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[-/5 Points]DETAILSSERPSE1O 13.6.0P.022.972-kg satellite orbits the Earth at constant altitude of 97-km How much energy must be added to the system to move the sate...

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[-/5 Points]DETAILSSERPSE1O 13.6.0P.022.972-kg satellite orbits the Earth at constant altitude of 97-km How much energy must be added to the system to move the satellite into circular orbit with altitude 197 km?What is the change in the system'$ kinetic energy?What is the change in the system s potential energy?Need Help?ReadiWatchlt

[-/5 Points] DETAILS SERPSE1O 13.6.0P.022. 972-kg satellite orbits the Earth at constant altitude of 97-km How much energy must be added to the system to move the satellite into circular orbit with altitude 197 km? What is the change in the system'$ kinetic energy? What is the change in the system s potential energy? Need Help? Readi Watchlt



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A $1000-\mathrm{kg}$ satellite orbits the Earth at a constant altitude of 100 $\mathrm{km}$ . How much energy must be added to the system to move the satellite into a circular orbit with altitude 200 $\mathrm{km}$ ? Discuss the changes in kinetic energy, potential energy, and total energy.

We're told that we have a one 1000 kill, a grim saddle eight and its altitude initial is 100 1000 meters. But then we're going to move it. Teoh, A new altitude that is 200 1000 meters. In both cases, it is in orbit. So the orbital velocity is the square root of G m over our But in this case, that's going to be our earth plus H radius of the earth. His six point 37 times 10 to the six power um mass of the earth, 5.97 times 10 to the 24th power. Okay, so how much energy must be added? Well, the energy final is going to be the kinetic energy final, plus the potential energy final. Likewise, the energy initial is going to be the kinetic energy initial, plus the potential energy initial. So if I take I want the change in energy. I need to do the kinetic energy final minus the potential energy final Whoops plus minus the kinetic energy initial minus of potential energy initial. Now we know that the kinetic energy initial is 1/2 m v squared, but V is the square root of gm over r E plus h gm over r E plus h So h is going to be a church final. Good potential energy final. Which potential energy is negative. By the way, G i m I m over our final. That's going to be our sub e plus h final. Okay, and then I need to subtract off the kinetic energy initial 1/2 i m gm over r e plus h initial two negatives make a positive gm i m over r E plus h initial. All right, so our change in energy is I'm going to factor out a GMM out of everything, g and I m So this is going to be 1/2 times one over r E plus H f minus one over r e plus each f minus 1/2 one over r e plus h i plus one over r e plus h i. And we can simplify this some more. G I am I m negative 1/2 r e plus h f positive 1/2 Oh, are e plus each eye. And you know what? I probably should simplify it more. 1/2 g m i m one over r e plus h i plus minus, I mean one over r E plus h f. All right. We know the values of all of these, so I'm going to put them into a calculator. 1/2 time. 6.67 times, 10 to the negative. 11 power times massive. The earth 5.97 times 10 to the 24th Power times mess of the satellite, which we wrote down up there as 1000 kilograms times one over r e plus each eye 6.37 times 10 to the six power plus initial altitude 100,000 and then minus. This time it's one over a 6.37 times 10 to the six power to 100,000. That gives me 4.69 This problem is taking longer than I thought it would. 4.69 times 10 to the eighth Power, Jules. And that's only part a. So let's go to Part B is asking for the changes in kinetic energy and potential energy. All right, well, we kind of have that, Um, but then again, we've got everything kind of jumbled together, so we just have to take the kinetic energy, um, ones. So this is kinetic energy, and this is kinetic energy. So the change in kinetic energy is gonna be 1/2. Let's keep going up here. Multiply by GMM one over r E plus h f minus one over r u plus h i one over r e plus h f minus one over r e plus h I. All right, let's put that into the calculator. I'm on dez most dot com and I'm just going to copy the whole thing 1/2 G Mm, I already have. And then I just have to subtract change the order. Well, that's just gonna make it negative. So that is negative 4.69 times 10 to the eighth power jewels. Now, to get the potential energy for part C, I could go all the way up here and add these two together, and that would be a good idea. But a better idea would be that the total energy is the change in the total energy of the change in kinetic energy, plus the change in potential energy. So the change in potential energy, um, needs to be twice a smudge because you're going from negative 4.69 to positive 4.69 That's two times 4.69 which is nine point 38 times 10 to the eighth Power Jewels.

