energy change orbit raise

Question

Energy required to move satellite from radius r to 2r (same planet) initially circular is:

RankGuru · Accepted Answer

Initial Total Energy $E_i = -\frac{GMm}{2r}$.
Final Total Energy $E_f = -\frac{GMm}{2(2r)} = -\frac{GMm}{4r}$.
Energy Required $\Delta E = E_f - E_i$:
$\Delta E = -\frac{GMm}{4r} - (-\frac{GMm}{2r}) = \frac{GMm}{2r} - \frac{GMm}{4r} = \frac{GMm}{4r}$.

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energy change orbit raise

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