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

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(C) The total energy of a satellite in a circular orbit of radius $r$ is given by $E = -\frac{G M_E m}{2r}$.Initial total energy at $r_i = 3 R_E$ is $

Vedclass · Accepted Answer

$\frac{G M_E m}{9 R_E}$

Vedclass · Answer

(C) The total energy of a satellite in a circular orbit of radius $r$ is given by $E = -\frac{G M_E m}{2r}$.Initial total energy at $r_i = 3 R_E$ is $E_i = -\frac{G M_E m}{2(3 R_E)} = -\frac{G M_E m}{6 R_E}$.Final total energy at $r_f = 9 R_E$ is $E_f = -\frac{G M_E m}{2(9 R_E)} = -\frac{G M_E m}{18 R_E}$.The additional energy required is $\Delta E = E_f - E_i$.$\Delta E = -\frac{G M_E m}{18 R_E} - (-\frac{G M_E m}{6 R_E})$.$\Delta E = -\frac{G M_E m}{18 R_E} + \frac{3 G M_E m}{18 R_E} = \frac{2 G M_E m}{18 R_E} = \frac{G M_E m}{9 R_E}$.

$A$ satellite of mass $m$ is in a circular orbit of radius $3 R_E$ about the Earth (mass of Earth $M_E$,radius of Earth $R_E$). How much additional energy is required to transfer the satellite to an orbit of radius $9 R_E$?

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