A satellite of mass m is in a circular orbit of radius 2R_E about earth. energy required to transfer

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7.Gravitation

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A satellite of mass $m$ is 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)

$\frac{{G{M_E}m}}{{2{R_E}}}$

$\frac{{G{M_E}m}}{{4{R_E}}}$

$\frac{{G{M_E}m}}{{8{R_E}}}$

$\frac{{G{M_E}m}}{{16{R_E}}}$

Solution

$(\mathrm{TE})_{\mathrm{i}}=\frac{-\mathrm{GM}_{\mathrm{E}} \mathrm{m}}{4 \mathrm{R}} \Rightarrow(\mathrm{TE})_{\mathrm{F}}=\frac{-\mathrm{GM}_{\mathrm{E}} \mathrm{m}}{8 \mathrm{R}}$

Energy required $=(\mathrm{TE})_{\mathrm{F}}-(\mathrm{TE})_{\mathrm{i}}=\frac{\mathrm{GM}_{\mathrm{E}} \mathrm{m}}{8 \mathrm{R}}$

Standard 11

Physics

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A satellite of mass $m$ is 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)

Solution

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