 The global positioning system, it's awesome. No, seriously, it's awesome. Like think about it, right? Using a device that basically you keep in your pocket, you're able to identify your location on the surface of our planet to inaccuracy of meters. This is truly a remarkable feat when you think about it and is a testament to the capacity of the human imagination in Chile. So the global positioning system was launched by the United States Air Force, starting in, I think, I want to say, 1979. And it consists of, Got it, okay. Yeah, he's just using an error. It's okay, wonderful. Next one. So the global positioning system consists of a minimum of 24 satellites that look approximately like this one. This is about the size of a small bus and as we explain what it does, you will see why. There are 24 of these satellites in six orbital planes that crisscross the surface of the Earth. There are four satellites in each plane and they orbit at, that's accurate, they orbit at about 600 kilometers above the Earth's surface in what is known as medium Earth orbit so that each one of them travels around the Earth in something like six hours. And the reason for this, of course, is that each one of these, the reason for this, rather, this arrangement of having these satellites crisscrossing the surface of the planet is that it means at any given time, there are at least three of them visible overhead from anywhere on Earth. This is what it looks like on the ground, of course. In addition to the 24 satellites, in 1998 there were 27 operational satellites. Now I think there's slightly more than that. But most of them were spared. There are 24 satellites, the US can keep a global positioning system working, I think, between like 60 degrees south and 70 degrees north for basically the entire planet. So how does this work? Well, well you may ask. So the GPS works by a process of what is known as multilateration. And what happens is the GPS satellites are constantly beaming to Earth a microwave radio signal that contains a coded time signal. On board, each of these satellites is an atomic clock that maintains a very, very precise time measure. Very precise clock. And each one of these satellites is constantly beaming what time it thinks it is down to the surface of the Earth on a coded signal. Now, the GPS receiver knows to listen for these satellites and each satellite has a different code so it can distinguish which satellites it's talking about. Now, these satellites also transmit information about where in the Earth's orbit they think they are. So your phone, you're picking up these signals, picks up from each satellite that it can see some information about where in the orbit the satellite is and what time the satellite thinks it currently is. Now, that radio signal takes time to reach the surface of the Earth because the Einstein special theory of relativity teaches us that the speed of light is constant in a vacuum, which means that if that radio signal travels 600 kilometers or more to reach you, it takes some very short, definite amount of time to get there, right? Now, by calculating the difference between the time that the satellite says that that signal left the satellite and the time that it arrives at your GPS receiver, right? The GPS receiver can multiply that time by the speed of light and arrive at a distance in meters. Now, the problem is that if we only know the distance to one satellite, we don't actually know where on the Earth's surface we are. We could be anywhere on a large circle that circumscribes the Earth's surface that gives us sort of the maximum possible range from that satellite for the signal to arrive to us within that time. But if we receive the same kind of signal from multiple satellites, then we can progressively, and you can see here in this way, we can progressively identify our location on the surface of the Earth as being within a given range in three dimensions from one of these satellites, and eventually those circles, right, on which we must somewhere lie, will eventually intersect to some level of precision, and that gives us our location on the surface of the Earth, right? So, pardon? Triangulation. I'm sorry? Triangulation. Yeah, multiliteration. It's similar to triangulation, the math is slightly different. Also, it's not triliteration because typically more than three satellites are used, and the reason why is that your X position, your X, Y, and Z position represent three unknowns, but time actually represents a fourth unknown because the clock that's on your mobile device, or your GPS receiver, is not as accurate as the clocks that are on these GPS satellites in orbit. And so as a result, your phone or your GPS receiver actually has four unknowns to solve for X, Y, Z, in time, and as you probably know, system of linear equations, you need four equations in order to solve for four variables. So, a GPS receiver will need four satellites to get a lock on your location somewhere on the planet's surface. And the more spread out in the sky, they are the better because that means the more sort of precisely you can hone down the intersection of those circles, of those circumferences. Isn't the clocks in the satellites are actually going slower? Oh, yes, I'll get to that, I'll get to that. So, what this means, however, is that remember that the GPS