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  4. The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be :

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Q. The time period of a satellite revolving around earth in a given orbit is $7$ hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be :

JEE MainJEE Main 2022Gravitation

Solution:

$T =\frac{2 \pi}{\sqrt{ GM }} r ^{3 / 2}$
$\frac{ T _{1}}{ T _{2}}=\left(\frac{ r _{1}}{ r _{2}}\right)^{3 / 2}=\left(\frac{1}{3}\right)^{3 / 2}$
$T _{2}= T _{1} 3 \sqrt{3}=21 \sqrt{3}$ hours
$\approx 36$ hours