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(B) The initial energy of the satellite on the surface of the earth is $E_1 = -\frac{GMm}{R}$.When the satellite is in a circular orbit of radius $r =

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$\frac{13GMm}{14R}$

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(B) The initial energy of the satellite on the surface of the earth is $E_1 = -\frac{GMm}{R}$.When the satellite is in a circular orbit of radius $r = 7R$,its total energy is $E_2 = -\frac{GMm}{2r} = -\frac{GMm}{2(7R)} = -\frac{GMm}{14R}$.The minimum energy required to be spent by the launching vehicle is the difference between the final energy and the initial energy:$\Delta E = E_2 - E_1$$\Delta E = -\frac{GMm}{14R} - \left(-\frac{GMm}{R}\right)$$\Delta E = -\frac{GMm}{14R} + \frac{14GMm}{14R}$$\Delta E = \frac{13GMm}{14R}$.

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