 Greetings and welcome to the Introduction to Astronomy. In this lecture we are going to talk about the Doppler effect, and this is another way we can use spectral lines, and in this case we use them to determine velocities, so how we can determine how fast something is moving in space. So let's get started, and what we see is a moving wave, a source. If the source of the wave is moving, that will affect the pattern of the waves coming from it. Let's look at the example here. Here we have a stationary source and putting out waves, and they are all equally spaced with the wavelength. So the wavelength is the same in each case. However, it's different if the observer is moving. They move from position 1 to 2 to 3 to 4 here, and that means that the waves will bunch up in the direction of motion. So an observer on position A will then see the waves all bunched up, an observer at position C will see them all spread out, and that is all because the source is moving at the same time. Now, this depends on the relative motion of the observer and the source, so it really doesn't matter who is moving. It could be the observer, you could have a stationary source and a moving observer, and you would get exactly the same effect. It is just that relative motion that tells us what the shifts will be. Now, we can be familiar with this for sound. So for example, sound here, when the car horn is blaring, two people standing will hear exactly the same thing. They will hear exactly the same sounds from it, and the pitch will be the same. However, when the car is heading away from one person, again, similar to what we showed before, the wavelengths are getting longer and longer here, and are getting more and more compressed on the nearside. So when the wavelengths get longer, you're going to hear a lower pitch. So even though the car is emitting the same pitch that it was when it was stationary, one observer will hear it stretched out, and one observer will hear it stretched out in a lower pitch, the other will hear it compressed, and at a higher pitch. Now, as I said, it depends on who is, it doesn't depend on who is moving, because you will get exactly the same effect if you are moving towards. So if we have person Y moving toward the source, they're going to see shorter wavelengths and hear a higher pitch. Person X moving further away is going to hear a lower pitch, where everything is stretched out. So when we go about measuring this, we can look at an example of an airplane here, and we can see that it's moving, and it has the velocity given by the red, sorry, the velocity given by the red arrow here. Now, velocity, if you recall, is a vector, and that means it can be split up into its components. A vector has a magnitude and a direction, but vectors can also be split up, and in this case, we split it up to a part along the line of sight. So the part along the line of sight would be given by the green arrow, and that means that at this point, position one here, we see the plane, and its component along the line of sight is toward the observer. So this would be a shift toward the observer. At position three here, we see that the green arrow is pointing away, and that means that it is moving away from the observer. Now, note that that's different than the actual velocity through space given by the red arrow. The red arrow is the combination of the velocity along the line of sight and the velocity across the line of sight. The Doppler effect cannot measure the velocity across the line of sight, and that's what's shown as the blue arrow here. So at position two, there is no Doppler shift. There is no Doppler effect because that plane is moving directly across the line of sight and neither toward nor away from the observer. Now, let's look at what we can do with spectral lines in this, and we see that when an object giving off spectral lines is at rest, we will see those lines at their rest wavelengths, where they are formed in the laboratory. And when it's moving, everything will be shifted toward the red portion of the spectrum. So each line is then shifted, and everything will be shifted towards longer wavelengths. Now, please note that does not mean it appears red. So this blue line might be shifted to a different shade of blue or green to a different shade of green, but it does not mean it will appear red. It just means that they are shifted towards longer wavelengths. In a blue shift, an object moving closer will be shifted toward shorter wavelengths. Again, it does not appear blue, and in fact, and for the most part, the shifts are so small that the color change would be insignificant. But the wavelength change is what is important. That is what will allow us to determine the velocity. And the greater that velocity, the greater the amount of the shift. So while you could technically shift blue light into the red portion of the spectrum, it takes incredibly high velocities, large fractions of the speed of light, to be able to get a shift of that size. So let's go ahead and look at an example of how we can calculate this, and we can calculate the velocity using the Doppler equation. So the Doppler equation, we want to look for v. v is the radial velocity, the velocity along the line of sight. That is the part of the velocity that we can measure. C is just a constant. That is the speed of light, so we know that value 300,000 kilometers per second. Delta lambda, delta means change. The lambda, the upside down y, means wavelength, so the change in wavelength, that's the difference between what is observed and what we see in the laboratory. And the lambda with the subscript of zero means the wavelength measured in the laboratory. So that is the true wavelength. That is the wavelength that the atoms are giving out with no velocity change. So we can go ahead and do an example calculation with this. And let's put some numbers in, and let's say here's our example. We're going to observe the spectral line in a star is observed to have a wavelength of 656.5 nanometers. The rest wavelength is 656.3 nanometers. What is the velocity of approach or recession? First thing to look at, it is observed at a longer wavelength than it should be. Since it's observed at a longer wavelength, it's a red shift, and that means it is receding. So that part of the question we can answer without any kind of calculation. Now what we want to do is rearrange this equation to solve for the velocity. So if we multiply both sides by C, then the C's cancel on here and we have just an equation for the velocity, which equals C times the change in wavelength divided by the wavelength at rest. V equals, then, C is 300,000 kilometers per second times 0.2 nanometers, very small amount, divided by that rest wavelength of 656.3 nanometers. So those are the values put in and if you do the calculation, you'll end up with 91.4 kilometers per second. So even this tiny shift of 2 tenths of a nanometer corresponds to a velocity change of over 90 kilometers per second. So it's an extremely fast, you don't need a very big shift to get a very large velocity. And again, this is the radial velocity, the velocity along the line of sight and is generally not the true velocity because there will also be a component along the line of sight. So let's go ahead and finish up today with our summary and what we saw is that waves are affected by the motion of the object. We looked at this for sound waves and we did some calculations to see if they behave exactly the same. We saw that a red shift shows an object moving away and a blue shift shows an object moving toward the observer and do remember, even though I state it that way, it could very easily be the observer moving toward the object or the observer moving away from the object. And we can use the Doppler effect to determine the velocities of objects in space, at least the component of their velocity either toward or away from the observer. So that concludes this lecture on the Doppler effect. 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.