And another ball here and as you know when i release this, both balls will fall at the same time. Did i not demonstrate that to you . Lets try it again. If at first, you dont succeed, why try again . No sense being a fool about it. Here we go. And indeed they hit the ground at the same time. And the rule there is gravity doesnt take a holiday on moving objects. Lets suppose i just dropped them, what would happen . No surprise, but do you know to some people, its a surprise that they do hit at the same time when theyre fired. Now im going to pull it back further. Still the same time . Thats got to be level, gang. And watch. Still the same time. The time it takes to drop has to do with how high it is, not how fast its going sideways. We learned that . And how far its gonna fall down will depend on how longer time. Does anyone remember the relationship for how far down will it fall as time goes by . Can i give you that relationship right here . 5t2, remember that . So in one second, how far will an object fall if you drop it . 5 meters. 5 meters, itll fall 5 meters down. If you threw it straight out, would it continue straight out or would it fall below the straightout point . Lets suppose, for example, you got in a tower. And lets suppose its five meters tall, where you are right here and youve just dropped an object. How long it takes to hit the ground . One second. Lets suppose i instead throw the object. How long does it take to hit the ground . Lets suppose i throw it faster sideways. How long does it take to hit the ground . One second, because what its doing, its falling beneath the Straight Line it would take if it didnt fall, isnt that right . And that vertical distance from here to here, that vertical distance, 5t2, so 1 second to fall 5 meters. Lets suppose i threw it really, really fast, so fast that the curvature of the world played a role, a second or longer than a second . Longer than a second. Can you kinda see that . Because lets suppose i talk about. Heres my Straight Line. It might be 5 meters here, but here its gonna keep getting more and more and more than 5 meters, so itll be in the air for a longer time when you take earths curvature to account, because we live in a curved world, dont we . Isnt the world curved like that . Now if you had a cannon at the edge of the beach and you grazed it right out so its grazing right against the water and you fire a cannonball. If theres no gravity, of course, it would just continue straight, straight, straight oon e water would be below it, yeah . Do you know how far out you have to go on the planet we live on before theres a 5 meter drop . Check your neighbor and see if youre sitting next to someone who happens to remember that fact from your reading or from previous lectures. How far out do you have to go along the earth to get a 5 meter drop . Can i have an answer . 8 kilometers. Again. 8 kilometers. 8 kilometers, thats right. If you go 8 kilometers straight out, you will be 5 meters further than the ground than you were over here. So let me ask you a question, gang. If you fire that cannonball at a low speed, plop, splasharoony. You fire a little higher speed, splasharoony down here. How fast would you have to fire that cannonball, no splash . Check the neighbor, see if the neighbor know. How many say its 8 kilometers per second . Can i have a show of hands . Yeah, my people, my people. 8 kilometers per second will do it. 1 second later, if youre 8 kilometers away, youll be just as far off the ground as you were here, cause dont forget this distance above to that Straight Line is a 5 meter drop, which tells us how satellites operate. Newton talked about that years ago. Newton says consider a Mountain High enough to be, not above gravity, a lot of people think above gravity, no, no, no, no, to be above the drag of the atmosphere. Put a cannon on there and fire that cannonball and guess how fast itll orbit. 8 kilometers per second. What you do is you orbit all the way around youre falling all the time, fall, fall, fall without ever hitting the ground. So that speed will put you in orbit. So next time youre watching the Television Set and you see theyre gonna put some satellite into orbit, see the rocket go off. Rocket climbing, climbing, climbing. Pretty soon youll see the rocket start to go sideways, right . Should it . Better. What if just went. Right back down, see . So itll go up, gotta get up above the air drag and its getting up, up, up and now its gonna get level. And when it starts to get level, down below at mission control, theyre pushing that thing up to guess how fast . Past tense of eat, 8, okay . 