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  4. For a satellite orbiting in an orbit, close to the surface of earth, to escape, what is the percentage increase in the kinetic energy required?

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Q. For a satellite orbiting in an orbit, close to the surface of earth, to escape, what is the percentage increase in the kinetic energy required?

Gravitation

Solution:

Orbital velocity for close to earth orbits $=\sqrt{g R}$.
Escape velocity required $=\sqrt{2 g R}$.
$\%$ Increase required $=\frac{v_e-v_0}{v_0} \times 100$
$=\frac{\sqrt{g R}(\sqrt{2}-1)}{\sqrt{g R}} \times 100=41 \%$