 Greetings and welcome to the Introduction to Astronomy. Today in this week's special topic in astronomy, we will look at the distance modulus, which is a way of measuring distances by looking at the brightnesses of stars. So let's see how this works. So the definition would be the difference between the apparent and the absolute magnitudes of an object. This value is related to the distance, how far away the object is. So what is the apparent magnitude? That's what we see from Earth. That's how bright it appears in the sky. The absolute magnitude is the brightness it would have if it were at a distance of 10 parsecs away. A parsec is about three and a quarter light years, so that would be about 32 and a half light years away. Now the absolute magnitude is a measure of the true brightness of a star or other object, whereas the apparent magnitude depends on the distance. So when we put them together, we can then figure out a distance. Now, we do this by subtracting the two values. You take the apparent magnitude, and from that you subtract the absolute magnitude. And you see what value you get. If it is equal to zero, that means that it appears just as bright as it would be at a distance of 10 parsecs. That means it is a star that is exactly 10 parsecs away. If it is greater than zero, then you would have a distance greater than 10 parsecs. If this is a bigger number, that means that the star looks fainter than it should. So it looks fainter, that means it must be at a greater distance. If you get a value less than zero, then the distance is less than 10 parsecs, and you would find it closer to Earth. So let's look at some examples of how we can do this, and here is the equation that you can use. The distance is given by 10 raised to the power, and there is our distance modulus. You take the distance modulus, you divide it by five, and add one, and then raise 10 to that power, and that will give you the distance in parsecs. So let's look at an example here. If we have a star that has an absolute magnitude of five and an apparent magnitude of five, well, we take this value here, that's the apparent magnitude, this is the absolute magnitude, so we take five minus five, which gives us zero. Now if we go back to our equation, then we would divide zero by five, and would still get zero, and we would add one to that and get one, and then 10 to the first power would then be 10 parsecs. Now we could do other examples of this as well. So let's look at a second example here. Here we have an absolute magnitude still of five and an apparent magnitude of zero. So now we take zero and subtract five from it, and that gives us negative five. Negative five divided by five will give us negative one, and negative one plus one gives us zero, so we would get 10 to the zero power. Any number to the zero power is equal to one, so this star would then be one parsec away. One more example we can look at, and let's take a look at three here, and we have now an absolute magnitude of zero and an apparent magnitude of five. So we do the same thing here, except now we're taking the apparent magnitude of five, subtracting zero, giving us five, and then we can go ahead and do our calculation. Five divided by five is one. Add one to that, we get two, and 10 to the second power is 100 parsecs away. Now you can certainly do this for more detailed calculations and differing values of the absolute and apparent magnitudes. For my classes, this is more than sufficient as to what you would need to know about the distance modulus. So let's go ahead and finish up what we've looked at here with our summary, and what we've seen is the distance modulus is the difference between the apparent and the absolute magnitudes. The value of this modulus tells us the distance of a star. A large value gives us a great distance, and a small value gives us a lesser distance. And of course one of the difficulties in using this is knowing the absolute magnitude, how to figure out exactly how truly bright a star or other object is. So that concludes this special topic on the distance modulus. We'll be back again next week for another special topic in astronomy. So until then, have a great day everyone, and I will see you in class.