 Last time I mentioned to you the levee breaks in New Orleans and what I Brought here was a photograph. I found this the most interesting photograph of the levee breaks That's there So I described this to you in words last time about the levees being this reinforced concrete and how they broke See these things aren't bent or curved They just broke there what actually happened was they were dug deep into the into the ground as the water pressure built up The ground begins to get begin begin to give way and this thing started buckling out like that started being pushed out When you take something that's straight and push it out it tends to break and it breaks along the expansion joints So there are lots of things that could have been done fundamental problem is You never know where to spend your money and A lot of money that could have been spent on this wasn't spent on other things which didn't happen So let's see should I give a quiz today no no quiz today Sorry, I know many of you were counting on that Gravity odd thing I Mean the first thing to ask is I Mean, you know the old story that gravity is the tendency of things to fall down We understand it a little bit better than that now I Aven before Columbus sailed people knew the earth was round the only dispute was over how big it was and So people knew that gravity was the tendency of things to fall towards the center of the earth It was Newton Who I've actually looked into this story. It may actually have happened that he watched an apple fall and This was gravity and he looked up at the moon and he realized. Oh It's gravity that's keeping the moon going around the earth That must have been one of the most exciting moments in his life Suddenly realized that maybe it's gravity that keeps the moon going around You would think that the moon which is going around the earth it has this velocity So why doesn't it just shoot out that way? Why doesn't it keep on going in a straight line after all once in motion things tend to stay in motion and the pull of gravity keeps it down Now Let me illustrate this. We're really getting into how satellites work the fundamentals of satellites so Little hose here. I'm going to shoot some water If I get this to work Because I'm shooting water horizontally and it begins to fall Probably goes things tend to fall Now If I tilt this back The water will go further may go off the edge if I don't Turn it down a little bit Let me turn that down a little bit Look at that pass sort of a whoop, you know a hill shaped thing. The path is actually if you ignore the air resistance, it's the shape of something called a parabola and It's not the water is moving this way and if there were no gravity we keep on moving But this is gravity gets pulled down and it goes in this curved path So gravity doesn't now imagine just for a moment That instead of this being 120 centimeters was 12,000 miles and so the stream goes up like this and it's being pulled down 12,000 miles away. The only problem is it wouldn't hit the earth Would miss so here we are on the earth here. We are shooting our water off and it starts to fall Well now it's going horizontal again, so it keeps on falling But it's the earth is bending away from it so even though it's constantly falling it never hits the earth and This is what Newton realized the pull of gravity will hold it in But if it's going at at the speed where it will never hit and then it'll actually go around forever Like this in some ways. This was one of the first Unifications of the laws of physics You probably may read about that in the newspaper people are always trying to unify the forces of physics those back 1600s I guess and Newton Unified the laws of physics what he recognized was the two separate laws the law of gravity and the law of the moon going around Celestial motion was actually just a manifestation of gravity And I like to think back in history and try to imagine what it was like before you understood that Now we take it for granted because you learn it, you know when you're two years old This is the interest. I don't know how many people here throw the discus or a shot foot or something like that But one of the interesting questions that's kind of fun is what angle should you do it for maximum range? Okay, some people said 45. What other answers do I get? 30 is that a guess or an answer? It's a guess anybody know Yeah Should be 45 Anybody else know Last semester when I taught this course there was a shock putter in the class I'm trying to remember the numbers. I think I put them in a text. It was Less than 45 for the shot quick discus. I think it got down to around 41 reason was because of air resistance So in in real athletics when there's really air out there if you do it with there's no air I guess you do it differently, but Watch what happens Here is horizontal so it starts falling and hits if you let the white line be the ground that hits the ground right Away, I tilt it back. It spends more time in the air because it's going upwards now before it hits the ground And some of its velocity is horizontal so it goes further. I tilt it even more Now what's happening is it spends more time before it hits the ground because it has a larger component of upward Because some of the velocity is going upwards If I could move this thing if I could run with it, but let's put it another way Let's say we all ran with it Let's leave this here and all run this way and I'll watch this water What I would see was that here's the water and it's going up and it's coming down That'd be a relativity experiment If I were to do that we'll do a demo of this in a moment But here's something I'd like you to think about it's not at all obvious But if I were to do that Suppose I said had this water with the same upward component of velocity if this is moving upwards at you know Ten centimeters per second, I don't know how fast upward the velocity is if I if it had the same upward velocity We'd get to the same height and would reach the level at the same time Let me do that another way I'll demonstrate with this chalk here. I am I'll lift it up It takes a certain time for it to come down If I throw it about this high it takes a certain time to come down and watch this I'll do the same thing the claim is if you measure this accurately You'd see it took the same time to me. It's obvious because to me. I'm you know, you're moving not not not not not me Your your whole classroom was moving to the side And I'm throwing this thing up and it comes up and then it comes down I catch it and if I stand here it throws it up comes down I catch it the fact that it's moving sideways doesn't affect its vertical motion. This isn't that's any inside in physics So here they'll it takes longer to come back down because it has some of its velocity is directed the upward direction Now I can put all the velocity in the upward direction and it takes a long time to come back down But it doesn't go very far in that time because so little of the velocity is in the forward direction so in the absence of air Some of