us to say we've classified this as a certain type of spectral class here, and we've said that it's a luminosity class that's here, and that allows us to get the luminosity. So we can then use the HR diagram to determine the luminosity and then just like other methods, use the inverse square law to get the distance. So we can then determine the distance to the star. Again, it needs to be calibrated. This is a running theme throughout what we're looking at here by stars of known distance. We have to calibrate exactly where the main sequence falls, and we have to calibrate exactly where the giant branch falls, and you can see that as you get up to super giants, it gets really hard to be able to match those up. But once you do that, you can then use this method to determine distances to the stars. So we then look at what we call our cosmic distance ladder, and that is because no distance measurement will work for all stars. Some stars are close enough that we can use parallax, and with Gaia that is expanding to be able to use more of those. Some stars are C-feeds or are our Lyrae stars. Sometimes we can use spectroscopic parallax. But we have to remember that variable stars and spectroscopic parallax are indirect. That means they have to be calibrated before they are used. The parallax allows us to determine the distances directly. So as we work with parallax here and we see the image, and here's the Sun and there's our Earth, that we can use a parallel, had an old parallax limit way in here, very close to Earth. Now with Gaia we've got a much larger parallax method, which allows us to better calibrate things like C-feeds and our Lyrae stars. So we can get these better calibrated to be able to determine distances. Then we use those two galaxies that might have C-feeds in them, and we can use that to determine distances to galaxies. And then we will need to use other methods we will talk about later to determine distances of much more distant galaxies. So we're going to need new methods to determine distances to most of the galaxies. The methods we've used here work great within our galaxy. They'll work with nearby galaxies, but we're going to need others to get to further galaxies. So what we look is that all measurements, remember every measurement we make has some kind of error associated with it. If we measure a star at 100 light years with an error of 10%, then we would say it is in between 90 and 110 light years away. As we go up the distance ladder, each step builds on the previous step, and therefore the errors tend to increase. So parallax works out to about 30,000 years once Gaia mission is complete. Our Lyrae stars visible out to 300,000 light years. Spectroscopic parallax to a little over a million light years. And C-feeds out to about 60 million light years. And that sounds like an amazing distance. However, we're going to be talking about billions of light years. And we're not even getting close to one billion light years, which is more than 10 times the distance that a C-feed can be used to measure this. And the edge of the galaxy, we're getting out to 10 billion light years, or more. So we're actually going to need many other methods to be able to help us measure the distances to the galaxies. So let's go ahead and finish up this with our summary. We talked about how we can use the HR diagram to determine luminosities, and therefore distances of the stars. We have what we need to know is the spectral class and the luminosity class. It's a two-dimensional spectral classification in order to determine this. And then we started talking about the cosmic distance ladder, as the steps used to determine those distances, but each step is built on the previous one, causing the errors to increase as well. So we need very accurate measurements in the very beginning steps to make sure we do not have tremendous errors in the later steps. So that concludes this lecture on distances to the stars, spectroscopic 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.