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  4. The ratio of the kinetic energy required to be given to a satellite so that it escapes the gravitational field of Earth to the kinetic energy required to put the satellite in a circular orbit just above the free surface of Earth is

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Q. The ratio of the kinetic energy required to be given to a satellite so that it escapes the gravitational field of Earth to the kinetic energy required to put the satellite in a circular orbit just above the free surface of Earth is

Gravitation

Solution:

$v_{e}=\sqrt{\frac{2 G M}{R}} $
$\Rightarrow k_{e}=\frac{1}{2} m v_{e}^{2}=\frac{G M m}{R}$
$v_{o}=\sqrt{\frac{G M}{R+h}}$
here $h=0, k_{o}=\frac{1}{2} m v_{o}^{2}=\frac{G M m}{2 R}$
$\Rightarrow \frac{k_{e}}{k_{o}}=2$