A satellite of mass 400 kg is in a circular orbit of raduis 2R about the earth where R is radius of the earth. How much energy is required to transfer it to a circular orbit of radius 4R? Find the changes in the kinetic and potential energies ? (R = 6.37 xx 10^(6)m)

A satellite of mass 400 kg is in a circular orbit of raduis 2R about t

1.	A satellite of mass 400 kg is in a circular orbit of raduis 2R about the earth where R is radius of the earth. How much energy is required to transfer it to a circular orbit of radius 4R? Find the changes in the kinetic and potential energies ? (R = 6.37 xx 10^(6)m)
Answer» <html><body><p></p>Solution :Initial total energy is `-(GMm)/(2r_(2)) = -(GMm)/(8R) = E_(2)` <br/> Final total energy is `-(GMm)/(2r_(2)) = -(GMm)/(8R) = E_(2)` <br/> The <a href="https://interviewquestions.tuteehub.com/tag/change-913808" style="font-weight:bold;" target="_blank" title="Click to know more about CHANGE">CHANGE</a> in the total energy is <br/> `<a href="https://interviewquestions.tuteehub.com/tag/delta-947703" style="font-weight:bold;" target="_blank" title="Click to know more about DELTA">DELTA</a> E = E_(2) - E_(1) = (GMm)/(8R) rArr Delta R = ((GM)/(R^(2))) (mR)/(8)` <br/> `Delta R = (<a href="https://interviewquestions.tuteehub.com/tag/gmr-468745" style="font-weight:bold;" target="_blank" title="Click to know more about GMR">GMR</a>)/(8) = (9.8 xx 400 xx 6.37 xx 10^(6))/(8) = 3.13 xx 10^(9)J` <br/> Change in kinetic energy = `K_(2) - K_(1) = -3.13 xx 10^(9)J` <br/> Change in potential energy `= U_(2) -U_(1) = -6.25xx 10^(9)J`</body></html>