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A satellite of mass $m$ is in a circular orbit of radius $2R_E$ around 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)
$\frac{{G{M_E}m}}{{2{R_E}}}$
$\frac{{G{M_E}m}}{{4{R_E}}}$
$\frac{{G{M_E}m}}{{8{R_E}}}$
$\frac{{G{M_E}m}}{{16{R_E}}}$
Solution
$(\mathrm{TE})_{\mathrm{i}}=-\frac{\mathrm{GM}_{\mathrm{E}} \mathrm{m}}{2\left(2 \mathrm{R}_{\mathrm{E}}\right)}=-\frac{\mathrm{GM}_{\mathrm{E}} \mathrm{m}}{4 \mathrm{R}_{\mathrm{E}}}$
$(\mathrm{TE})_{\mathrm{f}}=-\frac{\mathrm{GM}_{\mathrm{E}} \mathrm{m}}{2\left(4 \mathrm{R}_{\mathrm{E}}\right)}=-\frac{\mathrm{GM}_{\mathrm{E}} \mathrm{m}}{8 \mathrm{R}_{\mathrm{E}}}$
Energy required
$=(\mathrm{TE})_{\mathrm{f}}-(\mathrm{TE})_{\mathrm{i}}=-\frac{\mathrm{GM}_{\mathrm{E}} \mathrm{m}}{8 \mathrm{R}_{\mathrm{E}}}+\frac{\mathrm{GM}_{\mathrm{E}} \mathrm{m}}{4 \mathrm{R}_{\mathrm{E}}}$
$=\frac{\mathrm{GM}_{\mathrm{E}} \mathrm{m}}{8 \mathrm{R}_{\mathrm{E}}}$
