okay, let's begin. what are we gonna talk about today? physics. all right, all right.

so you go to a concert and at the concert, you're moved. emotionally, you are moved. i mean, the music comes and you just... you feel good, you can get into it, you're a part of it. you might even be moved to your eyes watering up a little bit, sometimes it's so beautiful. and as this is happening, you realize that musicians down below there or up in front, the thing there, are all following some sheet music and that sheet music can be given to different musicians and those different musicians can look at that sheet music and they can do the same thing and you wonder, "hey, that is really nice, "that this emotional response, it's evoked from me, comes from a pattern that's on pencil and paper." you think about that. and you look at the pattern and it's very complex and if you're not into music, it looks like, wow, it's just gibberish, isn't it? but the musicians are trained to read that pattern. and then you get out of the city

and you go up a country at nighttime and you're looking out a night when there's new moon, huh? the moon's on the other side and you look out and you see the milky way and you see all the stars and you see more stars than you can see when you're in the city. that's because the city lights, of course, light up the sky and the sky is reflecting light and only the brightest stars will show through, huh? but in the country, you see many, many, many. and sometimes you also are moved. you get that sort of emotional... all of a sudden you're connected, all of a sudden-- and you're not quite connected and you start to wonder and you wonder what is going on out there and then you realize there are more stars in the sky than there are grains of sand on all the beaches of the world. honey, a lot of grains of sand, more stars. not in your visible view, but out beyond. and you wonder is there a pattern that dictates what those stars are doing, why they shine, how they move, how they relate to one another? and you know what? there is a pattern. there's a pattern to the whole cosmos.

we're gonna talk about that pattern in detail. would you like to see the pattern? i'll put it right up there on the board. you wanna see it? here it is. that's it gang. that's called the universal law of gravitation and that law of gravitation was developed by, guess whom? isaac newton. you know what? a lot of people think that isaac newton discovered gravity. he didn't, the cavemen knew about gravity. the cave women knew about gravity. what newton discovered was what? check your neighbor and see if your neighbor be knowing. in other words, did you get a chance to look through the chapter?

what did newton discover about gravity? newton discovered that gravity is what, gang? universal, universal, you're right. universal, that gravity extends everywhere. and what this equation tells us? the equation of gravity just tells us that there's an attractive force, 'f' between all things and for any two things that attractive force depends upon, is proportional to, is related to the product of the masses of the two things. this might be a planet, one. this might be another planet, two. those two planets are tugging on each other with the force that depends very much on how much mass they have, but it also peters out with distance square. as the distance between those planets or those chunks of matter or those particles, as the distance between increases, guess what happens to the force?

just what you would expect to happen. - larger or smaller? - smaller. how many say, "oh, it seems to me "as the planets get further and further away, they pull harder and harder on each other?" stand up, i wanna see what you look like. nobody say that. but you see, we can say that statement here mathematically by putting this downstairs, huh? as that make the distance big, what happens to the force? can you see that mathematically? you see it conceptually too, far away, far away, less and less effect. so let's see what we mean by this. mass 1, mass 2, force. i wanna teach you how to read this. i have a planet, mass 1, another planet, mass 2. there's a certain force pulling those things together. let's suppose mass 1, all of a sudden, i don't how, but become twice as massive. what would the force do? be more, less or stay the same? this tells it'd be more. if you make this bigger, this gets bigger. let's suppose, this gets twice as massive, this one gets twice as massive then what's the force gonna increase to?