the students already knew the optimum angle is 45 degrees, but in the presence of air It's not you all know if you want to throw a frisbee for maximum range. You don't throw it up at 45 degrees a Shot put is closer Than most things to that that ideal But even the discus Here's an odd thing. I learned about the discus well known to do any discus throws in the group here I don't think we do but the oddest thing about the discus is the record to a set in a competition in Which the wind was blowing now, you know most sports Make it you don't you can't set a world record when the wind is blowing, but with the discus you can So the discus players who set this they all know the secret to take maximum advantage of the wind Usually when you're throwing the discus There's a certain angle over which you can throw it the wind is coming from that direction you throw it right into the wind That really surprised me When I learned it last year last semester But the reason it works is if you throw it into the wind You can move the discus in such a way that it stays up longer But the wind coming to it holds it up in the air longer it winds up going further So these things are tricky and complicated and most physics professors don't know that you should throw a discus into the wind And I didn't even know that until last semester Things are much easier when there's no atmosphere the air makes things complicated Newton worked out the case when there was no air Air introduces friction friction is hard to understand a lot of physics We'll talk about those realms in which we don't have air. We don't have resistance question You're saying it's actually the question. He says that for artillery the maximum is actually 45 degrees. That surprises me I would expect it to be a little bit less So the question is why is this and he wants me to explain why this answer that strikes me as being wrong is correct And I find it hard to answer that You're telling me figure out why you're wrong and then give the explanation I Find that hard to believe my guess is what would be less than for a little bit less than 45 degrees You have a very massive thing the air resistance is not very much and maybe the 45 degrees the rule of thumb But typically one uses tables in order to estimate these distances in the military or these days a computer and 45 degrees probably what I would guess that was an old rule of thumb because it's close because these things are so massive that the Air resistance doesn't play that much of a role at least for short distances, but I I would I'm willing to Bet that it's not 45 degrees a little bit less We can try to resolve that So the satellite opposite in this way now now think about this what it means So this water here is being shot out or Hello Take this chalk here now watch it once again now. I throw it up and it's falling Okay, now I throw it up and it's falling It was falling even though it was moving in an arc this water is falling even when it's moving in an arc This satellite is falling even when it's moving in an arc think of a satellite as something which is in perpetual state of falling Now what happens when you fall? What does it feel like when you fall you've all fallen if you fall a short distance most of what you feel is the ground if you feel if you fall a larger distance and Typically we I do this when I was a kid, you know, I jumped off something high just to see what it was like It was very scary. We have an instinct not fall We know that the ground comes up really fast. How fast does it come up? I put down a number here For every second that you fall Let's see did I put it up here? You've gained 22 miles per hour miles per hour For every second that you're full is called the acceleration of gravity It's given the symbol G G is 22 miles per hour Every second so if you're falling for two seconds you're going 44 miles an hour 22 miles per hour How fast is that that's about as fast as the fast run it can run You can run a little bit faster than that the real the real sprinters But if you go fast you're probably about 22 miles an hour So you fall for one second imagine yourself running as fast as you could possibly run into a brick wall That could do an idea of what it's like 22 miles per hour doesn't sound like much but into a brick wall it hurts After two seconds you're going 44 miles per hour two seconds 66 So you see your gaining speed every second that's called acceleration Little bit of an aside here now Let me give an illustration Some of you may wish not to listen to this Because it may just confuse you So be prepared to forget everything I say in the next two minutes or so Physicists Take this and they prefer the units G is equal to 10 meters per second Every second because 22 miles per hour is about 10 meters per second That's number they use and she's 9.8. Just so that you have more fun with your calculator 9.8 is more accurate now. They usually refer to this as 10 meters per second square Just because that's fun with math you have a per second per second pull out per second square And you start thinking about square seconds This is where a lot of students just leave physics But really all it is is the speed you gain per second and it's no such thing as a square second That's just the way the math looks when you do it that way, but so this is the number 10 meters per second Every second that's the number that we I'll use when I do some calculations That's the acceleration of gravity here at the surface of the earth If you are in space and you are falling towards the earth you better make sure that you go fast enough horizontally So that by the time you fall down the earth is also curved away and that takes about 8 kilometers per second So it's called the orbital velocity This is what's orbital velocity for a low earth orbit Or a Leo. I'll explain what I mean by this in a moment Be advised that I found the mistake in the textbook It was a place where I discovered when looking at it last night that I had dropped the factor of 10 and So this morning I posted a new version of the textbook with a calculation for a low-earth orbits fix It was just one minor calculation having to do with how fast a satellite passes overhead And I caught that error. So I Posted that new one so so if you're going eight now imagine what it's like to be falling But you're in orbit. So you keep on falling So the way this works it Suppose I Okay, there was there's an amusement ride that I went on a few years ago They've changed the name since then but it was at Marriott's great America. You know what they call it now But now it was called then the edge. I'll never forget the edge It was a wonderful thing All amusement park rides designed to do one of two things you either made designed to make you sick or To really scare the living-day lives out of you Some both maybe Anyway, the ones that are designed to make you sick. I stay away from I kind of enjoy being scared now and then so I The edge was supposed to be scary. So I tried that And it's a tower and have some tracks on it like this And