8 kilometers per second and then they just throw the controls off and go home. No more control needed. Gotta get going sideways, 8 kilometers per second, its gonna fall, aint it . But the earths got a curve and guess what matches up . The curve of the earth or the curve of the fall, hey, hey, hey, its what falls around and around. Hey, hey, we got that, yeah . So satellites are all the time falling. How come the speed, 8 kilometers per second, how come the speed at all these points is the same . Did you know what it is . If its going 8 kilometers per second here, its going 8 kilometers per second here, here, here, here, the speed stays the same. The speed doesnt change, so once they boost it up to 8, it will coast at that one speed, which begs the question. Hc, how come . Someone say because gravity aint pulling on it up there. What do you say about that . Uhuh, honey, if gravity aint pulling on it, whats it gonna do . Straight line off into space. Gravity is pulling on it, just about as hard as down here. So how come gravity dont speed it up . Got a bowling ball here, gang. Any gravity pulling on the bowling ball . Any gravity pulling on the bowling ball now . How many say, no theres no gravity pulling on it when it moves . Stand up. We know gravity pulling on that, yeah . How come the gravity dont speed it up . Its moving upwards down. Yeah, yeah, yeah. Gravity pulling straight down, straight down. Let me show you. Gravity pulling straight down. Is there any component of that force along this direction . No, no, if gravity was kinda pulling at an angle like that, guess which way it would accelerating when i let go . It would start accelerating that way, see that . I mean, lets suppose, like this was a hill. And now gravity is pulling on it. Does this force here have any component along the tabletop . Answer end with a p, begin with a y and the answer is yup, it do. Its kinda pulling down here. In fact, theres a way to do that where you kinda take the little rectangle. You guys been into vectors . And this component here, makes it accelerate down the incline. This component doesnt do any work anywhere, doesnt help it along, just holds it against the table, but this component, now itll pick up. But when you put it on a level, is there any component kinda this way, kinda this way . Only down, so what . Its pulling sideways all the time . So when youre bowling and you let go of the ball, you can tell why its rolling at constant velocity, because theres no force pointing that way or we say no component of force pointing that way. Are you getting the component, i mean, the part, thats pulling straight down. Is there anything out this way, thatno, no, no. Down, thats it. On a hill, yeah. So if we put a big bowling ball, i mean a big Bowling Alley around the world, what would we get . Heres the world and lets suppose we put a Bowling Alley up in the sky. Well put it up in the sky to get away from the air drag, about 50 miles up, yeah . Here, we kinda get a support there so it doesnt fall down, big structure. This is first class bowling man, okay . Now you take that bowling ball and you roll it. When its here, the force of gravity acting like that. When it gets over here, force of gravity acting like that. Is that down . Youre onto that and some people think downs always this way. Come on put yourself in a frame of reference of the world, get a cosmic view, yeah . How about here . Which way is down, gang . Australians know. Like that, okay . And everywhere here, note how the force is pulling, always perpendicular and if its pulling perpendicular, then theres no component along the alley. So once youve got it rolling, how is it gonna roll . Steady, steady, steady, unless you mess with it, okay . So lets suppose i get it rolling in a certain speed and lets suppose i cut part of the alleyway here, play a trick on it. Here it comes, im rolling it, maybe like 4 kilometers per second, thats pretty fast. Here we go. Later on, come to the edgeway, crash into the ground. Roll it faster. Crash into the ground over there. Roll it faster. Boom, still crash into the ground. I wonder if thered be a speed you could move it such that it would clear the gap. How many say, oh, no, theres no way to clear that gap . Stand up, go on. See if youre sitting next to someone who can calculate in their mind, the reason in their mind or come up with the answer, how fast it gotta go to clear the gap . Whatd be the answer, gang . Past tense of eat. 8, 8 kilometers per second, youre gonna clear the gap. How about if you make the gap this big . Gonna clear that gap . How about yomake the alley this big . Heres the alley, now heres your gap, get it going 8 kilometers per second, what are you gonna do . Youre gonna clear the gap, you come right back again. Take it away and send it so it keeps moving at steady speed because its always being pulled sideways to the way its moving, yeah . Have we got that . Someone asks you, how come