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 = 6.37xx10^6m)

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 = 6.37xx10^6m)
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 `DELTAE=E_2-E_1=(GMm)/(8R) rArr DeltaE=((GM)/R^2) (mR)/8` `DeltaE=(gmR)/8=(9.8xx400xx6.37xx10^6)/8=3.13xx10^9` J Change in Kinetic energy =`K_2-K_1=-3.13xx10^9` J Change in POTENTIAL energy = `U_2-U_1=-6.25xx10^9` J