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  4. For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is:

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Q. For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is:

AIPMTAIPMT 2005Gravitation

Solution:

$\frac{G M m}{R^{2}}+m \omega^{2} R=0$
$\therefore \frac{G M m}{R^{2}}=m \omega^{2} R$
$K . E .=\frac{1}{2} I \omega^{2}=\frac{1}{2} m R^{2} \omega^{2}=\frac{G M m}{2 R}$
$P . E .=-\frac{G M m}{R} $
$\therefore K . E .=\frac{|P . E .|}{2}$
$\therefore \frac{K . E .}{|P . E .|}=\frac{1}{2}$