 Greetings and welcome to the Introduction to Astronomy. In this week's special topic in astronomy, we are going to talk about altitude and azimuth and how they can be used to determine the position of a star in the sky. So, what do we mean by altitude and azimuth? Well, let's start out looking at the definitions here. The definition of altitude is the height of an object above the horizon. If it is on the horizon, just rising or setting, that would mean its altitude is zero degrees. The azimuth is the position of an object around the horizon. And we define that starting from the north point. North is zero degrees. So, we have here the north point noted here. We have a star, some point in the sky. We measure then would measure its altitude and azimuth. And we would say that it is so high in the sky, that's its altitude up above. So, this would be its altitude, which could be some number of degrees up above the horizon. Let's just say that's 60 degrees. So, we have an altitude of 60 degrees. Its azimuth would then be measured around from the north point. And in this case, it would be 45 degrees east. Now, there is only going to be one point that meets those two criteria, that is 45 degrees east and at 60 degrees north. So, we can exactly then locate the position of an object in the sky. Now, this measurement depends on your position here on earth. So, the altitude and azimuth that a person measures in one part of the world will not be the same altitude and azimuth that a person would measure in another part of the world. So, for example, a measurement on the east coast of the United States would give a different value than someone on the west coast and would be different than someone in Europe or Africa or Australia. Some objects may be visible or may not be visible, depending on what their location is. And in fact, the altitude itself can be negative. An altitude is negative if the object is below the horizon. So, at night time, the sun would have a negative altitude. It doesn't have no altitude. It still has a specific value. It would just be negative, and that tells us that it is below the horizon at that time. Azimuth, on the other hand, cannot be negative. It is always going to be positive and you measure it around toward east from the north point. But that would tell you whether an object is visible. Now, let's look at an example of this with our sun. So, here are paths of the sun on different days of the year. And in fact, prominent days, which are the summer solstice here, the two equinoxes, and then the winter solstice. So, the lower path is the winter solstice. That would have a very low altitude. The sun is very low in the sky during winter. It would be a little bit higher if you go up toward spring and fall, and it would be highest in the sky when you get to summer. So, the altitude of the sun would be different at different times of the year. It will also be different at different times of day. Here, we're looking at the noon time altitude when the sun is highest in the sky. It would also be different at different times of the day. When the sun rises off in the east, it would then have a zero altitude. It would rise, get higher and higher until it reaches a peak, and that would be around noon, and then it would go down to set. And once it's set, it would be back again to zero degrees altitude. And again, that changes depending on the person doing the observing. So, altitude is zero on the horizon. The maximum altitude you can get would be at the zenith, and that would be an altitude of 90 degrees. Altitude cannot be greater than 90 degrees. That is the highest point in the sky, which would be straight overhead. So, let's go ahead and summarize a little bit about what we've gone over this time. And what we've looked at is altitude and azimuth are things that can be used to determine a location of an object on the sky. The altitude measures how high an object is above or below the horizon, and azimuth measures how far around that horizon it is starting with the north point. So, the north point is the starting point for azimuth. The horizon is the starting point for altitude. So, that concludes this lecture on altitude and azimuth. We'll be back again next time for another special topic in astronomy. So, until then, have a great day, everyone, and I will see you in class.