A satellite of mass m is in a circular orbit | vedclass

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Question

(C) The total energy of a satellite in a circular orbit of radius $r$ is given by $TE = -\frac{GM_E m}{2r}$.Initial energy at $r_1 = 2R_E$ is $(TE)_i

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$\frac{GM_E m}{8R_E}$

Vedclass · Answer

(C) The total energy of a satellite in a circular orbit of radius $r$ is given by $TE = -\frac{GM_E m}{2r}$.Initial energy at $r_1 = 2R_E$ is $(TE)_i = -\frac{GM_E m}{2(2R_E)} = -\frac{GM_E m}{4R_E}$.Final energy at $r_2 = 4R_E$ is $(TE)_f = -\frac{GM_E m}{2(4R_E)} = -\frac{GM_E m}{8R_E}$.The energy required to transfer the satellite is $\Delta E = (TE)_f - (TE)_i$.$\Delta E = -\frac{GM_E m}{8R_E} - (-\frac{GM_E m}{4R_E}) = \frac{GM_E m}{4R_E} - \frac{GM_E m}{8R_E} = \frac{GM_E m}{8R_E}$.

$A$ 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 $R_E$ are the mass and radius of the Earth respectively).

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