Okay, so this problem is asking us to find the velocity. A satellite that is traveling in a circular orbit a certain distance above the earth soon as we see gravity of this is acceleration and acceleration in a circular orbit is modeled by the equation a equals B squared over r squared. So this is a good So I'm sorry, just be squared over R. So this will be a good starting point for us. And we will combine this with the gravity form of Newton's second law. So Newton's second law is f equals I m A. We're going to use the gravitational force, which is K g Big M little am over r squared. The G is the gravitational constant. Big M and Ms a case will be the mass of the Earth. But it took the stands for the larger of the two masses, and small m will be the satellite or the smaller to mass is in question. So now we can put all three of these equations together, so this expression here will go in for this, and this expression here will go in for this. And so we get m B squared over r equals the g big m them over r squared. So now we are looking for the velocity. So we're gonna have to solve this equation for this velocity right here. So to do that, we will first multiply both sides by our this will cancel. This are out. And one of these leaving us with m b squared equals big G big M little over our Sorry about my little ab. And now we can divide by m on both sides to get rid of the M So those will cancel each other out and we're left with the squared equals big G big M over our now Just one last step to do is take the square root. And so this will go to be equals the square root, uh, gravitational, constant times the mass of the earth divided by the radius to the satellite. And now that is all the information that we need to be able to solve our A. So with this G is equal to 6.673 speaking times, 10 to the negative 11 Big M is going to equal 5.972 times 10 to 24 and are equals the radius of the earth, plus our distance above the earth, which for this case is 700 kilometers, which is equal to 7.8 times under the five meters. Add that to the radius of the earth and we get 7.1. I times tend to the six years. So this is in meters. This isn't you May meter squared or kilograms square. Mm. Sorry. Mascot stuff. Kilograms squared and this is in kilograms. So you just plug these three numbers into here and we should get e equals 7465. And what we are assuming at this moment that the units are going to be meters per second because that's what we know velocity should be. But now we need to go and check to make sure that that's where it's equal. So we will go through and we will set this equation up here with our circle but a blue. So this is our velocity equation. And now we will go through. And we will do this with just the units, though, so we're not gonna worry about the numbers now. So and the gravitational constant. So first of all, it's all gonna be in a square root so B equals the square root of mutants. Meters squared over kilograms squared times, kilograms all that over meters. So this kilogram will cancel with one of those, and this meter will cancel with one of those some. Now we're left with Newton's times meters over, killer grabs and it's square rooted still. Well, that doesn't look anything like meters per second. So we're have to go a little deeper and break down the Newton's into their minutes. Newton is a kilogram times a meter square, no kilograms times meter over seconds squared. And then we still have times a meter over a kilogram and it's all square. It's still so this meter and this meter will combine after these to go and we have the square root of meters squared over seconds squared. You take those square roots, you get meters over seconds. It works out. We're good. So this is our answer for velocity Now moving on to part B. We need to figure out what the period of the orbit is for that satellite. Now that would be found using the equation for a circular period which is given by T. The period equals two pi r and we used to pie for a full circle of rotation. That wasn't a circle. It wouldn't be that simple over velocity. So now we have a velocity equation already. So let's just put that into this equation since we know this represents the velocity of our satellite. So what we're going to have is this is gonna equal to hi are times the square root. And since cities on the bottom, we can just flip this over instead of adding more ratios into our problem. So this will just be are over big G Big M. Now the only thing we need to do is combine these ours together. So when you combine those ours together, you get to because this is our to the 1/2. And if so, this would be our t to the 2/2, which equals R to the one to over two puts one over to you get 3/2 all over the square, root of gravitational, constant times, the mass of the earth. This is our equation for the period that simple. So we got to dio now you just pop your numbers in there and figure it out again. And after shutting through all the numbers, you should get something like 6000 and nine Teen. Now what we're looking for our units to be for a period is one over seconds. Which means it has one revolution every year. Revolutions per second. Yeah, yeah, yes, Yes. One over seconds is what we're looking for. So now we'll go through and do the dimensional analysis again for this one. So on top, we have the radius, which wasn't meters. And it is to the three halves. So t equals to Pai has no units, so we don't need to worry about that when we're doing our units. So this is meters to the three hands divided by, and we're going to use the full in form of G. So big square. Yeah. So we're going to have so first is the newton. So you've got kilograms times, meters over seconds, squared times meters, and then the rest of our units here is meter squared over kilograms squared. So all of that together is our units for G. It's why we like to use a little bit simpler. One like this and then we're going to be multiplying by mass, which is just Kipper grips. So Kilogram cancels one of the kilograms kilograms cancel kilograms. And, um, I got one too many MP's here. Oh, yeah, that end was unnecessary. It's in this one here. So now we're left with I m to the three halves over the square root of m, cubed seconds squared square root of em. Cute is the same as M to the three halves. So this will cancel with this and you are left with one over the square root of one over seconds squared, which means you will just invert this. This is the square root of seconds squared and you take the square root of that which equals seconds. So, yes, we were good. It's not one over seconds. It is just seconds that we are looking for. There we go. Now. If we want Teoh have something that makes a little more sense to us since we don't typically count 6000 seconds for things, divide that by 60 get 100 0.3 minutes, which is also equal to 1.67 hours, meaning that that satellite travels around the earth once every 1.67 hours. And if you divide that bites one or that means it goes around about 14 times a day, So thanks for watching.