If a satellite orbiting the earth is 9 times closer to the earth than the moon, what is the time period of rotation of the satellite? Given rotational time period of Moon = 2 days and gravitational attraction between the satellite and the moon is neglecte

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Solution

Q.
If a satellite orbiting the earth is 9 times closer to the earth than the moon, what is the time period of rotation of the satellite Given rotational time period of Moon = 27 days and gravitational attraction between the satellite and the moon is neglected. [2025]

1 1 day

2 81 days

3 27 days

4 3 days

Ans.
(1)

From Kepler's law, $T^{2} \propto R^{3}$

${(\frac{T_{m}}{T_{s}})}^{2} = {(\frac{R}{R / 9})}^{3}$

$\frac{T_{m}}{T_{s}} = {(3)}^{3} \Rightarrow T_{s} = (\frac{27}{27}) = 1 d a y$

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