Question:
A satellite is launched into a circular orbit of radius
$\mathrm{R}$ around earth, while a second satellite is launched into a circular orbit of radius $1.02 \mathrm{R}$. The percentage difference in the time periods of the two satellites is:
Correct Option: , 4
Solution:
$\mathrm{T}^{2} \propto \mathrm{R}^{3}$
$\mathrm{T}=\mathrm{kR}^{3 / 2}$
$\frac{\mathrm{dT}}{\mathrm{T}}=\frac{3}{2} \frac{\mathrm{dR}}{\mathrm{R}}$
$=\frac{3}{2} \times 0.02=0.03$
$\%$ Change $=3 \%$
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