A satellite is launched into a circular orbit of radius

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:

  1. $1.5$

  2. $2.0$

  3. $0.7$

  4. $3.0$

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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