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8. Centripetal Forces & Gravitation

Overview of Kepler's Laws


Overview of Kepler's Laws

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Hey, guys. So back before Newton, there was a guy named Kepler who came up with three laws while studying the motion of planets in our solar system. We're gonna check him out in this video. So Kepler's first law was that all orbits, even circular ones, are elliptical. That just means, like a circular orbit is really just a special case of an ellipse, an elliptical orbit and the sun Is that one of the focus points? That's the other point. So in any elliptical orbit there are to focus points called folk I, and the sun occupies one of them. Now you don't need to worry about this other focus point right here, or even the center of the Ellipse, because there's nothing physical. Actually, here there's nothing actually here. So if you were, like travel to spot in space, there wouldn't be like a thing or like a planet or anything. That is just a mathematical point. So there's nothing actually there. And while he was studying elliptical orbits, he wanted to know how elliptical are these orbits? Well, basically, that is the eccentricity. Eccentricity is just a number between zero and one, and it's a measure of how circular the elliptical orbits actually are. So a circular orbit is gonna be an eccentricity near zero. So when you have a very low eccentricity and number near zero, that is gonna be very nearly circular. So I have an example right here. Most of the planets in our solar system are actually like this. They're basically circular or very nearly circular, and they have extremely low eccentricities near zero. Whereas elliptical orbits like comments on things like that have very, very eccentric orbits. They come in really, really close to the sun, which is like that red dot right here and then they go very, very far away. So this would corresponds to an extremely eccentric elliptical orbit, and the eccentricity is going to be very near one. All right, that's basically it for Kepler's first law. The second law has to do with areas and times. So basically, what Kepler's second Law says is that equal areas, which is the these blue regions right here are swept out in an orbit in equal times. So if you had this earth between A and B, and it took three months to travel between those two points, so of this, T U is equal to three months and then later on in its orbit from C to D. It took another three months, although this in this case it's much farther away from the sun right here. Then if these two things take the same amount of time, then they sweep out equal areas between their in their orbits. So that means that these are the same if you have the same time. And that's basically all the Kepler's second Law says, you won't need to do any problem solve anything like that. But it's a good concept to know, and the last one here is called Kepler's Third Law, and it has. It is a relationship between the orbital distance, the distance away from this mass, the center mass here and the time it takes to go around. So basically, if we have the earth, that is that some distance are from the sun, then it takes a certain amount of time to actually complete its orbit. That's gonna be T well, if you have another object like, for instance, Mars and that has another different orbital distance. So I'm gonna call this like RM, and this is gonna be our E. Then it takes a different amount of time, which is T Mars verses this T Earth. And those two things have a relationship. So he noticed that the square of objects orbital period T squared is proportional to the cube of its orbital distance away. And so, because these things are have a relationship, then if you have two satellites that are orbiting the same exact mass, so, in other words, the mass of the sun. So if you have these things orbiting the same mass, then the ratio of our cubed over T squared is a constant. So that means that if you were to do our earth cubed over t earth squared, that's just gonna be a constant right here. It's just gonna be a number. And this number, actually, Onley depends. So this this number here Onley depends on the big mass that it's orbiting. So in this case, the mass of the sun. Well, that number is going to be the same as if you took our Mars and cubed it and divided it by t Mars squared. Alright, so that's basically a relationship. That's actually how we calculated, um with the massive like certain objects in our solar system are alright guys, that's basically it for this video. Let me know if you have any question.