check the neighbor. 2 x 2, gang, come on, about? - 4. - 4, okay. so you got it? okay. how about this? a couple of planets, it's a pull, right? now i'm gonna take the planets and put them twice as far apart, twice as far apart. everybody know the force gonna be less. every fool knows the force is gonna be half. but that's the fools. us, we're not fools, honey. what's it going to be when two planets are twice as far apart? check your neighbors and see if your neighbor can read that. i don't know if you can. how many say the force is gonna be reduced to a fourth, how about i take these planets and i move 'em to 3 times as far apart? this would be your test, 3 times as far apart. don't say a third

because it's a third times a third, a ninth, you got it? can you do big numbers? we're gonna see if you can do big numbers. two planets, 10 times as far apart, try it. the force gonna be 100th as much. did you see this? that's the law of gravitation. you know where this law of gravitation came from? newton's mind sure, but newton had some hints and newton says he climbed on the shoulders of giants.. and one of those giants was a fellow by the name of kepler, an astronomer type. kepler who spent his lifetime making sense out of the data of one of his contemporaries, brahe, tycho brahe who spent his lifetime gathering data about the planets. and back in the 1700s, kepler found some very, very interesting things. first of all, kepler found out that the planets go around the sun, not in circles, but in what? ellipses and i can draw an ellipse for you, gang.

an ellipse can be constructed as such. i wish i knew this when i was in high school in wood shop when i had to make a coffee table and i made an elliptical type coffee table and i thought i was very clever because what i did is i drew one quadrant of an ellipse on newspaper and cut it out and then folded it over, traced it, folded it over, traced it, folded it over, traced it and i thought i had what was a nice ellipse. if i had known about this, i would have had a better coffee table. i can construct an ellipse very simply, watch this. and turn the string around, gang. you kinda get the idea. that is an ellipse. an ellipse is a path whereby the distance at any point, like out here, the distance from here to here plus the distance from here to here is a constant. that's the definition of ellipse.

take a math class, you'll learn that, but the string has a constant length, doesn't it? so everywhere along there, it's always a constant, isn't that neat? and kepler found out that the planets travel that way and one of the foci, focus, focus, plural, foci, one of the foci right down here and that's the sun, okay? and he found out the planets go around like that but most of the planets go around in not so eccentric an ellipse, like more circular. if the foci are closer together like here and like here, they're kinda close now, yeah? okay, now the ellipse approximates a circle, isn't that neat? and when i have both points right together then i get what? it begins with... circle, that's right. and a circle is a special case of an-- not eclair, not eclair, ellipse, okay?

yeah, a circle is just a special case of an ellipse. get the idea, ain't that neat? and kepler found that out. and from that, newton deduced the law of gravity that we see here today. we'll talk more about kepler's ellipses and the link between here and gravity when we talk about satellite motion and that'll be pretty soon. what i wanna talk about now is this idea here, the inverse square law. the inverse square law is very important. it's important enough that i want you to be able to feel it and see that it makes sense. it looks complicated, doesn't it, to say that something depends upon one over distance square? i want you to see that that's intuitive and that it ought to be distance square. let's see if we can develop that. let's suppose, i have here, a candle flame and that candle flame shooting light out, sending light out equally on all directions,

oh, except straight down the candles in the way. but anyway, the influence of the light goes off in all directions. you will find when you study light that the intensity of light varies as the inverse square of distance. you will find when you study radioactivity that the radioactiveness varies as one over the distance square. you'll find out magnetism with the magnetic pole here that the magnetic field strength goes off as one over the distance square. you'll find out when you talk about electricity and you got a charged object here, that the further and further away you get, the electrical influence peters off as one over the distance square. all through physics, you'll see something over the distance square and i want you to see that that's intuitive. we'll do it now for the case of light. let's suppose this eraser is a piece of photographic film and i hold that photographic film right here. there it is, okay? i'm catching light.

in fact, a shadow's cast, isn't it? i'm catching all the light that comes in here and out to here. i can't draw this part out here, okay? but that's how much light i'm catching and let's say, i'm a particular distance away and i'll call that distance to there, okay? the question is, if i get twice as far away, will i catch less light or more light? 'cause if i hold it here and i bring it into the darkroom and develop it, the film there is gonna be darkened there, isn't it, with the light hit? how about if i held the film twice as far away, twice the distance? it's about here. now look at this, out here, this could fit in the shadow-- i could get two erasers in the shadow. could i get two erasers in the shadow or more in the shadow cast by this? some people say, oh, two, i can see two, one here and one there and that's the end of it. and other people say no, no, no, no, no, you'll get more than two, more than two erasers will fill the shadow.

