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 change in the kinetic and potential energies ? (R= 6.37 xx10^(6)m)

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 change in the kinetic and potential energies ? (R= 6.37 xx10^(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 `DeltaE=E_(2)-E_(1)=(GMm)/(8R) implies DeltaE=((GM)/R^2) (mR)/8` `DeltaE=(gmR)/(8)=(9.8xx400xx6.37xx10^(6))/8 = 3.13 xx10^(9)J` Change in KINETIC energy `=K_(2)-K_(1) =-3.13 xx10^(9)J` Change in potential energy `=U_(2)-U_(1) =-6.25 xx10^(9)J`