a-satellite-is-currently-orbiting-earth-in-a-circular-orbit-of-radius-r-its-kinetic-energy-is-k_1-if

Question

A satellite is currently orbiting Earth in a circular orbit of radius $R$ its kinetic energy is $K_{1}$ . If the satellite is moved and enters a new circular orbit of radius $2 R,$ what will be its kinetic energy? 
(A) $\frac{K_{1}}{4}$
(B) $\frac{K_{1}}{2}$
(C) 2$K_{1}$
(D) 4$K_{1}$

Khoobchandra Agrawal · Accepted Answer

I have driven. This is the problem. Based on motion Off satellite Here it is. Given a satellite is revolving around the planet In our orbit, off radios are having that kind of technology cable. So even when we have the M in tow AM upon our here M is the mass of the satellite capital. M is mass of the planet on the radius of the orbiting our If radius becomes toward, then we have to fight. Yeah, Kato. Now okay, to is to find us half g m m. Upon tour. So from equation to anyone Mhm two divided by one Hey to upon Kevin When Very half g m m upon tour upon half gmm upon our So you will get Kato upon Cuban is called toe half so okay to its cult toe. Kevan by two. That is the opposite. It&#x27;s correct, that&#x27;s all. Thanks for watching

Ravi Lall · Answer

is satellite is in a circular orbit. So around the earth, So we have the earth here and a satellite isn&#x27;t moving in a circular orbit around the earth. The mass off this satellite is given as M s and the radius of the circular orbit is RS. So we need to find out first the kinetic energy off the satellite. Well, for a satellite to move in a circular orbit, there has to be It&#x27;s centripetal force directed towards the center. This centripetal force should be provided by the gravitational force. Centripetal force formula is mass off the satellite times velocity of the satellite square divided by rs and the gravitational force between the earth And this satellite is given by a G mask off the Earth Times mass off the satellite divided by rs square. So in this formula, you know, this can be simplified to M S V Esquire. Dizzy equals to a g m e m s over our Esther&#x27;s one rs cancels from both the sights so we can get the formula for kinetic energy which is equals to have m S v squared. So therefore, we just need to multiply this equation behalf so Therefore, the kinetic energy is equals to have g mass off the earth times mass of the satellite divided by our s. So that&#x27;s the formula. The answer of the part. Okay, for the B barge, they&#x27;re asking the potential energy that is its potential energy wilder direct formula for the potential energy of a certain line in its orbit that is given by minus G mass off satellite Sorry, mass off Earth times the mass off satellite divided by the radius of the satellite in orbit. So that&#x27;s the formula for you and in the sea part. They&#x27;re asking the ratio off the kinetic energy to potential energy. Well, we just divide the Kennedy Kennedy obtained from the first equation, which has G m in M s, divided by two rs, and the potential energy is minus G M E M s by rs. That should give you negative half

Keshav Singh · Answer

for this problem on the topic of gravitation. We have a satellite that is in a circular orbit around the Earth and has a radius of our. The area that is enclosed by the orbit depends on R squared because we know the area is equal to pi R squared. We want to know how the following properties of the satellite will depend on our firstly the period, second the kinetic energy in the angular momentum and finally the speed. Now, firstly the period we can get from capitals law and we can see from kepler&#x27;s laws periods that T. Is proportional to our to the power 3/2. Since we have to take the square root of both sides of the capital&#x27;s law equation for part B. The kinetic energy from the kinetic energy equation we can see K is equal to a half mv squared, which is G times big time little em over to our so okay is inversely proportional to our for part C. We want to find the angular momentum dependence on our Now from the previous part, knowing that K is proportional to V squared, we find that the speed V is proportional to one over the square root of our so we&#x27;ll do the speed first, which is party and the speed V is proportional to one over the square root of our and the angular momentum which depends on the product. R times V. How is there for proportional to our over the square root of our and therefore our disproportional to the square root of our.

Mayukh Banik · Answer

the radius of the satellite, which he&#x27;s equal equal, equal distance over the art surface as its radius will be to our. It was two times 6.371 6371 time stand to the three major. It was 1.27 times 10 to the seven. Mayor is Canada. Energy is given by G massive The art massive The satellite over to our They were 6.67 times 5.97 times stand to the 24 the satellite weighs 1000 kilogram. Delighted by two times 1.27 times tend to the seven equals 15.68 Time stand to the nine June potential energy is given by minus g mass off the art. Massive decided. I know what are so that comes out to be negative two Gay. So that comes out to be negative. Two times 15.68 times 10 to the nine June digress. Negative 31 going 36 time Stand to the nine Jews and the total is going together. He becomes okay. That&#x27;s you remember that you week was native to okay so that because negative k it was negative. 15.68 time Stand to the nine jewels

Andy Chen · Answer

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&#x27;ve drawn a diagram of the satellite orbiting Earth, and I&#x27;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&#x27;s using force equation. So here, in circular orbit, the the centripetal force is equal to the gravitational force. And we&#x27;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&#x27;ll get rid of this one on the first M here on the right, because these two m&#x27;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&#x27;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&#x27;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&#x27;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

Donald Albin · Answer

we&#x27;re told that we have a one 1000 kill, a grim saddle eight and its altitude initial is 100 1000 meters. But then we&#x27;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&#x27;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&#x27;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&#x27;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&#x27;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&#x27;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&#x27;s only part a. So let&#x27;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&#x27;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&#x27;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&#x27;s put that into the calculator. I&#x27;m on dez most dot com and I&#x27;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&#x27;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&#x27;re going from negative 4.69 to positive 4.69 That&#x27;s two times 4.69 which is nine point 38 times 10 to the eighth Power Jewels.

Problem

A moon of Jupiter has a nearly circular orbit of …

Problem 12 Easy Difficulty

A satellite is currently orbiting Earth in a circular orbit of radius $R$ its kinetic energy is $K_{1}$ . If the satellite is moved and enters a new circular orbit of radius $2 R,$ what will be its kinetic energy?
(A) $\frac{K_{1}}{4}$
(B) $\frac{K_{1}}{2}$
(C) 2$K_{1}$
(D) 4$K_{1}$

Answer

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