a little elevator you get inside here and it's an open elevator You're looking right out and you take you up. I think it's a probably over a hundred feet high Anyway, and then then what happens? There's a little mechanism and the elevator moves out over here and it has some things loosely holding on to this track But basically you're suspended there in space and then without warning they release you Okay, and so you're free fall And it's only a second and a half or something like that But it's more free for the most free fall I'd ever felt before was once I jumped feet first off a high diving board I said once So when I went on the edge, I was prepared to do a physics experiment I wanted to sense the weightlessness for over a second So I had with me something like this and I was going to As soon as I fell I was going to let go of it and I would see it float in their weightlessness and then What happens is because of these rails you only free fall about this far and then the rails Gradually come like this and you want to stop and feet first down at the bottom so I will now try to give you an idea of What this experiment was like Okay, so here I was on the top looking out over the country side looking kind of Hi, okay, here we go Oh That's an accurate depiction What happened? the experiment was not successfully carried to fruition and I Discovered that I have an extremely deep instinct to grab something when I feel like I'm falling and it's probably very deep survival Instinct that we've had over the years. He's if you're falling grab for something But I wonder about the astronauts because you see if you're in space you're constantly falling and And so If I were in space, I'd take this thing and I'd let go and it would just float there in space Now in fact, we're falling you see when you're in orbit around the earth You're still feeling the force of gravity You are falling just like I was feeling the force of gravity when I was falling down the edge It was the gravity that was accelerating me But I feel weightless What does that mean it means there's no force on my feet see right now The only reason I'm not going through the floor is the force of my feet is keeping me from going down there But when you're jumping there's no force on your feet This is a weird thought My tongue is on the bottom of my mouth. I Don't know that's because it weighs something If I were weightless, it wouldn't be my internal organs would all be sort of floating inside of my body This is what gives you that strange feeling when you jump off something of The feeling of weightlessness you're all fall when everything in you is falling together That means you feel weightless and The astronaut is not outside of your gravity. The astronaut is simply constantly falling So having been through a second and a half of falling I Found myself in a count conversation with Sally ride the astronaut. I Had to ask her about this. How can you stand this for? You know for I wanted to ask her how you be up there for weeks So I said Sally let me tell you about this thing called the edge that I was on and and so You go up like this and there's some tracts and they move you forward like this and then they release you and she went That's scary So wait a minute. Oh, no, no, no. No, no, no. Look, hey, you were you were you were weightless You were you were weightless for for a week How can you say this is scary and she said oh you get over there for the first second or two So it's only the first second or two. That's really scary So this is this is this is gravity and this speed is the speed you need so that the pull of gravity Which accelerates you downward So it when you put a force on an object it starts moving Typically if you put a force on an object it will move and if you keep putting the force on it He keeps on moving faster and faster it gains a certain acceleration For the force of gravity the acceleration gain is 22 miles per hour every second If you put a bigger force on it, it will accelerate more You want to know how fast it's going you say how long is that force on it and how big was it? well, actually This is the equation if you have a force And you'd like to know the acceleration What you do is divide by the mass And that gives you the acceleration Depending on the units typically these units are designed to give it to you in meters per second But if you remember that that one meter per second It's 2.2 miles per hour You can translate it. I mean in Europe meter, you know, what's what's the velocity a meter per second? Well There's I'm going you know a meter every second. That's that's a meter per second. It's a nice number 22 miles per hour 2.2 miles per hour is also going 2.2 miles per hour and a really fast walk when I'm really in a hurry I go average three miles an hour When I'm taking a nice vigorous walk that I go two miles an hour Backpacking I typically average one mile an hour 60 pounds on my back But if you put a force on an object That out that object will it's going faster and faster as long as that forces on there just like the something falling in gravity gets going faster and faster as long as Well, it doesn't happen for the astronauts because the astronauts always changing its direction and and although the force of gravity is Actually turning the direction of The astronaut as opposed to speeding it up It'll wind up going the same speed as it goes around So force can also change direction of the object as well as making it go at a faster speed So this is the basic equation and it says if you put a force of gravity on me. Well, what's the force of gravity on me? It's the pull of the earth on my body, that's what we call the force of gravity. This is Newton figured out That the force of gravity is actually a force of attraction between mass So for example, if you have your When it's a big mass here and they and you have you with your little mass here That every atom on the earth Is pulling on every atom of you. You're also pulling on it You're pulling it up. Now you may you know you say hey, you don't have much mass So you can't pull very much. They didn't hit a lot of atoms here you're pulling on you're pulling on all of them Amazing thing about gravity is it goes right through things More effectively than even neutrinos You're pulling on atoms right now on the other side of the earth They're far away, so it's not as strong. In fact, the your force of pull depends on the distance The rule is given here the force of pull goes as one over r squared So we say the force of pull for gravity. It's a bunch of constants G as a mass of of of the first object mass of the second Divide by r squared. I'm not even going to ask you to know this. I what I do want you to know I but you may want to play with this Because it says it's something that's twice as far away this gravity between my two hands right now The masses of one hand first hand and the second hand are kind of small When you plug in the constant here and and so the force isn't very big G is 6 times 10 to the minus 7 if I remember correctly So