solve-the-given-problems-by-finding-the-appropriate-differentialif-a-spacecraft-circles-earth-at-an-

Name: solve the given problems by finding the appropriate differentialif a spacecraft circles earth at an
Uploaded: 2020-08-25
Duration: 4 min 58 s
Channel: Numerade
Description: 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 $6370 \mathrm{km}$.

Question

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 $6370 \mathrm{km}$.

Suman Saurav Thakur · Accepted Answer

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&#x27;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&#x27;s quite less 1000? What&#x27;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.

Joseph Lentino · Answer

now to solve this problem. We actually need the answer from the previous problem. So just be careful. Um, we in the last problem we actually calculated 3979 miles was equal to the radius of the Earth. This is gonna be an important piece of information to help us to solve this problem. OK, now, in this particular ka boom problem, we know that the satellite is traveling in a circular orbit which tells me that the circumference is equal to pi times two times the radius times pi will give us the circumference of the rotating. Sadly, now we happen to know that the satellite will travel a total distance of 26,000 miles. So if we find the radius which will be from the center of the earth all the way out into space to the satellite two times are times pine. So if I divide both sides by two pi when I take 26,000 and divide that by two pi, I&#x27;m going to end up with my radius being 4138 miles. So that means from the center of the Earth. Here&#x27;s my from the center of the earth. All the way up to the satellite is 4138. But we also know that the radius from the center to the outside of the earth is 3979. If we want to know how high the satellite is, all I have to do is take 4138 and subtract 3979 so 4138 minus 3979 will tell us 159 miles above the earth&#x27;s surface.

Charles Carter · Answer

Okay, so the best way to solve this problem is just too. Probably draw fairly big picture. We have the earth, and we know that one side is 140. We know that the other side is 440 for the satellite. We know that the radius of the earth is 3960 Okay, so we know that our major access length already is gonna be 8500 and therefore are a value is gonna be 40 to 50. It also tells us that, uh, the center of the earth is one of the focal points. And then I think it also told us that the center ah, being 00 Okay, So first thing I did was I found where the center would be. So if I subtract 40 to 50 you are take 40 to 50 and I subtract 1 40 39 60 I can see that we still have, like, another 152 g o eso The center of this lips would be somewhere inside the earth on the left side. So the very center of this ellipse all market is that blue dot It&#x27;s 150 away from the origin case. I can go ahead and start writing this as X plus 1 50 was to the left of the origin. It&#x27;s squared over 40 to 50 square. That&#x27;s her A value. Okay, this is on the X axis, Something that&#x27;s right. It is Y squared we need to solve for R B value. It&#x27;s just equal to one. Okay, So in order to find RB value, we need to know the focal length about the focal length, as he Comptel is ah is 150. So we can, because of the lips, we can say a square minus B squared has table focal length squared. So we have 40 to 50 square. Um, actually, we could do minus 1 50 square. There&#x27;s able to be swear. And so I just put that my calculator and I got that B squared is 100 180 So 18 million, 40,000 meant to be squared and the square room. But I did not get a pleasant number. So we know that B squared is going to be 18 million. 40,000. Okay, so that is how I got the equation for the lips of this satellite and the elliptical orbit of this satellite. Thank you very much.

Norman Atentar · Answer

So you have here is a circle at the center of focus off that orbit. So So the registration and 60 the 1960 end up Decide this one party and this one is for party. So here we have that trend. The major Oxus. So this also 39 60 So to eight Single store poor party. Okay, plus party plus two times around 3000. And exactly that is two equals 8400 60 plus 40 that this it was up by 100. So a that is equal store 4200 50. So here this is the sport off 200 pity And this one from here to here 39 60 plus one party that she goes toe 4100 for Here&#x27;s for here. That is equals to 1 50. This is a public t zero. This is 00 So is that sent center is at 1 50 or this is the sea from Father Teboho. So here is 4250. We can find the B squared by using formal abyss. Critical is toe a squared. That&#x27;s eastward. Now we have 4 to 50 squared plus humping the skirt. It is thesis P skirt The skirted equals toe. This is 18 million. 85,000. Sorry. That mistake. This is minus. So we spurred. Here is he goes toe thesis 18 million. 440,000. Or for 24247 one doctor paid. And we have a square that is equals toe 4 to 50 on the recipients toe he kept a million. 600 are 62,500. This is a long exercises. So we have, um X. That s h spring on there. Ace Berg. Yes, my line. Discreet. Squared off this card waas when? So we have a stitch. It&#x27;ll barriers we have It&#x27;s last, which is negative. 1 50. So we have to pass the bit. 150 here. Squared over 18. 52,500. Then the class y squared over meeting for 3000. But this equals toe one. Just us

