A 400 kg satellite is in a circular orbit of radius 2 R_(E)about the Earth. How much energy is required to transfer it to a circular orbit of radius 4R_(E) ? What are the changes in the kinetic and potential energies ?

A 400 kg satellite is in a circular orbit of radius 2 R_(E)about the E

1.	A 400 kg satellite is in a circular orbit of radius 2 R_(E)about the Earth. How much energy is required to transfer it to a circular orbit of radius 4R_(E) ? What are the changes in the kinetic and potential energies ?
Answer» Solution :Inttlally, `E_(1) =- (GM_(E)m)/(4R_(E))` whtle finally `E_(f) = - (GM_(E)m)/(8 R_(E))` The change in the total energy is `Delta E = E_(f) - E_(i)` `=(GM_(E)m)/(8 R_(E)) = ((GM_(E))/(R_(E)^(2))) (mR_(E))/(8)` `Delta E = (gmR_(E))/(8) = (9.81 xx 400 xx 6.37 xx 10^(6))/(8) = 3.13 xx 10^(9)` J Thekinetic energy is reduced and it mimics `Delta`E, namely ,` Delta K = K_(f) - K_(i) = - 3.13 xx 10^(9) J. ` The change in POTENTIAL energy is twice the change n the total energy , namely `Delta V = V_(f) - V_(i) = - 6.25 xx 10^(9) `J