Your math doesn't include up to me. Like as soon as I work that out and put it into my calculator, ns don't get the very same answer.

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

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Video Transcript

Hey, everyone. This is questioned by forty nine from chapter five. This difficulty asks us to calculation the period of a satellite orbiting the moon ninety 5 kilometers over the moon's surface, where to disregard the earth and were given the radius. For this reason from example five twelve. We need to be thinking of speed and time. We require some relationship between speed and period. So in instance five. Twelve, we room told that speed of an object in circular orbit that radios are around mass and also is offered by the equals the square source of G, the mass end our okay and from one motion, we recognize that V is same to 2 pi r end tea. Therefore we have actually rvn. Artie, we can equate this two and solve because that tea. Okay, therefore we have actually the square source of G m end our is same to two pi r end tea and we're addressing for this tea. So we rearrange, multiply. Let's check out what the easiest means is going to be execute that walking to it is in to perform this two. All right, for this reason we're gonna have actually with algebra. We're walk to gain t amounts to to pie. Time r cubed over g m. Okay. And also that's both whitey end the other side. And you divide. So this goes over 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 also you finish up combine our withthe e squared of are on the bottom. So you acquire two pi r cubed end three. So currently we have the right to solve t amounts to to pie square root r cubed were told the it is ninety 5 kilometres above the man and also the moon has a radius of seventeen hundred forty kilometers. So that is one suggest seven 4 time's often tend the six meters plus. Currently we had the elevation nine allude five times ten, the 4 meters were an altering kilometers demeanors, and you division that by G six point six seven times ten to the minus eleven Newmedia noon. We're squared per kilometre squared times and massive moon seven suggest three, 5 times ten come the twenty two kilograms. Okay. Plus all that right into your calculator and you get period of seven suggest Oh five. Is this ~ above the next page? T equates to seven allude Oh, 5 times ten come the 3rd seconds. And also if you division that by sixty, you gain one hundred and eighteen minutes