A satellite of mass 400 kg is in a circular orbit of radius 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 10^6m)

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

1.	A satellite of mass 400 kg is in a circular orbit of radius 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 10^6m)
Answer» Solution :Initial energy is `-(GMm)/(4R) = E_1` , Final energy is `-(GMm)/(8R) = E_` The change in the total energy is ` Delta E = E_2 - E_1= (GMm)/(8R) ` `Delta E= ((GM)/(R^2)) (mR)/(8) , Delta E = (GMR)/(8) = (9.8 XX 400 xx 6.37 xx 10^6)/(8) = 3.13 xx 10^9 J` Change in K.E ` = K_2 - K_1 = -3.13 xx 10^9 J` Change in P.E ` = U_2 - U_1 = -6.25 xx 10^9 J`