RC

# Sir Isaac Newton described the law of universal gravitation in his work "PhilosophiÃ¦ Naturalis Principia Mathematica" (1687). The law states that every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

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welcome to the first section in Unit nine Orbital motion in this section. We're going to talk about Newton's law of gravitation or simply Newton's law of gravity. All right, So Newton's law of gravity is the idea that two massive objects to objects that have mass or is he called the inertia will attract each other. They will experience some attractive force that will cause them to pull towards each other. And sometimes this results in, uh, simply running into each other. And sometimes it results in centripetal motion. If the initial conditions in which the different bodies formed were correct, that is that this body has a tangential velocity and a centripetal acceleration. Remember that centripetal acceleration will only cause a change in the direction of the velocity, not change in the magnitude. And thus we end up with thes orbital motion that we see so much in our solar system. Okay, so Newton's law of gravity, as I said before, was that F was going to be equal to something to do with the two masses, M one and M two, divided by the distance between them squared and he said, You know, I think it's thes air the important variables. And I'm just going to small to ply them by some constant G. And then he went and looked at data and fit the data with his model and came up with a G equal to 6.67 times 10 to the negative 11. Notice that the units you have to be Newtons meters squared per kilogram squared. Okay, Um, so that's a very small number here, and we call it the, uh you know, universal Constant. Okay, so this is the universal gravitational constant. So there's our capital G. It's constant, no matter where we are, what we're doing. And then we have the two masses divided by the distance between them square. So Ah, a couple of top a couple notes on this, things to talk about. We have mass one and mass to Doesn't matter how big they are. They will experience some attractive force towards each other and the force that they feel that attractive force is going to be directed along the line that connects their centers of mass. So I've drawn this dotted line dash line hear that connects the two centers of mass and the attractive force So the force of two on one and the force of one on two acts as if it is applied to the center of Mass K. So two important things there we have the dash line. So that says that we are exerting the force in this particular direction. And then we have that it's applied to the center of mass. Good. Okay, although a rather complicated a little bit of calculus later on to show why that is all right. So, uh, this is essentially the mechanics of how to use Newton's law again just for looking at it. Here is the law one more time in the coming examples, we're going to figure out how to use this thing.

RC
University of North Carolina at Chapel Hill

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