Question

The minimum energy required to launch a m kg satellite from the earth's surface in a circular orbit at an altitude $2$R, where R is the radius of earth is?

• A. $\frac{7}{6}\frac{GMm}{R}$
• B. $\frac{1}{6}\frac{GMm}{R}$
• C. $\frac{5}{6}\frac{GMm}{R}$
• D. $\frac{9}{7}\frac{GMm}{R}$

Answer 1

The correct option is C $\frac{5}{6}\frac{GMm}{R}$

We know, gravitational potential energy $=-\frac{GM}{r}$ and orbital velocity $v_0=\frac{VGM}{R+h}$ By conservation of energy,

$E_{final}=\frac{1}{2}m{v}_0^2-\frac{GMm}{3R}=-\frac{GMm}{6R}{E}_{initial}=\frac{-GM}{R}+k$

Minimum energy required$=E_f-E_i=\frac{5}{6}\frac{GMm}{R}$