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Everything in human experience, and really human history or human civilizations experience, is that everything

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seems to fall to the earth, that if you have water particles, they don't just float up.

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If they are small enough they are being held up by the wind and all that, but if they are large enough, they will fall.

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That you don't have people that are able to just float around, they will fall.

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You don't have taxi cabs that float around, they'll fall.

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Not only will the water fall, it will hit the ground, it will puddle up, and if there is a gutter it

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will fall into the gutter. It is just trying to get lower and lower and lower.

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If i were to drop a bunch of needles they would just fall. They don't... If i had a needle at rest here

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it doesn't just automatically for no reason jump and fly upwards and start to float.

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And so it is just a thing that is fundamental to everything that we have ever

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ever experienced.

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And so, for most of human history or human civilization, we just accepted it as a given.

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We thought, "well look it's just obvious, everything should just fall down, that's just the way the universe is.

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To think otherwise would just be crazy." And that's why this guy, this guy right over here, is one of the greatest geniuses

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of all time. He did many more things than just the things I am going to describe in this video,

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and any one of those things would have earned him his place in history.

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And this, as you may already know, is Isaac Newton.

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Easily one of the top five minds in all of human history. So a pretty fascinating dude.

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And one of his big insights about this 'things falling down' problem is:

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Do they have to fall down?

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Is this just something we should assume about the universe?

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Things just need to fall down, he said, or we were told he said that he was somewhat inspired by

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observing an apple falling from a tree. It's probably not true that you'll see in some cartoons

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on television that the apple hit his head or hit his head while he was sleeping and gave him the idea.

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Most people were to see... Let me draw a tree here.

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That's a twig right there, some leaves. So if most people... So that is an apple over here.

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So if most people... If i were to snap this twig over here, the apple would fall. Pretty much common sense. The apple would fall.

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And if most people were to see that, they would just think it's a normal happening in the universe. But for Isaac Newton, at least on that day,

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he asked himself, "Why? Why did that apple fall?"

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And this, to some degree, is a great example of "out of the box" thinking, because something

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for thousands of years or tens of thousands of years human beings had taken for granted, just

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because that's the way it always was. He actually asked the question why?

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Does it always have to be that way?

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And that question took him down a entire line of reasoning that set up the basis for all of

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classical mechanics for the most part we still use today.

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It has been tweaked a good bit by this gentleman in the last hundred years. [Albert Einstein]

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But for most purposes, when we're engineering things on the surface of the planet,

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and we are not going close to the speed of light, we can still use the mathematics that Isaac Newton came up with from this simple question.

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And not only was he able to kind of think that there's something...

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There's something that might be pulling, somehow,

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acting on this apple, bringing it to the earth.

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But he actually formulated an entire, an entire.. I guess

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Law around this thing. So, as you can imagine,

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the thing that Isaac Newton believes brought the apple to the Earth

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is gravity... is gravity.

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And he formulated the universal Law of gravitation, or the law of universal gravitation; either way.

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And in it, he theorizes that the forces between objects

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now it's a vector quantity, it's always going to attract the two objects to each other.

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So the direction is towards each other. The force of gravity between two objects...

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is going to be equal to this this big G, which is really just a number, its a very small number.

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I'll give you that number in a second. It's equal to this constant, this gravitation constant.

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Which is a super-duper small number, times the mass of the first object, times the mass of the second

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object, divided by the distance between the two objects. Distance squared.

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So this is distance between two objects.

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So if you're talking about the force of gravity on Earth, this right over here...

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You pick one of the masses to be Earth, so this mass over here. You pick one to be Earth.

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This is the object on Earth. Maybe it's me. Then this is the distance between the center

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of masses between those two objects. The center of me and center of the Earth.

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So really it's from roughly the distance from the surface of the Earth or if I'm roughly

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five foot-nine [inches tall] then about half of that distance to the center of the Earth

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is this number right over here. So right when you see this, before we even talk about me and Earth,

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or needles and Earth, or taxi cabs and Earth and that force of gravity, you might have something

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bizarre raising up in your brain. You might be saying, "the way gravity is defined

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by Isaac Newton, this formula we're given right here, it's saying we have gravity between

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any two objects" and you're saying, "Look, I'm looking at a computer screen right now,

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so you're looking at a computer screen right now..." And let me draw an old school computer,

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not a flat panel. How come your not attracted to the computer screen?

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How come it doesn't fly into your face? And the answer there is, this number, this number is

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really small. And there actually is some force of attraction between you and the computer.

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It's just that it's more than overcompensated for the friction between the computer and the desk,

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the friction between you and your seat, which is frankly being caused by the force

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between you and the Earth, the force of gravitation between the computer and the Earth.

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That you and the computer have such small masses that you really can't notice it. It's really negligible.

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It's being overpowered by other forces that are keeping the computer from even drifting

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into your face or your face drifting into the computer. So just to get a sense of that...

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This G, this big G,

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this constant of proportionality, just to get a sense of how small it is... This is, and I'm going to round

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it here, it's approximately 6.67 times 10 to the negative 11th Newtons.

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And we'll talk about Newtons, it is the metric unit of force.

