The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius ${\mathrm{R}}_1$ to another of radius ${\mathrm{R}}_2({\mathrm{R}}_2>{\mathrm{R}}_1) \mathrm{is}$

Total energy of the orbiting satellite of mass m having orbital radius r is

E = $-\frac{\mathrm{GMm}}{2\mathrm{r}}$ where M is the mass of the planet.

Additional kinetic energy required to transfer the satellite from a circular orbit of radius ${\mathrm{R}}_1 \mathrm{to} \mathrm{another} \mathrm{radius} {\mathrm{R}}_2 \mathrm{is}$

   = ${\mathrm{E}}_2-{\mathrm{E}}_1$

  = $-\frac{\mathrm{GMm}}{2{\mathrm{R}}_{\mathrm{E}}}-(-\frac{\mathrm{GMm}}{2{\mathrm{R}}_1}) = -\frac{\mathrm{GMm}}{2{\mathrm{R}}_2}+\frac{\mathrm{GMm}}{2{\mathrm{R}}_1}$

 = $\frac{\mathrm{GMm}}{2}(\frac{1}{{\mathrm{R}}_1}-\frac{1}{{\mathrm{R}}_2})$