see if your neighbor knows. it begins with 'f' and end with 'our. - four. - four, excellent, all right. because you get one here and one and out like this two, see. it's sort of like that, like 3d. so you know what? one eraser here would catch 1/4th as much light as if it were here. do you see that? 1/4th as much because the rest is going here, here, here, so 1/4th. let's suppose i get 3 times as far away. it's about up to here. up to here about, right? 1, 2, i'm not sure if it's--scale, gang, but over here, i get, look, 1, 2, 3, i can get 3 erasers. so someone say, gee, 3 times as far away, 1/3rd the light 'cause this would get 1/3rd and the rest will go up here. 1/3rd is wrong. what's the answer, gang? neighbor. how many got a neighbor not saying anything? how many got an antisocial neighbor, today, sort of a little smug, little stuffy, little uppity?

point, who? check that neighbor, what do they say? how much? so 9th, ain't it? see, you get like this. see that? see this eraser? here, it's over here. it's only getting 1/9th the action 'cause the rest is all coming out here and so then i could say what if i put it 10 times as far away and you guys would say, hey, it's not catching 1/10th the light, it's catching 1 what? 100th the light 'cause 10 times far away, i could have 100 erasers fill up the shadow that this one took. 100 erasers would be required to catch all the light that this one here caught. so the intensity out there would be 100th, guess what behaves the same way, gang, begins with a 'g'. gravity, the same one, and that's what we got up here. so it makes sense. here's the world here. there's gravity to the world. this is a particular mass and this mass is pulling on every other mass.

one mass is out here, 240,000 miles away, it's the moon that moon is being pulled, pulled, pulled toward the earth. but the earth is pulling on the moon, you guys know what else is happening? the moon is pulling on the earth, that's right. okay, they're pulling on each other and it pulls it right around and around and around. you guys are standing right here and you're standing right here, you got a mass too and this got a mass. take your mass, multiply by the mass of the world, then divide it between the distance between you and the center of the world squared. guess what you get? begin with 'w' end with 'eight'? try it. your weight, that's what your weight is. your weight is a gravity force. it's a gravitational interaction between you and the world, between the mass that makes you up and the mass that makes up the world and that's what it is. makes sense? you feel weight because the gravitational interaction pulls you

against the surface. what if we cut out the surface and you're here? well, honey, if you cut the surface out, then you kinda fall toward this, wouldn't you? you fall to it. what happens when you jump off a curbstone for a little bit? do you weigh anything? what happens when you jump off a cliff? do you weigh anything? is there a force acting on you? you're driving in your car or your friend's car and your friend says, "hey, i wanna do something different today." and you're driving, driving, driving and all of a sudden, stop, not this different. and as you fall down, is gravity pulling on you? how many say, oh, no, gravity ain't pulling anymore. gravity gonna take a holiday 'cause he was moving? stand up, i wanna see what you look like. nobody say that. you know gravity is pulling on you, okay? but you don't feel it. you know why you don't feel it? because there's no more support. when you're riding in your friend's car, steady, steady speed, huh?

and you're sitting right down, you're scrunching right against the bathroom scales. those bathroom scales are supporting you, holding you up. now when that car goes off the cliff, you looked at the bathroom scale, you wanna read the force of gravity, but what do you read, gang? you read zero because you and the bathroom scale are both falling together. and so you feel what you call weightlessness. in physics, we say there's an apparent weightlessness because there's really a gravity force acting on you, okay? it's like this. i got here this ball, okay? you're in an elevator. you're in an elevator and all of a sudden, you're holding a ball up like this and someone cuts the cable. and as you're falling down, it seems to you like someone cut the gravity off. watch this, i hold the ball in front of my face. i step off, let go and it's still in front of my face, okay? now why did it stay in front of my face? now if you wanna try this and you wanna really get the effect,

