Question

What is the energy required to launch a m kg satellite from earth's surface in a circular orbit at an
altitude of 2R ? (R = radius of the earth)

Moderate

Solution

E = Energy of satellite - Energy of satellite on surface of earth
$= - \frac{G M m}{2 (3 R)} - [- \frac{G M m}{R}]$ $(\begin{array}{l} ∵ h = 2 R \\ ∴ total distance = 3 R \end{array})$
$= \frac{5}{6} \frac{G M m}{R} = \frac{5}{6} m g R$ $(∵ \frac{G M}{R} = g R)$

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