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Let me actually make sure I say this correctly. Newton meters per kilogram squared. Newton times meter per kilogram, squared.

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It's this strange set of units here, but the units are really there. So when you multiply by two masses,

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which are in kilograms, and divide by a distance, which is in meters, you'll end up with Newtons.

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But I want to make it clear that this is a super small number.

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Ten to the negative 11th. If I were to just write 10 to the negative 11th, it would be 0.0 and

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then we would have eleven 0's. So this number right here is the same as 6.67 times

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this thing over here. So this is a super small number. And that is why if you multipy it by not so

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large numbers, if you don't use Earth, if you use yourself and a computer,

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you're going to end up still with a super duper small force. Something so small that you won't

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notice it. It is going to be overpowered by other forces, so these things don't fly into each other.

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But when you think about really massive bodies, like the Earth, the force of gravity

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starts to become noticeable, very noticeable. And I'm not going to give you the mass of Earth in this

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video, you can look it up yourself. But if you put in the mass of Earth right over here,

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if you put it in right over there, and if you put in roughly the distance from the surface

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of the Earth to the center of the Earth for R, and you multiply that by G. All of these terms over here...

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So this term, if you multiply that times that term and multiply by this term squared,

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they simplify to what is sometimes called little g. Little g. So this right here, we can view that

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as the gravitational field at the surface of Earth. It's also the same thing as the acceleration

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of gravity at the surface of the Earth, and this, and once again I'm just going to round it

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for the sake... This is... This comes out to be, units wise, 9.8 meters per second squared.

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Then you're left with just the other mass. So times M1. So for simplicity, if something

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is close to the surface of the Earth, the distance does matter. We can say that the force of

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gravity can be this "little g" times whatever the mass is close to Earth. For example,

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if you were to take me, and I weighed 70 kilograms... So, in the case of Sal, Sal has a...Actually I

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shouldn't say weight, I have a mass of 70 kilograms. I have a mass of 70 kilograms.

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Weight is actually a force, but we'll talk about that, clarify that more later.

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My mass is 70 kilograms, then we can figure out the force that the Earth is pulling down on me

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which is actually my weight. So in this situation, the force is going to be g, which is 9.8 meters

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per second squared, times my mass, which is 70 kilograms. And let me get my handy T85 calculator

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out to figure this out. So I get 9.8 times 70. That gives me...686. So this is equal to 686

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kilogram meters per second squared. OR this is the exact same thing as this thing right over here.

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This IS the definition of a Newton. So this is a newton, which is appropriately named for

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the guy that is the Father of All Classical Physics.

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So my weight on Earth, which is the same thing as the force that Earth is pulling down on me,

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or that the gravitational attraction between the Earth and me is 686 newtons. Now I will ask you

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an interesting question.

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So here is Earth,

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and I am not even a speck of a speck on Earth, but say for simplicity let's say

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this is me, I'm hanging out in the Indian Ocean some place. So that is me.

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And we already know that Earth is pulling down on me with a force of 686 newtons.

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Now my question to you is, "Am I pulling on the Earth with any force? And am I pulling on the Earth with

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a larger or small force that is pulling on me?"

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And your gut or your knee-jerk reaction might be: Earth is so huge, Sal is so tiny.

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Clearly the Earth must be pulling with a greater force than Sal is pulling on the Earth.

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Unfortunately that is NOT the case.

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That I am. So the Earth is pulling on Sal with the force of 686 Newtons and Sal is also pulling on the

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Earth with a force of 686 Newtons. So Sal is also pulling on the Earth. It makes me feel very powerful

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with the force of 686 Newtons. But you might say, "Wait, that doesn't make sense, Sal."

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If I have a building over here, and if you were to, let's say, jump from the building, you're going to start...

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The force of gravity is going to be acting on you, and you're going to start accelerating downwards.

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It doesn't seem that the Earth is accelerating up to you. Wouldn't we notice that, every time someone

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were to jump off a building, that the Earth starting accelerating in a major way. And the way to think

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about that is that the force is the SAME. And we'll talk about that in other videos.

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Force is equal to mass times acceleration. So when we are talking about 686 Newtons, in terms of

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the force of Earth, the gravitational attraction between myself and Earth. And this is going to be

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68 kilograms, then this provides a pretty good acceleration on me. So in this case, if you

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solve for A... Solve for A over here. You're going to get 9.8 meters per second squared. Now, if you

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do the same thing for Earth... I already told you that we are pulling on each other with the same

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force, 686 Newtons. Now if you want to find out how much is the Earth accelerating... That force

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you're going to get a... I'm not even going to put it here. You're going to put a huge number

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in here. Huge number times the acceleration of Earth towards me. And since this is such a huge number,

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very very very large number, this is going to be an immeasurably small number, super small number.

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And frankly it's probably averaged out by the acceleration of Earth, or the force of gravity

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and all the other people and things on the surface of the planet. So it all averages out in the end.

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But even if it didn't, it would be negligible, you wouldn't even notice the acceleration of Earth

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towards me. But you would notice the acceleration of me towards Earth because of our vastly

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different masses. Even though we have the same force of attraction.