Hey, guys. So in this video, we're going to talk about the universal law of gravitation. So the story is that Newton was sitting under a tree one day, an apple fell and hit his head, and he realized that the force that causes the apple to fall to the earth is the same force that keeps the moon in orbit around the earth. So basically, what Newton figured out was that all objects in the universe attract each other. They all exert gravitational forces on each other. So for instance, in this diagram, I've got these 2 spheres, these 2 blue spheres here. If they both are massive, so they have mass 1 and mass 2, then the gravitational force between them is known as Newton's gravitational law. And that equation is G ( m 1 * m 2 ) r 2 where G, that capital G is just a number. It's known as the universal gravitational constant. It's 6.67 ∙ 10 -11 . Here are the units for that number. You may or may not need to know those. Just check with your professor if you're unsure. And that little r that's in the denominator there is the distance between the objects' centers of mass. So if you have these 2 massive objects here, and they are separated by some distance r, Newton's law of gravitation says that mass 2 will pull on mass 1 in this direction, but because of action-reaction and because everything attracts each other, mass 1 also pulls on mass 2 in that direction. The magnitude of those forces is given by this equation. And as for the direction, those forces are directed along a line that connects the two objects. So these forces always act on a line that connects the two objects' centers. And that's basically it. That's the whole equation. The last thing I want to mention is that this capital G here is known as a universal constant, which means anywhere you go in the universe that number is always going to be the same. Don't confuse that with little g like we've seen in forces and kinematics. That 9.8 meters per second squared . That's what's known as a local constant. A local constant means that anywhere on earth that you go, that number is going to be the same. But as soon as you go off of the earth or you go to a different planet, that number is going to change. So just make sure that you know the difference between those 2 and you don't confuse them. Alright, guys. That's basically it. Let's go ahead and check out this example I've got here. So I've got 2 30-kilogram spheres, and they're separated by 5 meters. So let me go ahead and draw that out. So I've got 2 spheres and there have a mass of 30 kilograms. So I've got mass 1 equals 30, and I've got mass 2 equals 30, and they're separated by a distance of 5 meters. So then I know that that is equal to 5, and I need to find out what the gravitational force is between them. So in other words, I need to find out what FG is equal to, right? So that's not a 6, that's supposed to be a G. Great. So we know the formula for Newton's law of gravitation, that's FG equals capital G, constant, that's just a constant, that's just a number, and I've got this mass here that's 30 kilograms. The other mass, so I've got m 1 and m 2, and I also have the distance between them, that's r equals 5 meters. So I have all of those variables. I can go ahead and plug this stuff into my calculator. So just setting everything up, I've got 6.67 ∙ 10 -11 , then I've got the 2 masses, 30 and 30, and I've got to divide them by the distance between them squared, that 5. And so to do this, just make sure I plugged in everything correctly, I actually have a little calculator that's going to go and help us. So I'm going to plug all of this stuff in. So I've got 6.67 ∙ 10 -11 , and then I'm going to multiply it by the 2 masses, 30 and 30. And now we've just got to divide it by, in parentheses, the distance squared. Make sure the denominator is in parentheses because you don't want to mess up the order of operations. So if you go ahead and plug that in, we get the correct answer, which is that the force of gravity equals 2.4 ∙ 10 -9 , and the unit for that is in newtons. So that's basically the gravitational force between these two spheres. Let me know if you guys have any questions and if not, we're just going to keep moving.
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Newton's Law of Gravity
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