Transcription
Ok, let's start by drawing the Earth. Now that we've got the Earth, let's divide the Earth into two equal parts. We're going to call the the north part of the planet the northern hemisphere and we're going to call the south part of the planet the southern hemisphere, and that dividing line which divided the northern hemisphere from the southern hemisphere we're going to call the Equator. Equator for "equa" being equal.
We're also going to define the Equator at zero degrees of latitude and so the term latitude is the term that we're going to use for north and south. Now let's say that we wanted to determine what the latitude was of the North Pole. The North Pole of course is the northernmost part of the planet. All we need to do to figure this out is draw an imaginary line from the North Pole to the center of the planet and then from the center of the planet we're going to draw a line to the edge of the Equator. You'll notice that we've just made a 90 degree angle therefore the North Pole is simply located in 90 degrees north latitude or the North Pole is 90 degrees north of the Equator.
We can do the same thing down here in the southern hemisphere. Here at the South Pole we're going to draw an imaginary line from it to the center of the planet and we draw an imaginary line from the center of the planted to the edge of the Equator. Once again we've created a 90 degree angle therefore we know that the South Pole is 90 degrees south latitude or 90 degrees south of the Equator or south of 0.
Now that say we wanted to figure out where San Diego, California was located. Well we know the San Diego is right about here. Well what does right about here mean? We're 32 degrees north latitude. Wo what exactly does that mean? That means if you were to draw an imaginary line from the center of the planet to San Diego and another imaginary line from the center of the planet to the edge of the Equator that angle is going to be 32 degrees. So in essence San Diego, California is 32 degrees north of the Equator which makes it 32 degrees north latitude.
We can also do this in the southern hemisphere. If there is a point right here that say around 32 degrees south latitude we know that that position is 32 degrees south of the Equator, and a good example of that would be a place like Sydney, Australia.
Now here's a question for you. Is 32 degrees north latitude San Diego only or other other places on the planet which are also located at 32 degrees north latitude? Well the answer is obvious. Yes, I mean what about over here? This place is 32 degrees north of the Equator so it too has to be 32 degrees north latitude and what about here and here and here and here as a matter of fact along this entire line you're at 32 degrees north latitude. And the same is going to be true down here in the southern hemisphere all along this line, you're going to be at 32 degrees south latitude.
Well what about somebody who's up here at maybe 60 degrees north latitude? They're not the only ones. This is 60, this is 60, this is 60. So this entire line also represents 60 degrees north latitude. And we can play this game across the entire planet. And you'll notice that all of these lines that we're drawing -- all of these latitudinal lines -- are parallel to one another. Therefore we can also call these lines "parallels". So now the term "latitude" and "parallel" are used rather interchangeably. San Diego, California is located at 32 degrees north latitude and it's also located on the 32nd parallel.
Now here's my question for you. How do we know that San Diego, California is located at 32 degrees north latitude? Other than me telling you it's true and other than us using, for example, a GPS -- a global positioning system -- to verify it how in essence do we know that we are at 32 degrees north latitude? Well, there's a rather simple way to do this. Let's draw the Earth again and this time that's really concentrate on the North Pole, and let's put somebody up at the North Pole oh I don't know this call them Santa Claus. So here's Santa Claus up at the North Pole. If Santa Claus were to look straight up in the sky and it's night time he would see a North Star. And it's called the north star because there's going to be a star that's above north geographic pole, and it's always going to be above north geographic pole. In fact, that star today is called Polaris and so Polaris is the north celestial pole star.
Now if Santa Claus looked straight up he'll see Polaris. And during the course of the day as the Earth rotates on its axis Polaris is still going to be up and Polaris isn't going to move, at least not to him. However if there's a star here and a star here and a star here and a star here all of those stars will appear to move in the nighttime sky, and the reason, of course, is Earth is rotating on its axis and it's going to make one complete rotation in the time span of 24 hours. So during the course of the evening the Stars will appear to rise in the east and set in the west and they'll be doing this type of movement: nice circular movement in the sky but again it's not the stars moving, rather it's the Earth rotating on its axis giving the appearance of the stars moving. Now all the stars are going to do this except for one star and that one star is the north celestial pole star and the reason why it does not appear to move is because the north celestial pole star is on Earth's axis of rotation. So here's the axis of rotation. Earth is rotating on this axis and because Polaris is right on the axis it's not going to appear to move.
Now because of this we can actually use Polaris to determine our latitude in a position on planet Earth, and here's how it works. So this person looks straight up. Now according to Santa Claus here Polaris is going to make an angle of 90 degrees with his horizon and so your horizon is your point that extends outward that you see on the edge. So for example if you go see a sunset and you're looking out to the Pacific Ocean and the Sun appears to set and it goes below the ocean that oceanic plane is basically our horizon and the point directly above our head is called "zenith". So for the person standing on the North Pole, Polaris is located at zenith, and Polaris therefore makes an angle of 90 degrees with horizon. Therefore we know that North Pole is located at 90 degrees north latitude. So basically your latitude is simply how many degrees that the north celestial pole star makes with your horizon.
