 Greetings and welcome to the Introduction to Astronomy. In this lecture we are going to be talking about coordinate systems and the different coordinate systems used to measure position on Earth and in the sky. And we'll see some similarities and also some differences in between how these two are used. So let's start off looking at how we measure things on Earth and you're probably familiar with the terms latitude and longitude. These are how we can determine the exact latitude and longitude will give you a specific location of any object on Earth. And the latitude, first of all, is the angular distance measured north or south of the Earth's equator. So Earth's equator is labeled right here and you can see the equator. And the latitude is how far you are north. So a north latitude would be north of that. A south latitude would of course be south of that. It would go up to 90 degrees at the pole and the equator would be 0 degrees latitude. So any location on the equator has 0 degrees and then the 90 degrees north would be the north pole. Of course, 90 degrees south would be the south pole of Earth. Now longitude is again an angular distance. These are both angular measures. And this is measured east or west of the prime meridian. So the prime meridian is defined as the meridian that goes through Greenwich, England. And that is just a convention that has been accepted now for hundreds of years because there is no difference between any of these different meridians that we have. Any of them could be equally well used to set the zero point. However, when this was determined, England being the great naval power and a large lot of sailing going on there was selected as the one to use the standard point. Otherwise, if everyone was using their own major city, for example, maybe Paris for France or Madrid for Spain then everyone is going to be having different coordinates. So we had to agree on that. Now with the latitude, there's nothing to worry about because there is only one latitude line that goes there and there's a very easy definition. Now we can look for an example of this that if we want to locate the Washington Monument in Washington D.C. Well, you can use a latitude of 38.8895 degrees north and a longitude of 77.0353 degrees west and that would be the approximate location of the Washington Monument in Washington D.C. in the United States. So any location on Earth could be determined by giving its latitude and longitude. Now we can do something very similar in the sky. So in order to do this in the sky, we need two coordinates and in this case we use declination and right ascension. Declination is similar to latitude. It is an angular distance measured north or south of the celestial equator. That should sound very familiar to how we determined the latitude on Earth. So the celestial equator here and how far do you go north toward the north celestial pole or south toward the south celestial pole would tell you how far you are above or below the celestial equator. The right ascension is an angular distance measured east. Now note that that's a difference between longitude. In longitude we have east and west longitudes. In the sky we measure only east. So we measure all the way around and we don't measure it in degrees as we do with longitude and latitude and declination. We measure it in hours. So there are 24 hours in one day. So the right ascension of a point would be how far you are away from the vernal equinox, which is the point right here. And as you may recall, that is where the ecliptic, the path of the sun, crosses the celestial equator heading north, so heading north in the sky. And that would then give you a location. So if we're looking for this star, we have a right ascension here, we have a declination here, and just as we can pinpoint a location of an object on Earth, we can pinpoint the location of any object in the sky. For example, the bright star Betelgeuse in Orion has a declination of 7.40706 degrees and a right ascension of 5.91953 hours. Note that this is a little bit different. When we do latitudes, we do north and south. When we do declinations, we do positive and negative. So writing it just like 7 degrees means 7 degrees north of the equator. And again, the right ascension is almost 6 hours, meaning it is about a quarter of the way around the sky from the vernal equinox. So that looks a little bit about coordinates, and one more thing for this lesson. We want to quickly look at is how do we know that the Earth rotates? How can we tell that the Earth is rotating? Certainly when you walk outside, you don't feel like the Earth is rotating, spinning very fast. However, the thing is there, everything is moving with you, including the atmosphere. So since everything moves at the same speed, you don't notice that you are going at the Earth is rotating. However, Jean Foucault gave us a pendulum in 1852, and a pendulum here with the bob at the bottom, and the string going all the way up into the ceiling there, and could oscillate it back and forth. And what you would see is, again, here's a scientific method to look at. It makes a prediction. If the Earth is rotating, the position will slowly change as Earth rotates beneath the pendulum. So if the pendulum starts going back and forth in one direction, that would slowly change, and at another time it would be going this direction, and at another time it would be going this direction. So the central point would remain the same, but there would be a change in how the direction in which it is moving. If there was no rotation, it would just keep doing the same thing over and over again. So we can then do this, and do this as an example, and find that yes, it will rotate, and that the Earth is indeed rotating underneath the pendulum. So let's go ahead and finish up with what we've looked at today in our summary, and we talked about latitude and longitude on Earth. Those are ways to measure angular distances on the surface of Earth. Declination and right ascension are ways to measure this on the celestial sphere. And then we looked at the rotation of Earth and how that can be demonstrated with a Foucault pendulum. So that concludes this lecture on coordinate systems. 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.