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(C) The orbital time period for a satellite is given by $T = 2 \pi \sqrt{\frac{r^3}{GM_E}}$.From this relation,we can see that $T \propto r^{3/2}$.For

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$48 \sqrt{2} 	ext{ hrs}$

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(C) The orbital time period for a satellite is given by $T = 2 \pi \sqrt{\frac{r^3}{GM_E}}$.From this relation,we can see that $T \propto r^{3/2}$.For a geostationary satellite,the initial time period is $T_1 = 24 	ext{ hrs}$.Let the initial radius be $r_1$ and the new radius be $r_2 = 2r_1$.Using the proportionality $T \propto r^{3/2}$,we have the ratio:$\frac{T_2}{T_1} = \left( \frac{r_2}{r_1} ight)^{3/2}$.Substituting the given values:$\frac{T_2}{24} = \left( \frac{2r_1}{r_1} ight)^{3/2} = (2)^{3/2} = 2\sqrt{2}$.Therefore,$T_2 = 24 	imes 2\sqrt{2} = 48\sqrt{2} 	ext{ hrs}$.

$A$ geostationary satellite is taken to a new orbit such that its distance from the centre of the earth is doubled. Find the time period of this satellite in the new orbit.

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