the satellites keep going the same speed, oh, maybe theres a rocket pushing it all the time. What do you guys say . Uhuh, its coastin. It must be coasting where theres no gravity. Uhuh, there is gravity. Why dont gravity speed it up . If i take that object and let go, gravity speeds it up. Why doesnt it speed up the satellite . Well, thats the characteristic of satellite motion, honey, thats just the way it is, no reason for that. What do you guys say . Because, why . cause its moving, but gravity pulling sideways and so instead of moving out here, it moves to here. But then its pulling sideways again, so its always being pulled sideways. If you understand these things, if you do, then you can answer this question. I fire the cannonball at 8 kilometers per second, how fast is it going here . 8 kilometers. How fast here . 8 kilometers. Now i fired it 4 kilometers per second, 4. Smashes into the ground, it left the cannon at 4, it smashed into the ground at more than 4, no, no, no, no, no, less than 4, no, no, no, no, 4 exactly, no, no, no, no, theres no way to say. Take a pick. Let me ask you a question. I take these car keys. I toss the car keys 4 feet per second like this and youre gonna catch them out there, okay . They leave my hand 4 feet per second. Im at the top of the mountain, youre down below. How many say, oh, you only threw em at 4, ill catch with my bare hand. Honey, you got a normal hand. Theyre gonna speed up . Why they gotta speed up . Theyre gog with gravity. Wh you go with gravity, what gravityonna do to you . Pull you faster and faster and faster. So this cannonball over here, this cannonball is gonna gain speed, cause its not goin sideways to the gravity anymore, i mean, perpendicular, look when its in here, its being pulled like that, its sort of like a little angle in front of there, so the speed changes. Lets come back up to here. When i threw that rock up here, that ball, i threw with a speed, maybe like this. And when i got here, its got a speed still like that and when it gets over here, it still has a speed like that. These speeds are all the same. Thats the horizontal component. You know why these components are the same . Because theres been no force this way. You were neglecting air drag, gang. But you know what . When it gets to here, its kinda moving down a little bit, a nd over here, its even moving down further. And when i combine this motion and this motion, what do i get . I get motion like that. And when i combine this and this, what do i get . I get motion like that and so what happens is the speed, heres the speed, thats the hypotenuse of our little triangle in here gang. You guys would be knowing the hypotenuse is always greater than either side, yeah . So this speed keeps getting more and more, why . cause im going with gravity. Gravity giving me a component this way here. You see, when im on this Bowling Alley, everywhere im going, my speed is exactly sideways along the alley, see . cause theres no component of force this way, so it stays the same. Theres no component of force this way, so this part stays the same. How about this part . Going with gravity, it picks up, it picks up. And so what happens over here . Over here the speed is more here than it was up here, so if its 4 here, this component is 4, but the sum over here makes this greater. So when youre going with gravity, youre gonna pick up speed, cause gravity gonna help you along. Going down in an angle, theres a component of gravity along the direction of motion like rolling down the hill. Theres a force and what i do is im moving this way. I have a component of that force like that. Thats a force component and that force component means i have what that goes this way . Begin with a. Acceleration that way. And if i get an acceleration that way, what do i have in terms of speed, what kind of speed . An everchanging speed, thats acceleration is, yeah . So it picks up speed. So over here, a lot of people dont see this, over here, it picks up speed as it falls, but it doesnt pick up speed when it falls like that. Do you guys see that . If youre understanding these ideas, maybe you are, maybe arent, you can answer this question, which leads into the next aspect of everything were talking about here. Lets suppose instead of firing at 8 kilometers per second, its gonna put it in circular orbit and by the way, thats only in closed orbit. Out here, it turns out the speed is less and less, gravity is weaker, but for closed orbit its 8 kilometers per second. The moon is not moving 8 kilometers per second. Its moving much slower than that, its way out there. This satellite here whips around in 90 minutes, yeah . How long does it take the moon to whip around . About 28, we call it a month, about 28 days, yeah, okay. Lets suppose i fire my