Question

A launching vehicle carrying an artificial satellite of mass $m$ is set for launch on the surface of the earth of mass $M$ and radius $R$. If the satellite is intended to move in a circular orbit of radius $7R$, the minimum energy required to be spent by the launching vehicle on the satellite is:

(Gravitational constant = G)

• A. $\frac{GMm}{R}$
• B. $\frac{13GMm}{14R}$
• C. $\frac{GMm}{7R}$
• D. $\frac{GMm}{14R}$

Answer 1

Answer: (B)

$\frac{13GMm}{14R}$

Initially energy of the satellite $=-\frac{GMm}{R}$

Energy of satellite in circular orbit $=\frac{GMm}{2r}$

When the satellite is in the orbit of radius $7R$ it's energy $=\frac{-GMm}{14R}$

The total energy required to be spent by the launching vehicle $=-\frac{GMm}{14R}-(-\frac{GMm}{R})=\frac{13GMm}{14R}$