Question

A satellite of mass $1000kg$ is rotating around the earth in a circular orbit of radius $3R$. What extra energy should be given to this satellite, if it is to be lifted into an orbit of radius $4R$?

• A. $6.4\times {10}^{9}J$
• B. $4.8\times {10}^{9}J$
• C. $2.7\times {10}^{9}J$
• D. $3.9\times {10}^{9}J$

Answer 1

The correct option is C $2.7\times {10}^{9}J$


Total energy, $T.E=-\frac{GmM}{2R}$
Initial total energy at $3R$, $T.E_i=-\frac{GmM}{6R}$....(1)
Final total energy at $4R$, $T.E_f=-\frac{GmM}{8R}$........(2)
$\Delta E=T.E_f-T.E_i=-\frac{GmM}{8R}+\frac{GmM}{6R}$
$\Delta E=\frac{GMm}{24R}=\frac{gR}{24}$
Substituting the values,
$g=10m{s}^{-2},R=6400km,m=1000kg$
$\Delta E=2.7\times {10}^{9}J$