Question

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

Moderate

Solution

The kinetic energy of a satellite moving in an orbit around the earth is given by
$K= \frac{1}{2} {mv}^{2} = \frac{1}{2} m (\frac{GM}{r})$
or $= \frac{GMm}{2 r}$ ……….(1)
The potential energy of satellite and earth system
$U = \frac{GMm}{r}$ ………….(2)
where r is the distance of the satellite from the centre of the earth
$\frac{K}{U} = \frac{GMm / 2 r}{GMm / r} = \frac{1}{2}$

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