signals that are coming to your receiver are coming from 600 kilometers or more away, right? And they're being broadcast by a gigantic satellite that has a very limited means of power, very limited transmission power. And that's why these signals are coded because that way they can be discerned from the noise. What this means is that these signals are extremely weak and your GPS receiver has to strain to pick them out of the radio noise. And so, GPS signals will not go through solid objects, they won't go through hills, they won't go through buildings, they for the most part won't go through trees. And so this is why your GPS receiver doesn't really work indoors because the building just eats the signal, right? And this is why your GPS receiver may not work if you're walking down a very narrow alleyway or if you're in a very densely wooded area, you may have trouble getting a GPS lock. That circumstance has changed significantly in recent years as GPS chipsets have become more versatile and more sensitive and better at picking out GPS signals. So this has become less and less of a problem. But when you do surveying with the GPS receiver, always remember you need a clear view of the sky in order to get the maximum precision and accuracy out of your GPS receiver. Now, as Mikhail was saying, there's something really fascinating happening here, right? Not only do GPS receivers operate on the special theory of relativity, which tells us that time has a constant speed in a vacuum, but they're also impacted by the general theory of relativity which specifies that time travels more slowly in the presence of acceleration, right? One of the other things that the general theory of relativity says is that gravity is a form of acceleration which is indistinguishable from any other. And what that means is an object which are closer to the center of the earth, objects which are further down in the earth's gravity well and are thus subject to greater gravitational acceleration, time moves more slowly for those objects than objects that are further away from the earth and hence accelerating less quickly. Now this seems like a weird thing because your feet are here on the surface of the earth and so you don't feel like you're accelerating but that gravitational pull of the surface of the earth is, as you know, it's constant, right? And what that means for us is that here on the surface of the earth, the same atomic clock will take 12, will run 12 nanoseconds longer, sorry, told microseconds longer per year than the same clock in medium earth orbit, right? So think about that. Two atomic clocks, one here on the surface of the earth, one in medium earth orbit, 12 microseconds difference over the course of a year which is a tiny amount, right? But it's exactly the amount that was predicted by the general theory of relativity over 100 years ago, which is really quite incredible and what's even more incredible is GPS satellites have to correct for it. They actually have to manually slow down the atomic clocks on GPS trans satellites in order to account for that difference because that 12 microseconds is actually enough to completely throw off GPS multilateration measurements otherwise and this is a really quite stunning validation of Einstein's general theory of relativity. I find it really exciting because it's like, that theory deals with such macroscopic phenomena that we don't ordinarily have an opportunity to sort of experience the effects of that directly in our lives but you have in your pocket already proof of the general, not proof, but stunning evidence for the general theory of relativity based on the way that the GPS system has to be manually corrected for the difference in speed between clocks and the atomic clocks on earth. So how do we actually use the GPS? Well, that's a good question. So back down to earth, hope you've now definitely learned something. Yes, so this is a process for actually using this amazing system to collect map data. First thing we generally do is download the existing map onto the GPS device. So on all the GPS's that we have and I have six of them for us to all team up with, there is an existing map of the entire country of India on the map, so first step because you don't need to recollect data which already exists. Then go out into the world. This was a moment when I really admitted that I truly was a geek. This is my mapping setup from a few years ago when I lived in the UK. On my bicycle, the GPS is mounted in a clipboard where I would be taking notes as I went along. But the point is you should get out of the world and it's a really interesting way of like exploring your surroundings. You'll definitely see things that you haven't seen before if you are going out with the idea of mapping what's there. These are a few of my notes. Some people, you know, take maybe right down to the number of the GPS waypoint and then make some notes. I would try to sketch, when I was doing streets I would actually try to sketch out the street grid and use that as material for when I came back into editing. This is Jawsome which we'll use in a little bit. You load in the GPS traces which you can't see and you have your notes in together. You combine those and actually sort of like and say Illustrator actually traced out the streets and the points of interest. Make a map.