In 1940 kilograms satellite is put into a circular orbit about the earth were given that the radius of the orbit is 12,600 miles. And we want to find the kinetic energy of this satellite and circular orbit. Here. I've drawn a diagram of the satellite orbiting Earth, and I've indicated the radius of orbit, which is from the satellite to the center of the Earth. To find the kinetic energy, we first have to find the velocity. And to do that, that's using force equation. So here, in circular orbit, the the centripetal force is equal to the gravitational force. And we're using centripetal course because it is in circular motion. The satellite is in circular motion, so centripetal horses and B squared over R and gravitational force. It is biggie them one MM tube over R squared. And actually, I'll get rid of this one on the first M here on the right, because these two m's are the same. So here. Well, uh, go ahead and manipulate the left side, such that it looks like it looks like kinetic energy, and we can do that by multiplying are on both sides and we'll deploy 1/2 on both sides so that we get B squared on the left and 1/2 G and two over our And now this side is kinetic energy. And for here, this is the first orbit that the problem will deal with. So let's label that kinetic energy one and that will be equal to 1/2 G and mirth. M satellite divided by the radio, the orbital radius of the first situation and plugging in the numbers. We get a kinetic energy, uh, 1.90 times 10 to the 10 Jules. Now we are extending the second part of the problem extends the radio or the orbital radius from 2.3 times 10 to the seventh meters to 4.6 times 10 to the seventh meters were converted from miles. And again, we will be using this force equation to find the kinetic energy so kinetic energy to will be equal to 1/2 won her g e s divided by our two this time and we get a kinetic energy of 9.51 times 10 to the nine. Jules, this is Katie too. And to find the energy difference between on orbit of are too. From our one. We need to also find the gravitational potential energy, which is negative, G and Earth, um, satellite divided by our two. This gives us negative 1.90 times 10 to the 10 Jules. And now, finally, we need to find the gravitational potential energy when the settlement is that our one. Similarly, it's negative, g and earth and suddenly over our one which gives us a gravitational potential energy of negative 3.81 tons tend to the 10 Jules. And now, finally, we can find the difference in the energy. Sorry. This should be a e not on you difference and energy, which will be energy to minus energy one. And you, too. Energy to is composed of the kinetic energy in the gravitational potential. Energy on was attract the same components from energy one, and that gives us a energy difference of 9.51 times 10 to the nine. Jules, this is how much energy is needed to move the satellite from a circular orbit at our one to a circular orbit

A satellite is launched into geosynchronous orbit and we want to find the change in gravitational potential energy for this satellite of mass 3130 kilograms. To find the difference in gravitational potential energy, we first have to find the height at which this satellite is orbiting. And to you that let's start with Kepler's third Law, which states that the orbital period is equal to the constant too high, divided by the square root of Newton's gravitational constant times. A mess of the object around which de San Juan is orbiting times radius to the three has power now to put it into our problem, the orbital period, we'll be the number of seconds today and that is equal to two. I divided by the square root of Big G, and here Earth is at the center of the orbit. So we have mass on the earth times. The distance of orbit, which will be the radius of the earth, closed the height at which the satellite was orbiting and over get a three house power. No result. For this height, we'll get an expression of T times square root of big gene mass of the earth divided by to I to 2/3 two theories minus the radius of the earth. And we get a height of 3.59 turns turn to the seven meters. They have to find the difference in gravitational potential. Energy S O b. Don't say you, uh ah. Settling going from the surface to orbit that will be equal to the gravitational potential energy at all of it, minus the gravitational potential Energy at the surface and recall that you is equal to U is able to negative G 12 divided by the distance between the two objects so we can pull out negative G and satellite and earth since they're the same for both terms divided by one over the distance that orbit which would be R E course. The hype and minus one over R E, which is the distance when it's on the ground and we played all that in a difference in potential energy is 1.66 kinds tend to the 11. Jules. Now, if we want to find the difference in kinetic energy, we have to remember that we have initial speed for the satellite when it's on the Earth because the Earth is rotating and to find the difference in kinetic energy, we'll also need to know the velocity when it's finally in orbit. So to find the velocity when it's finally in orbit, that won't be. He f is equal to the circumference of the orbit, too high times radius of the earth, plus the height at which it's orbiting, divided by the number of seconds in a day. This will give us a velocity of three points here seven times 10 to the third years per second. That's the speed at which the sunlight is orbiting Earth. And to find the kinetic energy, I'm just move this over a little bit. The difference in kinetic energy from the surface to orbit is equal to the kinetic energy at orbit, minus the kinetic energy at the surface. And don't forget, the kinetic energy is simply 1/2 n V squared, so we can go ahead and bet it. The mess of the satellite has not changed, so I have times the mass of the satellite times, the final velocity in orbit miners, the initial velocity at the ground when we get a change in kinetic energy of 1.44 times turned to the 10 Jules

In the first part. The altitude is equal 200 kilometer, which is equal to zero point one month. I think about 6 m. We'll find energy. Is he good? Do minus G Must offered Must have supplied to it by two into our message. Well, absolutely. Reduce minus 6.67 Cross taking power minus 11 multiplied by 5.972 Multiply. I think about 24 multiplied by 1000 and you added by to into 6.37 plus 0.1 in tow. Thank you. Power six. When we saw this we get to you. One is equal to minus 3.78 30 to 9 months away Taking power 10 shower No, Each at H is called Consumers called 200 kilometers which is equal to zero point to multiple awaiting power six meters will find the energy You too is equal to minus G mass offered, massive supplied, divided by two in tow. Our pluses too. We should do six, minus 6.67 was thinking power minus leaven multiplied by 5.972 multiple take about 24 multiplied by 1000 This old went back to into 6.37 plus 0.2 cross. Thank you. Power six when we saw this for you too. We get your tools. Goto minus 3.31 Double four. Cross taking power 10 job in order to find the world done. Really separate you two minutes from U N. Which is good too. My 3.3 wonderful for multiple. A tank over 10 minus into minus 3.783029 miles away. Thank you. About 10 Joe. When we saw this, we could the least you could do 0.0 for six nine five Cross. Think about 10 Joe, which is equal to 469.5 Megazord. Right. This is the energy. Need you to take the supplies from altitude off. Annette Kellerman. Taito, do you need killing?


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