Ankit Gupta · Answer

No, it is given that excess wear up on a sweb. Plus why spied upon be Esquire, but one but it that it is acquittal Poor 465 on be equal toe poor 462 Our center is located in one of the focus off elliptical Arabic. So let&#x27;s make the bigger So I understand. Now this is the figure. This is the question portion. It is given B which is be Raila poor for six to So this is a B basically and it is this gap, is it? Sammy made it xx No, we need to find the focus because this is our This is up on This elliptical part is the part of self satellite exploder 14 Explorer seven toe. There&#x27;s first trying to stand up, off and lips because art is like at the Sentara. Let us find the center off. The part on Art center is situated at one of the focus. So this is saying this is one of the focus of one on here somewhere after the focus off the Ellipse. So art center and the focus light here No, on it is se got into the When do we have to make minus six 7502 675 Jiro on height minus 4 to 500 45 On our previous precede, the sister ideas are from year to year. This is radius outward and it is a given that 39 six digital minus 39 60 miles. So finally, we&#x27;re going to find the center of the art crushed and that this focus of the ellipse So let&#x27;s find the for the purpose of lives. I&#x27;m in a coordinated see coma Jiro on this coordinate minus equal Majuro. So it&#x27;s already known be is known. I need to find C So you itching the relation will see Esquire equal toe a square minus b squared there to find the cease fire. So C squared, which is 446 five Esquire minus four for six to Esquire and finally see is a Squire group off 4465 inspired minus 4462 squared. So which gives finally 1 63.6 So they see that coordinate of the center a fun coordinate, I said have fun Coordinate 1 60 Today wind six comma zero. So this is the center of circle. Also, no of be person that we need to find. We need to find the maximum and minimum height of the satellite our service so maximum in all its delights. Height. So how did find this? But let Maxime no Hydro Stiller tonight. So I just had to tell you that Spencer lives come here so that this minimum distance between our answer, the life and once it less come here. So this is the distance. Make some distance off the delayed. So we need to find this one. Say this d one and this is a deep, so I wouldn&#x27;t find anyone pushed hard to find anyone. So let&#x27;s find the business whole distance. Whole distance. That is a study that whole distance from here to here it is a minus centred distance from origin are okay distance against, say, the distance minimum distance The minimum distance minimum distance of the one B one equals toe a miner&#x27;s see, which is It was just given a minus, Not one. Let&#x27;s say basically a minus the sea, the sea a place are you will find within good distance. So this is C plus, uh, so a minus C plus so a which is given poor four six type minus C 1 63.6 plus 396 Deal. So finally, locate 3 41 No, the maximum distance. The maximum distance like some distance Is this distance this distance How confined Maxim distance. So I just went to see that a minus in this distance. Odd. What else you can find? This is another way to find this that first find the distance this distance minus subject the this distance. So Okay, that was the best course. Just find this distance wins. Say, this is this is a This is to be say look at this and then we&#x27;d be B and Q the 1st 1 b one B F one minus minus radius. So be at one minus radius. So here for how much it is, if you can let me up one. So this is equal toe 4465 plus 1 63 by six minus 36 between 1962 radius. So after calculus and you&#x27;ll find in this 66 night. So this is the answer

Problem

Solve the given problems by finding the appropria…

Problem 25 Easy Difficulty

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 $6370 \mathrm{km}$.

Answer

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