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Anderson Video - Newton's Big G and Earth's Little g

Professor Anderson
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 >> Let's talk about gravity that you are all familiar with. Which is when you are standing on the surface of the Earth. Which you will likely do for most of your life. You'll certainly go up in airplanes and you probably go down in caves, but for most of your life you're going to be standing on the surface of the Earth. Unless, you know, commercial space travel takes off and you guys can afford the $100,000 ticket on the spaceships, you know, and you can go up into outer space. That would be pretty cool. Hopefully those prices will come down a little bit. Do they have like an Expedia for space travel? What is the force on us? Well, we're clearly at the radius of the Earth. The Earth is roughly a sphere. It's not really a sphere, okay? It's a little bit bulged out in the center because it's spinning. The equator sort of bulges out a little bit. The Poles shrunk in a little bit. So, it's not really round, but it's closeish to round. We know that there's a force on us, because there is this big mass underneath us. The mass of the Earth, which is pulling us towards the center of the Earth. Let's calculate what that force is. What we just said was, "The force is GM1M2 over R squared." The negative sign indicates it's going down towards the center of the Earth. So, attractive force. Now we can punch in some of these numbers. Mass of the Earth there. The mass of us right there. The radius of the Earth squared right there. Okay? Let's rewrite this slightly. And let's put GMER squared. Put all that stuff second. And now let's punch in some of these numbers. So, what do we have for these numbers? Does anybody know what the mass of the Earth is? These are all SI units. Anybody know what the mass of the Earth is? Okay, what do you do when you're trying to figure out something these days, right? You pull out your phone and you immediately Google, "What's the mass of the Earth?" Okay. Why don't you do that right now and tell me what you find. Pull out your phone and try it. I know they told you to turn your phone off and I'm telling you to turn it back on and try it. Figure out the mass of the Earth and the radius of the Earth. >> 5.9 times 10 to the 24th kilogram. >> 5.9 times 10 to the 24th kilogram. Is that a reputable source that you're getting that number from? >> It was the first thing that popped up on Google. >> Okay. That's probably fairly reputable. If anybody else gets a different number let me know. What about the radius of the Earth? >> 6378.1 kilometers. >> 6378 point -- >> 1 kilometers. >> Okay. >> Is that right? Andy did I write that down right? 6.37 times 10 to the 6th? >> Yeah. >> And we said that the units of G, of course, were Newton meter squared per kilogram squared. Okay, so we take all those numbers and we punch them in here. Why don't you guys try that in your calculator and tell me what you get. And I will tell you what I get if I just approximate it in my head. I'm going to say it's 9.8 meters per second squared. >> I, of course, cheated, because I knew the answer. But double check and make sure if you punch in all those numbers you get 9.8 meters per second squared. >> What we know is that force has to be equal to mass times acceleration. So, the acceleration, due to gravity, at the Earth's surface is negative 9.8 meters per second squared, which is what we call negative G. That's where that 9.8 comes from, right? We've been hearing about 9.8 meters per second squared over and over and over, where does it come from? It comes from Newton's universal law of gravitation. If you put in the mass of the Earth and you put in the radius of the Earth into this equation. You put those numbers in here, you get negative G. Which I think is kind of cool, right? Kind of ties it all back together.