Anderson Video - Gravity at Altitude

Professor Anderson
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There's something called Newton's Universal Law of Gravitation. And it says the following. The force due to gravity is equal to negative Gm1, m2 over r squared. And what that means is the following: Let's say I have a planet like the Earth. And now I look at the force of me on the Earth, right, what is the force of gravity due to where I'm standing? Well, it's this. The force F is negative Gm1, m2 over r squared where r is this distance right here. How far am I from the center of the Earth? And so what's the force? It's negative G times the mass of the first object which is the Earth times the mass of the second object which is me divided by r squared where r is the radius of the Earth. G turns out to be a number, a universal number, 6.67 times 10 to the minus 11. We know the mass of the Earth. We know the radius of the Earth. And if I plug in all those numbers guess what I get? Thomas, what do you think I get if I plug in all those known numbers right there? >> What the given gravity is at that point. >> Which is what? You know this already, at the surface of the Earth? >> Nine point eight. >> Exactly, 9.8 meters per second squared. This is exactly equal to mg. Where did that 9.8 meters per second squared come from? It came from this stuff right here. It came from big G times the mass of the Earth divided by the radius of the Earth squared. But that was at a fixed r. If I go up much higher, let's say I go up a distance h above the surface of the Earth, what is the force on me now? The force on me now is negative G times the mass of the Earth times the mass of me divided by how far I am from the center of the Earth. And now that's no longer just the radius of the Earth, it is, in fact, the radius of the Earth plus h quantity squared. And that is certainly a number that is smaller than mg. The force of gravity decreases as you go up an altitude away from the center of the Earth. And, in fact, you can measure this which is kind of weird. How do you measure it? Well, I can, in fact, go to the top of the Empire State Building with my scale, and if I weigh myself at the bottom and I weigh myself at the top, they don't agree. It's a difference, all right? It's not much. For a 170 pound person like myself it's about an ounce, okay? So you need a pretty good scale to measure that, but you can really measure that. Just that change in height above the surface of the Earth you can measure the change in gravity. Obviously as you keep going out further and further it gets weaker and weaker because it goes like one over r squared. And so it gets weaker as you go out. [ Music ]
There's something called Newton's Universal Law of Gravitation. And it says the following. The force due to gravity is equal to negative Gm1, m2 over r squared. And what that means is the following: Let's say I have a planet like the Earth. And now I look at the force of me on the Earth, right, what is the force of gravity due to where I'm standing? Well, it's this. The force F is negative Gm1, m2 over r squared where r is this distance right here. How far am I from the center of the Earth? And so what's the force? It's negative G times the mass of the first object which is the Earth times the mass of the second object which is me divided by r squared where r is the radius of the Earth. G turns out to be a number, a universal number, 6.67 times 10 to the minus 11. We know the mass of the Earth. We know the radius of the Earth. And if I plug in all those numbers guess what I get? Thomas, what do you think I get if I plug in all those known numbers right there? >> What the given gravity is at that point. >> Which is what? You know this already, at the surface of the Earth? >> Nine point eight. >> Exactly, 9.8 meters per second squared. This is exactly equal to mg. Where did that 9.8 meters per second squared come from? It came from this stuff right here. It came from big G times the mass of the Earth divided by the radius of the Earth squared. But that was at a fixed r. If I go up much higher, let's say I go up a distance h above the surface of the Earth, what is the force on me now? The force on me now is negative G times the mass of the Earth times the mass of me divided by how far I am from the center of the Earth. And now that's no longer just the radius of the Earth, it is, in fact, the radius of the Earth plus h quantity squared. And that is certainly a number that is smaller than mg. The force of gravity decreases as you go up an altitude away from the center of the Earth. And, in fact, you can measure this which is kind of weird. How do you measure it? Well, I can, in fact, go to the top of the Empire State Building with my scale, and if I weigh myself at the bottom and I weigh myself at the top, they don't agree. It's a difference, all right? It's not much. For a 170 pound person like myself it's about an ounce, okay? So you need a pretty good scale to measure that, but you can really measure that. Just that change in height above the surface of the Earth you can measure the change in gravity. Obviously as you keep going out further and further it gets weaker and weaker because it goes like one over r squared. And so it gets weaker as you go out. [ Music ]