the force of gravity isn't very much But if you have enough fists and have a whole earth native fists Then it all adds up So we're being pulled in every which direction by gravity But because the earth is a sphere it all feels as if I mean the sideways forces tend to cancel that thing over there That thing over there are pulling me in opposite directions where they cancel each other So the net effect is this as if I'm being pulled straight down. Let me show you that again. Here's the earth Here am I Every bit of mass is pulling me in its own direction These forces are weaker than these because this is closer and the close forces have more force It's the one over r squared you go twice as far away the force is one quarter go a hundred times as far away The force is one one hundredth squared, which is 110,000. So most of the forces coming from nearby stuff And that's pulling me straight down Now suppose The earth is not a completely uniform sphere like this Suppose there's a hole over here. What do we fill that hole with? Well, you could fill it with vacuum, but those don't really exist. Let's fill it with something. That's much lighter than rock You could fill it with rock, but then it wouldn't be a hole Fill it with something that's light like oil So let's make this oil Now look at the gravity on me The rock over here is pulling me down this way. The oil over here is pulling me, but not as much They no longer cancel So if I have a very accurate meter, I can search for oil By looking at the gravity anomaly The fact that the gravity is no longer straight up and down But that the rock over there is pulling me more than the oil over there So this is one of the most effective methods being used today in searching for new oil deposits is using gravitational mapping So they make maps Here's a map. This is a map that was that was It's a gravity map now. Okay, you measure the strength of the gravity if you measure the direction of the gravity That's harder to do than just measuring the strength So typically what they'll do is they'll fly an airplane and measure the strength of gravity and Then if there's some oil around it'll be less because this nearby rock is missing Now what they do is they fly back and forth over the land making a map of the gravity Then they're looking for strange things that might be under the ground things that have more gravity or less gravity more gravity might be a Lead deposit or uranium less gravity, which is where it's mostly used is for the oil industry Yes, now once you've done that you measure the gravitational strength everywhere. You can assign it a color and Say the you know blue is low gravity green is high gravity And you make what looks like a map and it's a gravity map It's a representation of the strength of the gravity and if you say high gravity you can even contour it So it looks like a hillside. Here's a gravity map This isn't a textbook. There's a gravity map and There's something very interesting in that gravity map. Look at that mound right in the center But that looks like rings How big is this thing? It'd be amazed but there's actually a scientific debate over how big this thing is as if it matters Why is there a scientific debate? Some people say this is the biggest ring other people say no no see that out there No, there's evidence of a bigger ring. Why? Well, it turns out this is in Mexico and this photograph was taken over the Yucatan Peninsula and You can't see the peninsula here because it's measuring gravity not ocean The ocean is pretty shallow there anyway, but but here's ocean on this side, and this is Yucatan on this side and This is a structure that we now know was created 65 million years ago This is the location of the impactor of a comet or asteroid that wound up killing the dinosaurs and extinguishing most life on Earth and The way this ancient crater was located 65 million years ago You get a crater doesn't stay a crater it gets filled in with water and the sediment begins to fill up and pretty soon You don't see much of a crater there This gravity map allows them to find the crater because the sediment that filled it up had a different amount of mass different density then the material Then the material that was Was there previously so this is how the crater that killed the dinosaurs was found this By gravity mapping gravity mapping I've seen it used very effectively Find tunnels That go from Mexico into the US for smuggling drugs They have gravity maps now. They put them in a car the ones they have now actually don't work so well What they have to do is they have a suspected tunnel somewhere along here They put the car here and they wait there for 15 minutes measuring the gravity Then they move it a little bit further and measure the gravity very slow But they are improving the technology very quickly because this is already found at least one tunnel There's a 300 foot long tunnel that went all the way from the Mexican border from a little shack that was 50 feet on the other side of the border to a tiny little shack that was several hundred feet on the other side Being used at night and they found this by looking at the gravity So when you're over a tunnel, it's a little bit less gravity because of the earth not being there Now an odd thing about this Usually we assume the gravity The earth is pretty what is pretty spherical. It takes very precise measurements to see any difference than that and so the net effect is that the gravity is coming from straight down and One can show by using the mathematics And you get exactly the same gravity if you put the entire mass of the earth At one point and up here just had a hollow shell that you still stood on And you feel exactly the same gravity as you do with the filled up earth as long as the total mass was the same This is a point that confuses a lot of people So I mentioned it Partly because it helps you understand black holes In a key way that many people misunderstand Let me say this again If you're standing on a spherical surface like this, you feel the force of gravity You'd like to know how big that force is going to be you it's hard because you got to add up all these things that's a three-dimensional integral and You can do it. I've even done it but There's this rule of thumb that works and perfectly correct. If this is a pure sphere Then it's exactly the same force you would get if all the mass were at the center Now the reason this relates to black holes Is the following Suppose here's the Sun. We haven't really told you what a black hole is. We'll be getting to that soon too Here's the Sun and here's the earth going in orbit around the Sun constantly falling by the way We go around the Sun. We're like falling towards the Sun except we always miss it We wind up going it's not quite a circular orbit. The orbit is slightly egg-shaped. We call it elliptical But only about a couple percent and one I think a little over one percent The force of gravity is the same that we would get if that Sun were simply a point mass Located at at the center the fact that the