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Circular Orbit of the Moon

Patrick Ford
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Hey, guys, we got a fun little problem here involving the moon's orbit. So we're told that the move and travels in a roughly circular orbits and we're told the radius of that orbit. Right? So this is the earth right Here is like little earth like this. You know, uh and so we have the moon that's gonna be traveling in a nearly circular orbit, which means it has some tangential velocity like this, and it has also some centripetal acceleration. Now we're told what the orbital distance is, basically between the earth and the moon, that's that's this big are here. And because of this really large distance, we also have a really small centripetal acceleration. So we're trying to figure out how fast the moon would be traveling if it's suddenly broke free of the orbit and then stopped orbiting to basically what this means here is that over three variables were actually trying to figure out the tangential velocity. Remember that the tangential velocity is the velocity you're going to have. If you were to suddenly stop turning in circular motion, right? Basically, it's just always changing direction like this. So if you were to suddenly stop turning in your orbit. You go flying off in this direction. So we're trying to figure out how fast what's the magnitude of that tangential velocity? All right, so basically, we're just gonna go ahead and look at our equation. We know that a C equals vis a vis tangential, divided by our which variable we're trying to look for. We're looking for the V tangential, so we're just gonna get everything over to the other side. Right? So we have that v tangential squared equals a C. Times are. And so now we just take the square roots. This is gonna be the square root of our centripetal acceleration, which is 0.26 and then our radius, which is 3.85 times 10 to the eighth meters. If you go ahead and work this out, you're gonna get about exactly 1000 m per second. And if you go ahead and look up or Google, what is the orbital speed of the moon? This is basically what you're gonna find. It's about 1000 m per second as it travels around the earth. All right, so that's it for this one. Guys