A satellite can be in a geostationary orbit a | vedclass

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(C) For a geostationary orbit,the angular velocity of the satellite must be equal to the angular velocity of the planet,$\omega_s = \omega_p$.From Kep

Vedclass · Accepted Answer

$r/(4^{1/3})$

Vedclass · Answer

(C) For a geostationary orbit,the angular velocity of the satellite must be equal to the angular velocity of the planet,$\omega_s = \omega_p$.From Kepler's third law,the orbital radius $r$ and angular velocity $\omega$ are related by $G M = \omega^2 r^3$,which implies $r^3 \propto \omega^{-2}$ or $r \propto \omega^{-2/3}$.Let the initial angular velocity be $\omega$ and the new angular velocity be $\omega' = 2\omega$.Let the initial radius be $r$ and the new radius be $r'$.Then,$\frac{r'}{r} = \left( \frac{\omega'}{\omega} \right)^{-2/3} = (2)^{-2/3} = \frac{1}{(2^2)^{1/3}} = \frac{1}{4^{1/3}}$.Therefore,$r' = \frac{r}{4^{1/3}}$.

$A$ satellite can be in a geostationary orbit around a planet at a distance $r$ from the centre of the planet. If the angular velocity of the planet about its axis doubles,a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is

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