In the case here of San Diego we know we're at 32 degrees north latitude but how do we really know that we're at 32 degrees north latitude? Well let's draw a picture here here's our zenith point, which is the point directly above our head. Here is our horizon line and here is Polaris. And we will note that Polaris makes an angle of 32 degrees north of that horizon. Makes sense?
Now we can play this game all over the world. Here's somebody standing at the Equator. And for someone standing at the Equator Polaris is going to be right on their horizon. So basically Polaris makes an angle of zero degrees relative to that person's horizon, and that's exactly what we're seeing here.
Now here's a question for you. What if you're down here in the southern hemisphere? Can you use Polaris to determine your point of latitude? And the answer of course is no because the second that you go beneath the Equator or at least really close to it, Polaris is now below your horizon and you're unable to see it. So for someone standing here in the southern hemisphere they can't use Polaris as their point of reference. Rather they're going to have to use the South celestial pole star, right? And that's going to be down here beneath the South Pole. Make sense?
Now let's clear this out and let's summarize this one more time and try to make it clearer on the picture. So here's Earth, here's the Equator at zero degrees. For someone standing right here on the North Pole, here's the north celestial pole star, and their horizon makes an angle of 90 degrees relative to the north celestial pole star. As this person continues south, continue means starts walking southbound, you'll notice that as they do the pole star gets lower and lower in their sky. So again you start at 90 degrees, you start walking south, you're going to smaller and smaller numbers until inevitably you hit zero and then beyond 0 the north celestial pole star will be below your horizon, you're unable to see it. Right?
So here's my question for you. If I took you out, in the middle of the night and I said okay you guys you're grade depends on this. Tell me what our latitude is? And by the way, we're not going to be in San Diego. I'm gonna throw you in a car, in a bus, in a boat, on a plane. We're just going to go somewhere random. The only promise to you I'll make is that we'll stick to the northern hemisphere. Would you be able to find your latitude? This is a daunting question. You could say, "Okay Professor Yanow, all I need to do is find Polaris and then if I find Polaris I'm gonna figure it out." And, by the way there's a really cool way to determine angle and you can just simply use your fist. You don't in fact have to use a sextant. For example let's say you're standing outside and here's your horizon and let's say that there's a star right here. First of all what we're going to do is the following, we're going to count knuckles or fist i should say, one, and start putting hand over hand 123456789. So for me when I go hand over hand it takes me about nine complete fists to go from here to there. Well I know that that angle is 90 degrees so 90 divided by 9 is 10 degrees, therefore if I see Polaris in the sky and I start here for my southern horizon and I start counting upward then i can actually determine what the angle is of that star above my horizon by just simply counting the number of knuckle, excuse me, the number of fists that I have. It's not like super super accurate but it's better than nothing and I could probably round up or down to the half. So if we're at 32 degrees I can probably guesstimate 35 or to 30 pretty easily if I can find Polaris.
But the question now becomes, again, how do you find Polaris? Contrary to popular belief, Polaris is not the brightest star in the sky, in fact it's relatively dim and so in order for you to find it we need to come up with a clever way to figure this out. Well here's how we're gonna do it. Polaris is the tale of a tiny asterism called the Little Dipper. Now the Little Dipper is called the Little Dipper because it looks like a little spoon in the sky. The Little Dipper is an asterism which is actually a component of a constellation and this little dipper is connected to Ursa Minor which is called the "little bear". So the Little Dipper is part of the little bear. Now if you can look up in the sky and if you could find this tiny little spoon in the sky you could probably find Polaris but again the problem is Polaris is very very difficult to find and frankly finding the Little Dipper is relatively challenging as well. But what's not too challenging is finding the Big Dipper. And the Big Dipper actually looks like a rather big spoon in the sky and the Big Dipper is an asterism. It's part of Ursa Major which is called the "big bear". So all we need to do is find this big spoon in the sky and the very last star of this spoon we're going to follow it to the very first Star that it runs into and that first star is going to be Polaris. And so now you can go outside and find Polaris if it's a nice clear evening. And that is going to be the north celestial pole star.
Ok so that my friends is latitude. We have latitude. We know what latitude is. We know that latitude are also parallels and we know how to find latitude, at least to a certain extent Of course nowadays everybody's got their smart phones you whip out your smartphone you got your GPS unit on and voila you're going to see San Diego, California at 32 degrees north latitude. Yes? Ok so that's latitude.
