A 400 kg satellite is in a circular orbit of radius 2 R_(E)about the Earth. How much energy is required to transfer it to a circular orbit of radius 4R_(E) ? What are the changes in the kinetic and potential energies ?

A 400 kg satellite is in a circular orbit of radius 2 R_(E)about the E

1.	A 400 kg satellite is in a circular orbit of radius 2 R_(E)about the Earth. How much energy is required to transfer it to a circular orbit of radius 4R_(E) ? What are the changes in the kinetic and potential energies ?
Answer» <html><body><p></p>Solution :Inttlally, <br/> `E_(1) =- (GM_(E)m)/(4R_(E))` <br/> whtle finally <br/> `E_(f) = - (GM_(E)m)/(8 R_(E))` <br/> The change in the total energy is <br/> `Delta E = E_(f) - E_(i)` <br/> `=(GM_(E)m)/(8 R_(E)) = ((GM_(E))/(R_(E)^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>))) (mR_(E))/(8)` <br/> `Delta E = (gmR_(E))/(8) = (9.81 xx 400 xx 6.37 xx 10^(6))/(8) = 3.13 xx 10^(9)` <a href="https://interviewquestions.tuteehub.com/tag/j-520843" style="font-weight:bold;" target="_blank" title="Click to know more about J">J</a> <br/> Thekinetic energy is reduced and it mimics `Delta`E, namely ,` Delta <a href="https://interviewquestions.tuteehub.com/tag/k-527196" style="font-weight:bold;" target="_blank" title="Click to know more about K">K</a> = K_(f) - K_(i) = - 3.13 xx 10^(9) J. ` <br/> The change in <a href="https://interviewquestions.tuteehub.com/tag/potential-1161228" style="font-weight:bold;" target="_blank" title="Click to know more about POTENTIAL">POTENTIAL</a> energy is twice the change n the total energy , namely<br/> `Delta V = V_(f) - V_(i) = - 6.25 xx 10^(9) `J</body></html>