Sun is spread out doesn't really change the gravity does a little bit Because the Sun isn't completely uniform But approximately very closely Approximately, it's the same as we'd get from there now suppose the Sun Where to suddenly collapse into this thing called a black hole which I haven't haven't described yet? One startling conclusion a black hole is something which has the same mass But in a very tiny volume black hole if you took the Sun and stuff all of its mass into something the size of the earth Then you would have a black hole And you could ask what would that do out here if there was a black hole in here Answer turns out to be nothing. Well, we wouldn't have the sunlight but other than that gravity would be the same See with the same distance from the center And a black hole having the same mass as the Sun Would be the same gravity Science fiction sometimes gets this wrong the thing a black hole sucks everything in well it does if you get really close If you land on the black hole, you know, we have all this huge mass Let's let's go in here. Let's say this thing turning to a black hole We have this huge amount of mass that's all stuff to the size of Berkeley So here we have something the mass of the Sun and the distance to the center if we get to the surface It's just five miles instead of it being 93 million miles And so if we use our gravity equation, which you don't have to know There this gravity equation We're the same mass as we had before but now we've made arm much smaller. You divide by a small number and you get a huge force So the key thing about a black hole is that you can get super super duper fast. I guess I just bore some people Okay Now what is a black hole? Well, I Mentioned this thing here about going to orbit around the earth. How high do you have to go to orbit? I'm going to talk now about different kinds of satellites about escape and about black holes So the first question is how high do you have to go to orbit? And this is an important fact that many people don't appreciate The answer really has very little to do with gravity it has to do with the earth's atmosphere If you try to orbit suppose you're on the moon Let's see. Let me find a nice board here. You may have seen things like this on the moon Here's the moon. Suppose you want to go into orbit above the moon. How high do you have to go? 100 miles a thousand miles Well, actually one inch would be enough Except you might run into a mountain The main problem with orbiting the moon is avoiding the mountains You don't have to get up high Because all you have to do is to make sure that as you fall you keep on missing But on the earth we have this atmosphere at the bottom if with all this atmosphere on the earth If you go if you go eight kilometers per second pretty soon, you'll slow down just by roll the air resistance So on the earth the only reason you have to go up high to orbit is to get above the realm of the air resistance That's the only reason how high do you have to go? Well, you know depends on how long you want to stay up Some people say a hundred kilometers Well, in fact is if you're orbiting at a hundred kilometers You'll probably come down after one or two cycles because you lose speed against the air once you lose speed You fall the same amount But you don't move forward as much I'll demo. I'd like to show on this We have our volunteer monkey up there and he has agreed to Let go of the tree and fall to the ground In exchange for that we're giving him a little bit of food So I've gone here designed to shoot food for the monkey to catch And I'm aiming this right at him. So there's my laser sight aimed right to his Aimed right to his arms By the way, and people took this course previously may have told you about a demo that we used to do calling shoots the monkey But we don't do that anymore. Now we feed the monkey Okay. Now if we were in space The light beam is going in Actually, not quite a straight line. Why isn't the light beam going a straight line? It turns out it's bent a little bit by gravity But we it's not enough to be measured here because it's going so super fast going so much faster than bullets go so because of that It's it's about it's about a straight line and if we were in space I would just shoot this at him and he would catch it and have his little bit of food But because there's gravity here The thing will start falling now I think of falling as being with respect to where it would be if we're in space It's instead of being in that straight line. It's now falling from the straight line. It's just like the water here What's going that way, but it starts to fall this thing will fall too How much will it fall? Well depends on how much time it gains? 22 miles per hour down the velocity every second suppose it takes a second to go there Oh, by that point it's moving downwards at 22 miles per hour and it's somewhat below the path What about this monkey? Well, if I can get him to let go at the same instant that I fire Then he will also be going down at 22 miles per hour every second And we take the second to get there. They'll be at the same spot So as long as he releases that exactly the same instant I have here He should be able to catch the food Okay To help them do this we put a little wire right across the gun here. I mean the food liver and When the when the bolt the the banana comes out it breaks the connection of the wire That then turns off a magnet, which is right up there So he doesn't have to think about it. He'll just start falling sort of like me on the edge and If he has his act together he can then catch the food So let's see if I can do this I lost my reading glasses make sure I was said, okay, okay So let's turn up turn. Oh, we're gonna actually shoot that. I mean shoot the banana with air pressure. So Kind of the air pressure here and we'll suddenly release the air pressure That will put a force on The bullet I mean the banana or the food and that will accelerate it outward It will accelerate as long as there's a force on the forces gradually decreasing because the gas is expanding So the pressure isn't quite so much so it's most of its acceleration here, but the acceleration depends on the force That's F equals ma which is Newton's fundamental law of physics Now, let me turn this Don't want it to come out too fast Okay About where I want it now we were we're going to see if this were in space that'd be a straight line It would go right to them. They're both falling but the claim is even though this is going horizontally It's falling at the same rate with respect to its path that that guy is 22 miles per hour every second So let's see if I get this to her. You ready? Watch the monkey watch the gun watch the combination see what you can see Well, we're fine except he forgot to catch it. We did hit the monkey Okay, where that ball good. Did that anybody find that? Oh, there it is. I don't blame them It's not very edible. No wonder he didn't catch it Okay So let's get back into space now. We're talking about talking about orbiting Suppose and