What about longitude? Well let's draw this picture again. Once again there's the Earth and we'll put in here the Equator. And now what we're going to do is draw an imaginary line from the North Pole all the way down to the South Pole. Now this line is relatively arbitrary. The fact of the matter is with the Equator that was easy. The Equator is simply the dividing line between the northern hemisphere in the southern hemisphere. However with this line that we just drew we're also going to define this at zero degrees but again it seems to be arbitrary. There's a history to this which we'll talk about a little bit later on. We're going to define this line going from the North Pole to the South Pole as zero degrees longitude. So unlike latitude, longitude is going to give us east and west.
Now we're going to draw another imaginary line and if we draw this line going to the west we know we're in the Western Hemisphere. If we draw a line this way and we go to the east we know that we're going in the Eastern Hemisphere. Now this might be a little bit confusing and it's hard to see on this picture so you know what I want to do I want to erase this and start over again. So here's the Equator and 0 degrees and here is 0 degrees of longitude. I'm going to draw a sister image right here and on this image imagine that we're staring down on top of Earth and we're looking at the North Pole. So let's call this "NP" for the North Pole. Therefore this circle basically represents the Equator because again we're looking down on planet Earth straight from above so this line here is pretty much the edge that we're looking down upon.
Now this line that we drew here, it's right there. So we're going from the North Pole all the way down to the South Pole and again we're calling this 0 degrees of longitude. And if we go in this direction we're going into the Western Hemisphere and if we go this direction we're going into the Eastern Hemisphere. Now if we were to draw an imaginary line over here on the opposite side of the planet we've just made an angle of a 180 degrees. So remember with latitude we said okay well how many degrees are you going above or below the Equator to find your location, we're doing the same thing with longitude but in this case it's how many degrees are you going east or west from zero degrees of longitude, and by the way we're going to call this line a "meridian". In fact all these lines here are going to be called meridians and this line here that represents 0 is going to be called the Prime Meridian. So in this picture we've just gone 180 degrees west of the Prime Meridian. So we're going to call this 180 degrees longitude.
Now you might say well did you forget adding the west or east designator and the answer is no. The fact of the matter is if you go 180 you're neither east nor west you're right in the middle just like if you write 0. If you were to go this way toward the west and make an angle of 90 degrees relative to 0 then you would be at 90 degrees west longitude. If you went this way and made an angle of 90 degrees east of the Prime Meridian you would be at 90 degrees east longitude and so again it works in the same way the only difference is when we're dealing with latitude our numbers are going between 0 and 90 when we're dealing with longitude our numbers are going between 0 and 180. Makes sense?
Now here's something clever as well. You'll notice that opposite 90 degrees west is going to be 90 degrees east; opposite 0 is 180. What about something like 120? What would the opposite of 120 west be? Well here's a very very simple solution for you. The opposite of 120 west has to be 60 east. So this plus this always has to equal 180 degrees. By the way, San Diego, California will right around a 120 west so that puts us over here 32 degrees north latitude 120 degrees west longitude more specifically we're about 117.
Ok so remember all these lines here going north and south are called meridians; all these lines here going east to west but giving us north and south are called parallels, and you'll notice we just turned the world into a giant grid system this is called the "geographic grid" hence the name. Now, by the way, we determine how we can figure out our latitude and we can do that by looking at for the north celestial pole star if you're in the northern hemisphere or the south celestial pole star if you're in the southern hemisphere. What about longitude? Longitude is much more quirky and it's a little bit more complex and in order for us to figure out longitude what we actually have to do is use a clock and we're going to get to that in just a second. But before we do I'd like to look at north, south, east, and west in a little bit finer detail.
Let's say that you're a navigator and you're out at sea, and you determine that you need to go from, I don't know, 32 degrees north to maybe 33 degrees north. That's not that much, that's only but 1 degree but here's the caveat 1 degree of longitude and 1 degree of latitude if you're at the equator equals 69 statute miles. So imagine this: you're a navigator out at sea, you want to go from 32 to 33, you know that 69 miles, let's say that you're off maybe you're off by a half a degree for your destination all of a sudden you've missed your mark by about 35 miles. That's big, that's really big therefore we need to figure out a way that we can define distances a little bit more precisely especially if we're talking about latitude and longitude and if we're out at sea which of course is the early days of exploration.
Well here's how it's going to work. We know that 1 degree equals 69 statute miles, and i'm using the term statute because in a second i'm going to use the term nautical so statute miles basically is distance on land. Now let's say I want to break this down into a finer part well what I can actually do is take this degree and break it into 60 equal parts. So 1 degree is going to equal 60. What that is is an arc minute. So little tick mark so 1 degree equals 60 arc minutes and that equals 69 miles. Well now i can just do a little bit of math; I can divide 69 miles by 60 and that equals about 1.15 statute miles. So we know that 1 arc minute equals about 1.15 statute miles now that's not bad so when you look in your atlas and you see San Diego, California it won't say 32 degrees or it won't say 117 west. It will say like 32 degrees 25 arc minutes or it will say 117 degrees west 33 arc minutes, right, so those arc minutes are just simply giving us finer details and according to this map that we've just done we know that one arc minute equals 1.15 miles. So now if you're a navigator at sea, if you're off by only an arc minute you're only off by about 1.15 miles which is now not too bad but keep in mind that 1.15 miles could be the difference between your boat hit a big rock or your boat going into a bay so frankly we want to get this into even finer detail and we can.
