 Okay, so I realized that we're going to start talking about circular motion and in my book I don't really talk about something that's really important and makes great examples and that's gravity. Sure, we kind of talk about gravity, this is what we have so far. We have, if I have let's say a one kilogram object and then I would have, if I just drop it, let's say, then I'd have the gravitational force F, gravity, Mg, that's a g, where g is the gravitational field of negative 9.8 Newtons per kilogram y hat. That's all we've done so far and this is the, technically this would be the gravitational force is the force the earth exerts on that and that's what we've done. Okay, but that's just a cheat, really. That's not the whole story. So let me just describe a really cool experiment and then I'll show you the real gravitational force and then I'll show you how they're the same thing and then maybe we'll all be happy. Okay, so there is a way to demonstrate that what is gravity, first of all? I mean, what we can just say the following, gravity is an interaction between objects that have the property mass. I think that's the best thing. You can demonstrate, you can't, it's not easy. I mean the earth have mass, you have mass and so you're attracted to each other. There's an experiment called the Cavendish experiment and basically it takes a rod with some masses on it like that and hangs it down and makes it so that these masses can rotate without being pushed by air or wind and stuff like that. And then what you do is you take a large mass and put it right here, another one and put it on the back behind that one and what happens is the masses are attracted and the rod will turn and by measuring, you know, there's some torsional force in here. So the more it bends, the greater the torque on that, we haven't talked about torque. And so you can, from that by knowing the distance between those masses and how much it bends, you can actually, and knowing the masses, you can determine an expression for the gravitational force. So the great thing about this is you're looking at the interaction between objects and it's not using the earth. The earth pulls down on these, but since this is pulled up by the string, you're not looking at that interaction. It doesn't, that's not what makes it move. Okay, so what is the real gravitational force? The magnitude, the model we find for the magnitude of the gravitational force, Fg, I'll put big g and this is just the magnitude, is g mass 1 mass 2 over r squared. So this is the magnitude of the gravitational force. G is a universal gravitational constant. These are the products of the masses that are interacting. And r is the distance between their centers. Okay, so you can see how this works. I'll show you two cases. G is a constant. I wrote it up here. It's 6.67 times 10 to the mega of 11th Newton's meter squared per kilogram. And let me show you that this is such a small thing with a quick example. Okay, let's say I have a book, a one kilogram book, and let's say I have a pen that's 0.1 kilograms. And let's say these are 50 centimeters apart, 0.5 meters from the center. Okay, so if I draw the forces on this one, I have the gravitational force from the earth. I have the normal force up. And then I have this Fg. I'll call it pen. Let me call it the pen on the book. Now, the book doesn't move. So clearly there should be some frictional force pushing this other way. But let me just, I just want to calculate the magnitude of that. If I went over here, I would have the force of the book on the pen and then I'd have, this has a gravitational force from the earth and a force from the table pushing up on it also. And then friction. But I want to calculate this, the magnitude of that. It's pushing it that way. Okay, so all I have to do is plug into this right here. So I have 6.67 times 10 to the negative 11th. I'll leave off the units just for, to make it smaller. I have 1 kilogram, 0.1 kilogram. Over the distance between them squared, 0.5 meters squared. So what does that give me? Let me put it in my calculator right here. Okay, I get 2, I'll just write it as 2.7 times 10 to the negative 10th, Newton's. Okay, so this force is extremely, extremely small. Gravity is extremely weak force. How would you make this force bigger so that you can notice it? Well, I could get them closer together or I could increase one of these masses. And so that's how we get a great gravitational force from the earth, is that one of those masses, the earth, is very, very large. You know, even if there was no friction, what would this tiny, tiny force do? It caused it to accelerate this way, but I mean, in just one second, it would take, it would increase the speed by 2.7 times 10 to the negative 10th meters per second. I mean, that's super small. You wouldn't even be able to measure that, okay. Okay, that's another problem. So let me go ahead and compare this to the gravitational force from the earth. So let me just say, okay, here's the earth right there. Now how far apart are they? They're essentially, if it's on the surface of the earth, the distance to the center of the earth. Plus some small amount, but that's super small. So this is the radius of the earth. 6.38 times 10 to the 6 meters. And this is the mass of the earth, 5.97 times 10 to the 24th kilograms. So let me put those values in and see what we get for the gravitational force of the earth on the book, the magnitude. If I made this, back to this one, if I made it a vector, I could call that x and that y and I would just add an x hat on there. And if I wanted to make this a vector, it'd be in the negative y hat direction. Okay, so I have 6.67 times 10 to the negative 11th. I have mass one is just one kilogram and the other mass is 5.97 times 10 to the 24th kilograms over the distance square, which is going to be 6.38 times 10 to the 6 meters squared. So if I put that in my calculator, mass one is one, the mass of the earth, 5.97 times 10 to the 24th, oops, divided by 6.38 times 10 to the 6 squared. And I get 9.78 and just compare that to mg. It's going to be one kilogram times 9.8 newtons per kilogram is 9.8 newtons. So you see we get a sense of the same value. Okay, this is a shorthand notation. As we get further and further away as I increase the distance between this object and the earth, this thing on the bottom, unless I increase it by a lot, isn't really going to change too much. If I go, you should go ahead and do this, add 100 meters to this 6.38 plus 100, 6.38 times 10 to the 6 plus 100 and find the new force and it's going to be essentially the same thing. So we make the approximation that near the surface of the earth the gravitational force is constant, the gravitational field is constant and has a magnitude of 9.8. Now, it's not true the further way you get from the earth than the less this gravitational force gets. Even in orbit, even when you get all the way up to orbit, there's still gravitational force. Okay.