so you could orbit just above the surface of the earth If it weren't the atmosphere so you have to get above the atmosphere how thick is the atmosphere not very much you go up Go up about five miles and you have half the atmosphere Go up Mount Everest and the and you have I think 40% of the air that you have down here So I have to go higher than Mount Everest but it falls off it very rapidly in a way that that will falls a Half-life rule If you get up to 100 kilometers, it's not really enough, but you get the 200 kilometers. It's pretty good So to go into orbit the first thing is get above the atmosphere The second thing is get enough speed that you can get all the way around How much energy does it take to do both of these almost all of the energy is to get above the atmosphere? That's the heart. I'm sorry to get the speed getting above the atmosphere isn't that hard It was done many years ago with the v2 rockets And so getting up is not the hard part, but getting that speed. I actually work out the numbers in the book and See do I say it here? Yeah, it takes 30 times as much energy to get the speed up as it does just to get up 100 kilometers You have to do both so if you're going to get to the speed getting up 100 kilometers isn't that hard Typically you'll watch the rocket take off vertically Get altitude and they quickly start turning because what they really need is the speed and It takes 30 times the energy. That's that's more than five times. It's just going straight up to 100 kilometers isn't much Amateurs can do it. It was an amateur competition with rockets. It was done by Goddard in the 1940s But going horizontally to that speed you have to have 30 times the energy that typically means 30 times the fuel That wouldn't be so bad 30 times the fuel. It's only 30 times figure out. No, it's not 30 times bigger The reason is you got to get that food the fuel it isn't exploded all at once like in a gun But it's exploded slowly so you have to have enough fuel to carry the fuel up So that you can release the fuel gradually so that that's that the acceleration is low enough that you don't crush the astronaut So getting someone into orbit is enormously harder and getting them up to 100 kilometers You wouldn't guess that if you'd been following with any excitement the X prize competition The X prize competition is something that was In the newspaper about a year ago They wanted to have a private company get humans into space So how do you get them into space the trick was you had to be able to hide them up to an altitude of 100 kilometers in a rocket and so the X prize was finally one last year or a year ago about a year ago by a company that managed to get people into space and if you think about it They did the easy part getting up on your kilometers So the things that that got it that we did with a u2 not a u2 with a v2 rocket back in in the in the 50s But there were nowhere near getting into orbit because that requires that horizontal velocity Nonetheless the X prize got a lot of newspaper coverage I think by people who didn't know the difference But don't the people who won the X prize know the difference. Yeah, they know the difference Therefore, they're not intending to ever put anybody into orbit their vehicle is completely useless We're putting people in the orbit would have to have delivered 30 times the energy So what are they going to do very interesting think of Jurassic Park? What do you do when you have a scientific breakthrough you make an amusement park? So what they intend to do with this rocket is to send people up a hundred kilometers When they come back down they can certify that they are now astronauts So you get wealthy people who will go on this ride so they can say I'm an astronaut and That's how they'll make a business model out of this, but they're not going to get things into orbit this way If you want to go Into a higher orbit and you frequently do why? Well, let's take a look at low-earth orbit and let's look at some of the numbers in the low-earth orbit You're really close. That's really useful which want to be a spy. You want to spy satellite one of a camera You want to look at the Kremlin or or or the Beijing or wherever North Korea We want to look at North Korea and see what sort of nuclear things are they building these days from a satellite So what do you do? Well, you don't want to be way out here thousands of miles away Any more than if you're taking a picture of your boyfriend or girlfriend you want to stand back a hundred feet and they're getting real close So the cameras have to be in close they make them as low as they can typically 200 kilometers So here we have something whizzing overhead at a height of 200 kilometers and let's look at that number This is a very important for future presidents Very fundamental result So here we are and here's the earth and here's the satellite going over an altitude of 200 kilometers and It's looking at this little nuclear plant here to see whether it's getting electricity You know you can tell some things a big power plant You can look at the electrical lines going in you could try to measure how much heat is coming from this using invisible light Something that we have a whole chapter devoted to later on in the semester So you want to you want to study this as best you can using whatever remote sensing techniques you can now here's the problem You're moving eight kilometers per second So you don't stay over it very long How long do you stay over it? Well, let's just draw some triangles here here You're approaching it and this is 200 high. This is 200 that way. This is also 200 So you're going to get you're over it for basically 400 kilometers I mean, yeah, okay. You're over there too. You can still see it. You're so far away You can't take good pictures. So the useful amount you're over for only 400 kilometers You're going eight kilometers per second. So you cover those 400 kilometers in 50 seconds about a minute So the spy satellite is over the location for about a minute. I want you to know that a Lot of people think spy satellites can hover No, we use airplanes for that Or drones we use non-human airplanes now I mean, you may have seen the news a few weeks ago that we took some shots at at the second al-Qaeda figure Zarkawi Zawahiri Zawahiri and and apparently missed because he came on television making fun of President Bush yesterday You know, haha try again that was done from a low-flying airplane It was it was Without any human it has TV cameras it can hover it can watch and it can shoot It's called the predator So the predator is an airplane, but the satellite doesn't hang around for more than a minute So what happens in North Korea? Well, let's take a look at the earth now. You have to get within 200 kilometers Here to see it likewise you better not be more than 200 kilometers off to the side so if we have a big picture of the earth here and I don't know here's here's Korea Japan and so on and the satellite is flying over Very close to the surface because you want to be a low-earth