Your math doesn't include up come me. Like as soon as I work-related that out and also put it right into my calculator, i don't acquire the exact same answer.

You are watching: Calculate the period of a satellite orbiting the moon

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### Video Transcript

Hey, everyone. This is doubted by forty nine from chapter five. This problem asks us to calculation the duration of a satellite orbiting the moon ninety 5 kilometers above the moon's surface, whereby to ignore the earth and were provided the radius. For this reason from example five twelve. We need to be thinking of speed and also time. We require some relationship between speed and period. Therefore in instance five. Twelve, we space told that rate of things in circular orbit the radios are around mass and is given by the amounts to the square source of G, the mass over our okay and also from circular motion, we know that V is equal to 2 pi r over tea. Therefore we have rvn. Artie, we can equate this two and solve for tea. Okay, for this reason we have actually the square root of G m over our is same to two pi r end tea and also we're addressing for this tea. So us rearrange, multiply. Let's view what the easiest method is going to be execute that going to be to perform this two. All right, for this reason we're gonna have with algebra. We're going to obtain t equates to to pie. Time r cubed end g m. Okay. And also that's both whitey over the other side. And also you divide. So this goes end the other side, multiplying, and also then this you divide over. And also that's why Gene I'M go down, Teo. That's why Gene, um, walk to the denominator and you finish up combine our withthe e squared of are on the bottom. Therefore you acquire two pi r cubed over three. So now we have the right to solve t equates to to pie square source r cubed were told the it is ninety 5 kilometres above the man and also the moon has actually a radius the seventeen hundred forty kilometers. So the is one allude seven 4 time's tend the 6 meters plus. Now we had the elevation nine allude five times ten, the 4 meters were changing kilometers demeanors, and also you division that through G six suggest six 7 times ten to the minus eleven Newmedia noon. We're squared per kilometre squared times and massive moon seven allude three, 5 times ten come the twenty 2 kilograms. Okay. Plus all that right into your calculator and also you get duration of seven point Oh five. Is this top top the next page? T amounts to seven suggest Oh, five times ten come the 3rd seconds. And if you division that by sixty, you obtain one hundred and eighteen minutes