The minimum energy required to launch a satellite of mass $m$ from the surface of earth of mass $M$ and radius $R$ in a circular orbit at an altitude of $2R$ from the surface of the earth is:
Answer & explanation
Correct answer: option 1
The correct answer is option (1) : $\frac{5GmM}{6R}$
Apply energy conservation.
$U_i+K_i=U_f+K_f$
$⇒-\frac{GMm}{R}+K_i=-\frac{GMm}{3R}+\frac{1}{2}mv^2$
$⇒-\frac{GMm}{R}+K_i=-\frac{GMm}{3R}+\frac{1}{2}×m×\frac{GM}{3R}$
$⇒K_i=-\frac{1}{6}\frac{GMm}{R}+\frac{GMm}{R}$
$K_i=\frac{5}{6}\frac{GMm}{R}$