jump off a very, very tall building and as you jump, --there's no gravity acting. there's plenty of gravity acting, okay? the thing is you're both falling together and it feels like there's no gravity. talk to an astronaut type who's been in the orbit. guess how they feel. the same way you feel when a car goes over a little lump... you're not supported for a moment. you feel that little queasy feeling? they feel like that all the time. that's why they bring barf bags. it's an apparent weightlessness, because everything, your whole environment, the people in the space shuttle. you look up in a space shuttle. your friends say, "hey, look at those dudes up there, honey, they got no gravity." they get no gravity 'cause they seem to be floating around. they take this ball out, let it go and just hover right there. take a pen out like that, it just kinda floats in front. it looks like there's no gravity 'cause the tv cameras inside are recording that and they see the astronaut type like that and they see it floating like this. hey, no gravity up there. it's a common idea that there's no gravity up where the satellites are.

what do you guys say? if you use that equation to guide you thinking, 'd' up there is not very much bigger than it is down here. that 'd' is toward the center of the world. newton figured that out. when you wanna measure the force of gravity between you and the world, you take a distance between your belly button and the distance to the earth's belly button, that's the center of mass that distance and when you go 100 miles high, honey, that's not much more than 4,000 miles you are to begin with, so they have just about as much gravity up there in space shuttle territory as they do down here. but those video cameras, make it look like gravity's been cut off, much of the public does not understand that. we do because we are a little more educated than much of the public? is that true? do we see that, hey, everything is falling together, it's falling around, around, around? and gravity is very, very much there. if it weren't there, space shuttle would be long gone. but it falls around and around and around

then we'll come back to that idea when we get to the next chapter, force of gravity everywhere. well, let me preface that with a statement like this. how far out would you have to go before the earth's gravity would be no more? if you go to the far reaches of the universe, is home still pulling on you? check your neighbor. how many say, yeah, i'm thinking so? how many say, i don't know enough physics yet? give me a chance, give me a chance, i don't be knowing, don't know everything. i don't know enough physics to answer the question if you wanna know, hands. how many say, i think i'd be knowing enough physics, i know the answer to that question? hands. can i do that one more time? i think i caught two.

come on, you guys. we can see why because that equation kinda tells us, doesn't it? how big do you have to make 'd' before 'f' goes to nothing and you know what it turns out? honey, you can make 'd' out to infinity and even then as 'd' approaches-- any mathematics types here? as 'd' approaches infinity, 'f' approaches but never gets to zero. so you get out to the far reaches of the universe, take that distance, square it, multiply the mass of the earth times your mass and you'll get the force that acts on you, not very much way, way out, but it's there because this holds all throughout the universe. so what did newton discover about gravity? it's universal. let's try some more equation reading, gang. here's the world, here you are standing on it and all of a sudden, i don't know what happens, the earth is all of a sudden twice as massive.

as twice as massive doesn't mean twice as big. it just means that it has twice the amount of mass for its size. maybe like the iron atoms become lead atoms or something like that, you hear what i'm saying? let's suppose, it's just a thought experiment, gang, let's suppose you're on the earth and all of a sudden, it became twice as massive. what would your weight do? how many say, all of a sudden, honey, you'd weigh twice as much? show hands. suppose you're standing here on a bathroom scale and for some reason your mass becomes-- you're eating a lot of doughnuts, a lot of eclairs for a long time, you become twice as massive. oh, what happened to the force of gravity between you and the world? hey, that's easy. more, how much more? how many say that tells me how much more? make one of those twice on the top, the force becomes twice. you see that? so you become twice as massive.

i mean twice the weight. so people that are twice as massive, weigh twice as much. do you see there's a difference between the two ideas? some people don't. they say, are you saying the same thing? no, no, no, no, how much mass you have is altogether different then how hard it's being pulled by gravity? but you can take the same mass, take your same mass and go to the top of the mountain, at the top of a mountain, strictly speaking, you weigh more less, same, same, or there's no way to say? what is it? begin with an l end with an s. less and why do you weigh less? because you made the distance greater. want me to give you a type of question that wipes out about half the students on an exam that has to do with equation reading? let me show you what it is. here's a ladder. the girl right here weighs 400 newtons, it's about 90 pounds. she climbs a ladder that is just as tall as the radius of the world.

up here, she weighs less, more or the same when she stands on a bathroom scale. forget the effects of rotation, more, less or the same? how many would be saying, less? i got that far, honey, i got that far, less, okay. how many say, hey, not only less, i know how much less? in fact, if she weighs 400 newtons here, up here, she will weigh... check the neighbor. here's how far she is away when she weighs 400, one earth distance away, the radius of the earth away, distance of the radius of the earth. when she's up here, she's two earth radii away and you all know, i think all of us, yeah? we all know what the value is gonna be up here in newtons. let's hear it altogether, louder, a little louder.

