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  4. A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius (1.01)R . The period of the second satellite is larger than that of the first one by approximately

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Q. A satellite is launched into a circular orbit of radius $R$ around the earth. A second satellite is launched into an orbit of radius $\left(1.01\right)R$ . The period of the second satellite is larger than that of the first one by approximately

NTA AbhyasNTA Abhyas 2020Gravitation

Solution:

In the problem orbital radius is increased by $1\%$
Time period of satellite $T \propto r^{3 / 2}$
$\Rightarrow \frac{\Delta T}{T}=\frac{3}{2}\times \frac{\Delta r}{r}$
Percentage change in the time period
$=\frac{3}{2}$ [ $\%$ change in orbital radius]
$=\frac{3}{2}\left(1 \%\right)=1.5\%$