Hey, guys. So this video, let's talk about the motion of satellites. All right, So the first question is, what exactly is a satellite? Well, satellite is defined as any object that orbits another. So the idea is that if you have a large mass and a smaller mass that is going around it in, you know, some kind of shape, then that thing is a satellite. We have a couple of example this in real life. So the moon travels around the earth and an example that's the little M, whereas the earth is that thing in the center, the big M and the Earth also travels around the sun. So in that situation, the earth is actually a little M. And the thing in the center of the middle is the son that big m. Alright, So in satellite motion questions, you're often gonna need to know what the shape of the orbit that that satellite makes. So the shape of that orbit depends on two things. It depends on the objects, speed and also its distance. So here's how this stuff came about right now. It was thinking one day. What if you were to build like a huge cannon on top of a large tower off the earth and start to fire projectiles off of it. So I got a little, like, sort of like velocity timeline here. That's gonna show us what's gonna happen as we vary the velocity. So first things first. If you were to go, if you were to just drop this thing with a velocity of zero and obviously we just fall towards the center of the earth because gravity is pulling on it. Right? Okay, well, so that's V zero. Well, what if you were to give this thing some initial velocity If you were to toss this or fired from cannon off this Well, we have the object that has some horizontal velocity, but gravity still pulls on it, and so eventually it's just gonna come and hit the Earth. If you were to throw this thing a little bit faster, this thing would travel farther around the Earth because you start having some curvature here. But eventually this force of gravity still means that the object hits the ground. And so we we know how to deal with this stuff. This is just project on motion. We've dealt with this stuff before, All right, Well, Newton had this idea that if you could throw an object fast enough, there is a minimum speed that will which it'll just barely scrape the surface and eventually come back to where you started from. And that's the minimum speed required for orbit. So the idea is that you're just barely scraping the surface of the earth, and the earth is still pulling on you, so you're still falling. But you're traveling so fast that the earth is basically curving beneath you as you fall around it. So that is the minimum speed required for an orbit. And so if there's a whole wide range of speeds that you can have that will give you an orbit, and the idea is that there is a specific speed for which your orbit will be perfectly circular. That is the V circular, and you'll have a perfectly circular orbit. If you don't have this philosophy of your somewhere around it, then you're orbit is going to be elliptical. So that's why this V circular is just like a very specific point. Whereas all of these values here are elliptical. Alright, So Newton had the idea of. Okay, Well, what if you through this thing even faster than that? And faster than elliptical orbit? Well, he thought there was eventually a minimum speed for which this object will escape, and so it will never return. So the idea is that as you through this thing farther, the force of gravity gets weaker, and eventually it gets so weak that this object will never return. And that is the escape velocity. Okay, so we said that the shape of the object depends on speed, which we looked at here, but it also depends on the height. So what I want you guys to remember is that these values that I've made here, if I would actually give them numbers, will change as your height changes. So, for instance, if you were to build this tower even taller or shorter than all of these velocities will actually change slightly. Okay? And the last thing is that you're always gonna assume that when you're working with satellite motion problems, you're gonna assume that this is their circular orbits. Just because the equations you're gonna be simpler unless you're specifically told that it's not circular. Okay, so I want to put some numbers to these kinds of this kind of diagram here. So let's go ahead and check out this example. This is gonna be mostly like conceptual example. So we have a We're standing on a tower on some mysterious planet. And so from the height of that tower, the minimum speed to go around the planet without crashing is 2000 m per second. We said that the minimum speed that you're just barely scraping the surface of that planet is gonna be that V orbit. So that means that that is equal to 2000 m per second. Then we're told that these circular orbit speed is 5000 and the escape velocity is equal to escape. Speed is equal to 10,000. Okay, so the idea is that we're gonna be given these four speeds. We're gonna have to figure out just sort of conceptual. What's going on here? Okay, so first things first is a so a is saying, What if we were to launch something at 1500 m per second? Well, on the timeline, that's gonna be less than this 2000 here, so it's gonna fall somewhere around here. So we know that those things are going to be projectiles. So that means that a is going to be a projectile. All right, so what does B se b is 4000 m per second. So we're past the sort of threshold for the minimum orbit speed. But we're also less than this circular velocity. So any worth anything in this green line here is gonna be an elliptical orbit, remember? So that means that this is gonna be elliptical. So you've got elliptical over here. So what is C? So see Says we have 6000 m per second. We're not quite yet passed the 10,000 m per second escape speed. We're gonna be somewhere over here. So this object is also gonna have an elliptical orbit. It's gonna be a slightly bigger elliptical orbit. Um, depending on this faster velocity, but it's still going to be elliptical. And lastly, if you have a launch speed, that's 15 0 m per second. Now we have to ask if that's greater than the escape speed and it ISS so it's gonna be somewhere over here. So remember that is the escape speed. So that means that d this object has an escape. It's not really calling orbit. It's just actually just escaping that. That would be the shape of the orbit that it makes. Alright, guys, let me know if you have any questions with stuff.

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