100ths. i heard, everybody say 100, right, even the wimps, right? there's no wimps in here but its 100, gang, 100, you see that, you see that? could you guys have got that under pressure? could you? well, maybe under pressure that's something different but you see what you do? you just simply say, hey, if this changes then how does this change? and if i make this like twice as much, then 2 squared is 4. so you'd have 1/4th the force. i hope you can kind of do that kind of stuff, relationships between different things. some people thought, some people thought that gravity was rather local and some evidence for that was back in the early 1700s when looking at the planets, the astronomer types know that when a planet goes by jupiter, for example, the planet coming around the sun like this, when it goes by jupiter, it sort of wobbles a little bit

and that was to be expected because there's an interaction between the planet and jupiter too like the planet, uranus, okay? but when uranus is way out here and jupiter is over here, they found out that uranus was acting a little differently out there too. they call that a perturbation and they found out that the planet uranus was undergoing a perturbation where no other planet was and the popular idea at the time was, well, way out there the law of gravity, newton's majestic law of gravity is obviously breaking down, but not everyone believed that. a couple of mathematician types made some calculations as to where another planet would have to be to cause those perturbations and they made about the same time in history. one was an englishman, the other one was a frenchman and the englishman reported his hypothesis and sent it to the observatory in greenwich, england. when the observatory type got his letter,

opened it up and says, what's this? some mathematician is telling me that there's a new planet so and so coordinates in the sky, what is this stuff? i'm exaggerating. the frenchman sent his findings to the observatory in berlin and the berlin types said, what's this, a new planet? if i turn my telescope so many degrees that way, i will find a new planet? son of a...[bleep] there it was, they discovered a planet, predicted by the law of gravity and that planet, they called neptune, that's right. neptune was predicted. that's a nice thing about science, if you know some science, it will allow you to predict things, see? and they predicted where neptune was, ain't that neat? and later on in 1930, this century, they found other perturbation of uranus and all those other perturbations

led to the discovery of what planet, gang, you know? pluto, that's right, pluto. and pluto was predicted before it was discovered and it's awfully hard to find those little specs in the sky and kinda neat. let's be talking about this becoming an exact equation. you see, this reads the force is proportional to the masses and the distance square, but in your textbook, you see, the equation written like this... what's the g? the g relates the force and the masses and the distance square so that this is in newtons and these will be a newtons also and you know how g was found? it wasn't found by newton, it was found much later.

it was found, i think, in the early 1800s or early 1700s and i should be knowing that gang, it was found by a fellow by the name of cavendish and he had kind of a neat way of doing it and someone shortly after that by the name of philip von jolly found an even simpler way to find what g is and here's what von jolly did. von jolly had a mass that was balanced with a known mass over here. underneath this mass, he rolled six tons of lead. and that's m2. and he knew this very, very accurately and he knew this very, very accurately. and when he did that, guess what happened, gang? this side pulled down a slight, slight bit. it got out of equilibrium. so what von jolly did

was he put some other little masses on here, now he didn't have this equal like this, i mean, you can see the darn thing, okay? but he puts some other little masses there and restored the balance. when he put the other little masses here to restore the balance that's to say he has the force that pulled this down. he knows the force? he knows the mass? 1, he knows m 2 and he could measure the distance very accurately. he has everything except g. all you got to do is take that force, numerical value, divide it by the product of the masses, divided by the distance square and when he did that he, got a tiny, tiny number 6.67 times 10 to the -11, that's not-- 6.67 times 10 to the -11,