Question

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 :

• A. $\frac{5GmM}{6R}$
• B. $\frac{2GmM}{3R}$
• C. $\frac{GmM}{2R}$
• D. $\frac{GmM}{3R}$

Answer 1

Answer: (A)

$\frac{5GmM}{6R}$

Answer 2

The total energy in orbit is:
$E = \frac{-GMm}{2r} = \frac{-GMm}{2(3R)} = \frac{-GMm}{6R}$.
Minimum energy to escape is:
$\Delta E = \frac{GMm}{R} - \frac{GMm}{6R} = \frac{5GMm}{6R}$.