A satellite of mass $m$ is orbiting in a circular orbit of radius $2R_E$ about the Earth. The energy required to transfer it to a circular orbit of radius $4R_E$ is: (where $M_E$ and $R_E$ is the mass and radius of the Earth respectively)

: Initial total energy of the satellite is $E_i=-\frac{G{M}_{E}m}{4R_E}$

The final total energy of the satellite is $E_f=-\frac{G{M}_{E}m}{8R_E}$

The change in the total energy is

$$\begin{gathered} △E=E_f-E_i \\ △E=E_f=-\frac{G{M}_{E}m}{8R_E}-\left(-\frac{G{M}_{E}m}{4R_E}\right) \\ =-\frac{G{M}_{E}m}{8R_E}+\frac{G{M}_{E}m}{4R_E}=\frac{G{M}_{E}m}{8R_E} \end{gathered}$$

Thus, the energy required to transfer the satellite to the desired orbit $=\frac{G{M}_{E}m}{8R_E}$