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» Solution :Initial total energy is `-(GMm)/(2r_(2)) = -(GMm)/(8R) = E_(2)` Final total energy is `-(GMm)/(2r_(2)) = -(GMm)/(8R) = E_(2)` The CHANGE in the total energy is `DELTA E = E_(2) - E_(1) = (GMm)/(8R) rArr Delta R = ((GM)/(R^(2))) (mR)/(8)` `Delta R = (GMR)/(8) = (9.8 xx 400 xx 6.37 xx 10^(6))/(8) = 3.13 xx 10^(9)J` Change in kinetic energy = `K_(2) - K_(1) = -3.13 xx 10^(9)J` Change in potential energy `= U_(2) -U_(1) = -6.25xx 10^(9)J`