orbit Just hugging the surface. It's over it for one minute. Get all the pictures you can Now the satellite goes in a circle and it comes back, but by that point the earth is turned At eight kilometers per second, how long does it take to go around the earth another number? You should know it's about an hour and a half to go around the earth You work that out. I mean it's 24,000 miles around and So it's nothing turns out to be about an hour and a half so When it comes back unfortunately North Korea isn't there anymore because the earth rotates it's An hour and a half. It's probably Well, it's 24,000 miles around with the equator in an hour and a half Up here where where North Korea is rotating around. It's probably more like 15,000 20,000 miles Let's say 24,000 miles. It's going a thousand miles an hour. It's a couple thousand miles. It's a thousand miles away 1500 miles away. It's so far away. You won't see it on the second orbit This keeps them going around The earth meanwhile rotates bummer, how do you spy with these things? Well, it's not easy Well put more of them up there, how many do you think we have up there? How many spies are I still we have up there? Numbers classified but people on the web try to keep track of this and They claim the number is just a few like three So not easy to watch the world from a satellite What about Google Earth? We're the entire earth Satellites well a couple things in Google Earth one is the pictures They're kind of out of date Now you look at them and you see oh two years ago if you by the way if anybody here hasn't used Google Earth It's one of the most fun things you can do I mean you you you know you put in you put in your address and it Fly and it starts off wherever it is I know maybe maybe in the maybe went to Mount Everest Then you say you put in your address in Berkeley and then we can show it sometimes And you go zooming out and you go flying over and then you land right in Berkeley and zoom right into a close-up of your house Really a wonderful free program But those photos are old and they were taken a high altitude and if you try to see any of the details of your house You'll be disappointed you could probably identify your house But you you won't be able to identify any automobiles to not read license plate numbers Now we'll be talking about how good you can do when you get up close it depends on the physics of light and I'll show you that that you probably will never read license plates From space, but you get close But if you really want to track Osama bin Laden, you need something which is lower and closer to do that So this is serious a lot of people simply assume the USS Allied coverage of the whole globe and The numbers are so far from that But you need to know that So the issue of how do you dwell well? What answer is you go into a high high orbit now? This one is actually called the medium-earth or any oh Maybe 12,000 miles up and maybe you orbit then a couple times a day instead of every hour and a half In that case you'll be up here for quite a while You can also go to a high orbit here Suppose you go to a high enough orbit That you go around the earth once a day and let's choose it over the equator So here's our high earth orbit. That's right above the equator Now we do it just right the earth is turning this way. We're up there. You'll stay above the same place It's about 22,000 miles up It's only one tenth of the weight of the moon. It's five Earth's radii up there But now you're in an orbit that has its own name called geo Geosynchronous with geosynchronous it has to be above the equator to really be truly geosynchronous. Why is that? Well, if you're above the equator Watch it. Here's the orbit above the equator Looks like Saturn, right? So here's the above the equator and and the earth is turning and you're moving You're a higher so you're moving faster than the surface of the earth, but you stay above the same point all the time Okay, suppose you're up here. What do you have your orbit like this? You go around once per day Well, right now you're right above that spot But this thing moves over here and you're moving down here pretty soon. You're in the southern hemisphere So the only way to be truly geosynchronous is by staying above the equator This becomes a very important international issue reason is It gets kind of crowded We are filling this place up with geosynchronous satellites. What do we do with geosynchronous satellites? Well weather satellites for example, if you look on the web and you find a weather satellite for Berkeley You'll see a photograph that's updated every few minutes But they have a satellite that's dedicated to the West Coast Another satellite that's dedicated to the East Coast. So these are taking pictures. They're very far away But you don't have to be able to see individual clouds or raindrops We have to be able to do a see where the storms are They have them in different colors some of them what I call invisible light in the infrared Because these can sense the amount of moisture and other features of the So they but these are in geosynchronous so that you can always get a picture. Some of them will even operate at night They have visible and they have infrared the ones that operate in the visible that you see night is very boring It's just a lot of black but the Infrared you can still see signals at night and you can see the cloud cover from that It has to be and it's getting crowded. What else do we put up there? Well, I have the luxury of a satellite TV dish The instructions are get up on the roof take your dish and try to point it at the right satellite now the satellite Has to be above the equator. Why is this the reason is once I've pointed that satellite. I don't want to touch it anymore. I Want the satellite to always be right there That will be the case if it is above the equator and if it's in a geosynchronous orbit So it goes around once every day Then it will stay in the same location of the sky with respect to me Of course, it's moving around the sun is moving around the earth and But but it's going around the earth the same rate that the earth is turning So my satellite coverage like that now. Why not put a geosynchronous satellite to observe North Korea? The answer is it's just so far away. It wouldn't get much better resolution than you can from a weather satellite Build a better camera Well in principle you could do that for the camera would have to be the size of a football field and We'll talk about that when we get to optics about how big the camera has to be in order to be able to see things So that's the most serious limitation right now for spy satellites Weather satellites. What about medium earth orbit? What do we do with a medium earth orbit? One of the most interesting things we do is GPS the global positioning system GPS how many of you own a GPS receiver? How many of you have ever used one? I have one in my automobile You know, I turn it on and it picks up the signal from the satellites works in a very interesting way I want you to understand how