cannonball not at 8, not at 4, at 9, 9 kilometers per second. Thats like over 20,000 Miles Per Hour by the way. If i fired it 9 kilometers per second, aint it gonna overshoot . Its not gonna follow here, is it . Its gonna overshoot, yeah . And when it gets out here, i gotta question for you. I fired it at 9, i wanna know if you know enough whats going on to be able to say with some certainty whether its going 9, more than 9, less than 9 or say, you know i dont really be knowing. Its not that id be annoyed, i dont really be knowing how to think about it and thats now one here, yeah . Check the neighbor, more than 9, 9 or less than 9 when it gets to here . More than 9. The question is wouldnt the rotation of the earth affect all this . The answer is yes. Guess what we aint gonna count right now . In fact, let me tell you something about the rotation of the earth, okay . The earths turning all the time, yeah . Lets see, how does it turn . So the sun comes out, the sunlight lets see, go this way, oh, i get mixed up. Which way does the earth turns, gang . It turns this way . Yeah, it turns that way, okay. Which part of the earth is moving faster in kilometers per second . Up here or down here . If i hold it towards you like that, which part of that earth is traveling faster, gang . We talked about these ideas, near the equator. Guess why they launch from Cape Canaveral instead of nova scotia . Guess why they get their eyes on the big island of hawaii for future launch . Why do you suppose theyre looking at hawaii for future launch . That 8 kilometers per second translates to 18,000 Miles Per Hour. It turns out hawaii is going about 1,000 Miles Per Hour. Up here, going slower, so you know what you get . You get a free boost. So if you launch near the equator, you dont have to fire it off at 18,000. Fire it off at 17,000, save you some fuel. So yes, the spin of the earth is a factor. So far im neglecting it and i neglect a lot of things in my course because i want you to see the base parts and then you can put the little embellishments on later. So in answer to that question when the satellite we went to another satellite yet, huh . When the projectile gets out here, 9, less than 9, more than 9, how many people say less than 9 . Ooh, how many say no, exactly 9, itll always stay the same, i learned that over here . How many say, well, im a free spirit, i say more than 9, cause its going against gravity and gravity gonna kinda push it out there . Now wait a minute, wait a minute, its going against gravity, gravity gonna push it out, oh, wait a minute, no, no, if its going against gravity, oh, i think its less than 9. How many of you saying that . Just like if i take this thing and throw it up in the air, when it leaves my hand, lets suppose it leaves at 9 feet per second, anyone know if its gonna be more or less than 9 feet per second when it gets up here . Common sense, come on, gonna be less, going against gravity. Aint that going against gravity . Up here, gravity is pulling it to the center of the world. Gravity pulling it like that. Now look at this. Its moving like that. Theres part of that gravity going against. This part here, gonna change course, so it wont end up over here. Itll end down here. So youre going against a component of gravity and when you go against the component of gravity, it gonna slow you down. And so this thing gonna get slower. Lets look at it over here. Now it doesnt keep spiraling for ever cause it slows down, slows down and right over here, its going sideways again so that maybe now its only going 3 kilometers per second. Its been going up all the time and now what goes up. Does it bother you when i say up . What goes up comes. Down like that. And what itll do is slow, slow, slow, fast, fast, fast. Let me do this so how many australians here . Okay, watch this. This might be satisfying to most of us. Lets go like this. Kepler, Johannes Kepler never comprehended why it was that the planets been going around the sun in their elliptical paths. He never comprehended why it was they went so slow out here and so fast down here, he made the law, he discovered it. He discovered how much fast never had a model for thinking that allowed him to answer the question. When we look at the thing, a satellite, as simply a projectile interacting with the world, doesnt it make sense, when you throw it up, its gonna slow down and finally come back again . Honey, you put the landscape here and throw a rock up in the air. If some one had said to kepler, kepler, watch this, honey. Take a rock. Is it any mystery why its going slower and then gain speed . Its just the responding to the gravity, yeah . And kepler would go. Kepler didnt have that model. You know what keplers hangup was . Kepler thought that if the planet is moving this w