So that's take 1 arc minute and again we know that one arc minute is the equivalent of 1.15 statute miles. By the way before i continue, 1 arc minute equals 1.15 statute miles that is what a nautical mile is. So 1 nautical mile is 1 arc minute and that translates into 1.15 statute miles and if you're talking about a knot, a knot is simply how many nautical miles you're going per hour. Right? So we're going to use knots and nautical miles when we're out at sea vs statute miles when you're out at land and again we see why we're using arc minutes or nautical miles because that just makes navigation more precise when were fact looking for more precision. Of course nowadays you're going to use a lot of decimal degrees and in decimal degrees its kind of decimal point representation of a degree but for now we'll stick with this arc minutes.
Okay so we know that 1 arc minute equals 1.15 statute miles which of course equals a nautical mile. We can break down that 1 arc minute into 60 equal parts. So 1 arc minute equals 60 arc seconds and we know that equals 1.15 miles. So again we're going to do just a little bit of math we're going to divide both sides by 60 arc seconds therefore 1 arc second equals 1.15 miles divided by 60 which is about two-tenths of a mile. So now we've got really nice fine detail. When you break up in your atlas and you find San Diego, California, it'll give you a little bit more precision. You'll have an answer in degrees, arc minutes, arc seconds. And again the more detail you want then you're going to start to see arc seconds because that gives you distance up to two tenths of a mile which is really quite precise or accurate especially if you're a navigator.
Ok let's do a little bit of trivia. Let's draw Earth here. Here's the Equator. Here's the North Pole, and again let's take a look at the perspective from looking straight down on the planet so here's the North Pole. And let's draw all these meridians. You'll notice as we approach the North Pole meridians are getting tighter and tighter and tighter together until inevitably all the meridians converge at the North Pole and the same is true with the South Pole they'll converge there as well. Let's say that at the Equator this distance here represents 1 degree or about 69 miles. As you go higher and higher and latitude clearly the distance between 1 degree gets less and less and less until eventually you're at 0. So if you are standing right here 1 degree of longitude is 0 miles. If you're standing right here 1 degree of longitude is 69 miles. Right? It's quirky but that's what's going on so the fact of the matter is we know that 1 degree of longitude equals 69 times cosine of whatever your latitude is, so if your latitude is at 0 degrees then we know that 1 degree longitude equals 69 times cosine 0 equals 69 If you're at 90 degrees latitude then we know that 1 degree longitude equals 69 times cosine 90 which equals 0 so we can actually use this little equation here to determine what a degree of longitude is as you go higher and higher and higher north or higher and higher and higher south and if you want to use the term higher.
Now this will become important for us a little bit later on especially when we start to talk about great circles and small circles. In fact, let me give you a quick quick example. Let's say we're here in San Diego, and so let's draw the United States of America. And here we are and that said that you want to fly all the way over here to England. So let's say we want to go to London, Heathrow which is way over here. Now that's a that you take this flight; it's a long flight and let's say you're line in a Boeing 777 and right in front of you, in the seat in front of you you've got a little TV screen and the little TV screen shows you a map and this map is going to show you the path with which the pilot is going to take to get you to your destination. Now you and I were going to look at this map and go okay well let's go to shortest distance and we would think that the shortest distance is going to be like this straight line. Well as it turns out that's not the case. The shortest distance on a sphere is going to actually look like this and that line is called a great circle, and so a great circle route on a sphere basically means that the center of the sphere is the center of that arc or the equal distant point of that arc, that's the great circle. So here around the Equator that's a great circle. Here is not a great circle that would actually be called a small circle. On a sphere the shortest distance is always the great circle and part of that we can actually understand by again referring to this whole idea of longitude. As you go to higher latitude your distance of a degree of large to get smaller and smaller and smaller until it converges at the North Pole and it turns to 0. So here you're flying this route you're actually flying a shorter distance on the sphere and that's what a great circle is.
Ok let's go back now. We know how we can determine latitude and again determining latitude is all about finding the north celestial pole star if you're in the northern hemisphere or the south celestial pole star if you're in the southern hemisphere. But what about longitude? Well in order for us to figure out longitude the first thing we actually need to do is talk about time zones. Right? So let's do time zones really quickly (see Part II for a continuation of this discussion).