a GPS receiver works They're in medium earth orbit, but that means You really interesting to think about why that was the case But let's let's understand how it works then you can see why they pick the medium earth orbit if here's the earth and You are right here, and you'd like to know you don't know where you are One thing you can do is to contact radio stations and there's an old system called Loran that worked this way and By timing you can get your distance to radio stations Loran actually use the differences of distances between two radio stations, so that's a detail If you know you're a certain distance from radio station, then let's look at the map here. Here's California and Here's Nevada by the way the biggest surprise I think of the satellite maps that anybody ever showed me is the fact that these images from satellites actually show the state boundaries with these Solid lines on them. They've never realized you were visible from space Laugh louder, please Now suppose you're here in the lost in the desert somewhere You could locate yourself if you knew how far you were from San Francisco Well, not really, you know, you know, you know, if you knew the distance in San Francisco, you'd know where you are in the circle Somewhere, but suppose you also knew your distance to Los Angeles You knew that distance, you know, you're on that circle somewhere and where they cross. That's where you are This is the same principle now for the GPS satellites except the satellites are moving Well, no problem these days you got computers So your little GPS receiver is not just a receiver. It's also computer It picks up a signal from the satellite the satellite tells it When it admitted that signal and where it was when it admitted it It's like saying, you know, it's like like you may pick up a signal from here from San Francisco And it says by the way, I'm the San Francisco signal and this one says I'm the Los Angeles signal So the satellite says and my location is blankety-blank It also tells you when it admitted that signal now How do you know how far away it was you look at the time that you receive it and From the speed of light you can tell how far away you are. What is the speed of light? sort of a nice number it's One billionth of a second it goes one foot That's how fast light travels. What is one billionth of a second? It's about one computer cycle if you have a one gigahertz computer That's one cycle on the computer like goes that far not surprised that computers are small, right? Because in one computer cycle No signal can go more than a foot The computers have to be small this light. That's fast one computer cycle a billionth of a second Goes a foot, but it's also slow It's slow enough that if the satellite tells you when it admitted that signal and you know when you receive it Because you have a clock too, then you can tell how far you work from the satellite now if if here's the earth And there's a satellite here You know you're certain distance from it what that actually means is you're in some sort of a of a circle on the earth You're on that circle somewhere All the points in the circle the same distance from the satellite You know your distance, so you know you're on the earth So your little GPS receive has to have a map inside of it if you had two of these Let's say there's another satellite here, then you know you're right on the intersection point typically you require three satellites Better to have four because then you don't need an accurate clock, but this is what's happening now Where do you put the GPS satellites you put them in low earth orbit? Let's say 24 GPS satellites are in low earth orbit you get to see each one for 50 seconds Then it's gone You'd never see three at the same time You could put them in geosynchronous orbit Then they'd be so far away that you'd have trouble receiving the signal They'd have to have much more power to reach you and you'd lose some accuracy too So they put them in a medium earth orbit Put them up maybe a thousand miles now when that happens it means the satellite is not whizzing over you It's not geostationary somewhere in between So if you have a GPS receiver some of these receivers have little maps to show you which satellites are on the horizon You actually watch the satellite move and and it may be within Your detection for an hour or so they have enough satellites up there so that almost every place on earth You can pick up at least three or four at any given time But my car has this it also has a built-in map So it figures out where I am Then it displays the map showing me where I am and it can do this to within within a few feet So GPS receivers now are being made a standard part of all cell phones I don't know how many people here have cell phones. They know our GPS Being done for just ever just every cell phone and the reason is actually a rather interesting one It's so that in an emergency you can dial 911 and they'll know where you are So you'll notice the GPS receiver does not send out a signal typical GPS receiver is solely a passive receiver Interesting reason for that Anybody here have a guess as to why The GPS was designed so that it doesn't send a signal to the satellite, but only receives a satellite. What's your guess? That's right. So other people couldn't know where you were the GPS was designed originally for the military It got its first big publicity boost in the first Gulf War when they had a few GPS receivers for our troops over in Iraq and They were so valuable They couldn't the troops couldn't get enough of them So they actually wrote home to the United States Then would you go down to Radio Shack and buy me a GPS receiver and mail it to me? Now these things were not mill spec. They were not military specifications But the soldiers quickly learned that the best way to avoid getting lost on the in Iraq was to have your own GPS receiver So these things started going over there being mailed by my friends and family to the soldiers So each one would have his own GPS receiver was a big scandal of the Iraqi war one That the US military wasn't doing it. They weren't doing it because these weren't military spec military spec ones are terribly expensive Military spec means you know you can roll a tank over it. It's still functions. These things probably Have 50% chance of not working after tank goes over them at the same time the value was so enormous but they basically changed the rules and started a lot and and and let What's called off the shelf? Commercial off the shelf It's an interesting acronym COTS. Everybody in the military knows this commercial off the Shelf so now we have a lot more like that That's basically the satellite picture. We'll be talking a lot more about sat about airplanes on Thursday, don't forget to hand in your homework tonight Oh, let me show you this before you go. This is kind of neat. I'm going to put a force on the card But the force the card puts on the mass won't be enough Make it move so the mass falls right down. I May set this up with some wine glasses next time