Physics - Gravitation Question with Solution | TestHub

Energy required to raise to satellite of $m$ to a height $h$ is equal to change in its potential energy. $$\therefore \mathrm{W}=-\frac{\mathrm{GMm}}{\mathrm{R}+\mathrm{h}}+\frac{\mathrm{GMm}}{\mathrm{R}}=\frac{\mathrm{GMmh}}{(\mathrm{R}+\mathrm{h})\mathrm{R}}$$ The energy of a satellite moving in a circular orbit is given by $$\begin{array}{rl}& \mathrm{E}=\frac{\mathrm{GMm}}{2(\mathrm{R}+\mathrm{h})}\\ & \therefore \frac{\mathrm{W}}{\mathrm{E}}=\frac{2\mathrm{h}}{\mathrm{R}}\end{array}$$