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Solve the given problems by finding the appropriate differential.If a spacecraft circles Earth at an altitude of $250 \mathrm{km}$, how much farther does it travel in one orbit than an airplane that circles Earth at a low altitude? The radius of Earth is $6370 \mathrm{km}$.

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 8

Differentials and Linear Approximations

Derivatives

Campbell University

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

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SATELLITE ORBIT A satellit…

we have 65 number problem facilitated to on the set of late and attacking station. So according to given data, this is the earth. And this is the orbit off satellite system on orbit of the satellite. Okay. Okay. No. Ah, we have radius off earth. 6400 kilometer. And the satellite is of 1600 kilometers from the radius of the earth from the surface of that, and it takes two hours. That is of 1 20 minutes to orbit orbit. Okay, so we have been provided with a figure like this is a tracking station. Second station. Is this checking a cane station? This is tracking station. Okay, so if this is all taking a citizen, we should write it with Ah, let us late a baby. And it is given that at 12 for 12 hours at 12:03 p.m. So that would be M. We need to find that its distance from Tacna station. So if this is C so we need to find a c no o c. Will be equal to definitely will be called toe six and $6400. 1600 kilometers. That is 8000 kilometer. And if you would find this angle Ah is he can be fined very easily. So for this and reality him A or that is their ease off earth. So who is 6400 kilometers? But get the value off this angle A To sit eaters until angle we should follow. Proceed as it takes 1 20 minutes. Toe covered 3. 60 degree. That is one devolution. So in one minute it will cover 3 60 degree by 1. 20. So in three minutes, that is three minutes means at 12. Known it was here. And at 12 um three drove at 12 hours. Three minutes It is here, so in three minutes, it will be It will have central angle 360 degree divided by 1 20 into 33 that is nine degree. So we have to take all to 93 so we can utilize call sign law. So because I love to find the value off a C is he will be equal. Do is he will be called you. Who s square plus Docs Square who s squared plus C square minus +20 a. Who will see cost teeter on the route so we have way square that is radius of the earth 6400 square plus you'll see that is 8000 square minus two into 6400 into 8000. Course nine. Degree the route. So we will be using our calculator six for two days ago. Who's quite less 1000? What's class minus doing too? 6400 into 8000 into cost my degree. What? So this is 1954 point 66 So approximately the distance between the tracking station and the satellite will be equal toe a C approximately 1955 kilometers. Thank you so much.

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