 Greetings and welcome to the Introduction to Astronomy. In this video, we're going to talk about the Doppler effect and how we can use that to be able to determine velocities of objects out in space. So, learning how things are moving is quite important. What, how are they moving and what direction are they moving and how fast are they moving are all very important. About a hundred years ago, Edwin Hubble was able to use a similar method to be able to find out that the universe was expanding because all galaxies were moving away from us. So let's look a little bit about how this works. And we'll start off a little bit with, first of all, waves. When waves are moving, it, they will change their pattern. In fact, a moving wave source changes the pattern of waves that we see. And what we notice is that in the direction of motion, the waves get bunched up, and opposite the direction of motion, the waves get spread out. So here, we have an object which must be moving in this direction because the waves are getting bunched up on this side and pushed closer and closer together, shortening their wavelength, and here they're getting stretched out, getting to be longer wavelengths. So depending on the motion, the wavelengths are actually, the wavelengths can actually be changing. Now, this can depend on the relative motion. It does not matter. It could be either the observer or the source. Either one of these two could be doing the moving. So you could be moving closer to an object making a sound, and that would cause a Doppler effect, or that object could be moving towards you. The effect we see would be exactly the same. So when we look at some of this, as we look at the example here, a moving wave, as the moving wave affects those patterns, we can see here with the car now moving a little bit closer, and you can see in the direction the car is moving, the waves get all bunched up, and in the opposite direction, they get stretched out. So it changes the wavelength of example that the sound of it would be making, and then that will give us, in this case, the change in pitch of, say, the car's horn. Now, if you've heard this, if you've had a fire engine go by as you stand on the street, and you hear a fire engine or a police car or an ambulance go by, you hear that as it comes towards you, you get a much higher pitch, and as it leaves, it gets a much lower pitch. There's really no change, and the person driving or riding along with the truck will hear exactly the same tone the entire time. It is only because it is moving towards you and then away from you that you're changing the actual pitch that you hear. So how do we go about measuring something like the Doppler effect? In order to measure it, what we have to do is note that it only measures a part of the velocity. It only measures what we call the velocity along the line of sight, and that is the part of the velocity that is either directly toward or directly away from the observer. It cannot measure the velocity along the line of sight. So if we look at the example here with an airplane, at this point over here, the green arrow shows the part of the velocity that is moving towards the observer. The blue arrow shows the part of the velocity that is moving along the lines of sight, and the middle arrow here then shows the actual true velocity of the plane through the sky. So we can only measure, the Doppler effect can only measure this green portion. It cannot measure the blue, so it measures only that portion. That means as the plane goes by right here, if you look at this middle one, you can see that there is the blue arrow, that the motion along the line of sight is the entire motion, and there is no green arrow. At this instant, there is no motion towards or from the observer, and therefore you're not going to get any Doppler effect. You're not going to measure any velocity. So the fact that we do not measure a velocity does not mean that an object is not moving. It means that we can only measure, in this case, the green portions of the velocity, and that is the part of the velocity that is either moving towards or away from the observer. So let's look at the shifts that we get here, and what we get is that we can get two types of shifts. We can get a red shift or a blue shift, and a red shift means that the object is moving away. A blue shift means that an object is moving towards you or closer to you. So if we look at the example here, we have the lines here in the laboratory spectrum. This is where everything would be if nothing was moving relative to each other. A red shift will move everything towards the red portion of the spectrum, so all the lines are shifted in this direction. In a blue shift, the lines are shifted the other way they're shifted towards the blue part of the spectrum. When we talk about a red shift or a blue shift, it does not mean that the object appears that color. It only means that they are shifted really towards longer wavelengths for a red shift or shorter wavelengths for a blue shift. So it is only telling you whether we're shifting towards longer or shorter wavelengths. A red shift would say it's moving away, and a blue shift means it's moving towards you. The amount of the shift tells you how great the velocity is. A very small shift means a small velocity, and a very large shift means a very large velocity. So the greater the shift, the greater the velocity that occurs. Now let's look at an example of how we can calculate this. So an example here that we're going to do that shows how to calculate this. Now this is the equation for the velocity. We can calculate the exact velocity, and what we're looking for in this case is the velocity v here. So what do we know here? Well, c is the speed of light. This is 300,000 kilometers per second. And that's the v is the velocity. We're looking for c is the speed of light. The change in wavelength, so we call delta lambda here. Delta is the Greek letter that we use to represent change. So this really means the change in the wavelength, between what we observe and what we should observe if nothing were moving. Lambda, again the Greek letter we use for wavelength, with a little zero behind it, means the true wavelength. So this is something that we know for a specific line. This is something that we measure. The speed of light is a constant, and then we can then use that to make a calculation to find out what the velocity of this object is. So how would we go about doing that? Well, let's look at and do the example here, and keep our equation up there in the corner. Let's go ahead and do the calculation. So let's say we observe a wavelength of 656.5 nanometers for a line that should be in a laboratory at 656.3 meters. So it's only been shifted by two tenths of a nanometer. First point, it is shifted towards a longer wavelength. That means it's receding or moving away from you. You can tell that immediately without doing any calculation. If the wavelength is longer than the rest wavelength, it's moving away. If the observed wavelength is shorter than the rest wavelength, then it is moving towards you. Now, we can rearrange the equation to solve for the velocity, which is just equal to the speed of light, c, times the change in wavelength, divided by the rest wavelength. We know what c is, that's 300,000 kilometers per second. The change in wavelength was two tenths of a nanometer. The rest wavelength is 656.3 nanometers, and if we multiply and divide everything there, we would find a velocity of 91.4 kilometers per second. And just recall, that is what we call the radial velocity, the portion of the velocity that is going towards or away from us. In this case, it's the part going away from us. That is not the true velocity of the object through space. That is only a portion of it. It could be that velocity, if this object is moving directly away from us, or it could be only a small portion of the velocity, if this is moving along the line of sight. We have to do other measurements to try to determine the rest of the velocity. So, let's finish up here and summarize a little bit. As we looked at the Doppler effect, first of all, we noted that waves are affected by the motion of the object. So, the way an object is moving, and I could say, or the observer here, because it also could be the observer that is doing the moving. When we look at the shift, a red shift shows an object moving away, a blue shift shows an object moving towards the observer, or again, a blue shift can also show the observer moving towards the object, and a red shift can show the observer moving away from the object. It is all a matter of perspective who is actually doing the moving. And we went through an example and looked at how we can use the Doppler effect and the formula to be able to determine the velocities, and remember that was radial velocities, of objects in space. So, that concludes our lecture on the Doppler effect, and 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.