Question

What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2\,R$ ?

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

Answer 1

Answer: (A)

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

Answer 2

E = Energy of satellite - energy of mass on the surface of planet
$= -\frac{GMm}{2r} -\bigg( - \frac{GMm}{ R} \bigg)$
Here, r = R + 2R = 2>R
Substituting in about equation we get. $E = \frac{ 5GMm}{ 6R}$