Question

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 first one by approximately

• A. $ 0.5\% $
• B. $ 1.0\% $
• C. $ 1.5\% $
• D. $ 3.0\% $

Answer 1

Answer: (C)

Period of a satellite $T \propto r^{3 / 2}$
Hence, $\frac{\Delta T}{T}=\frac{3}{2} \frac{\Delta r}{r}$
As $\frac{\Delta r}{r}=\frac{1.01 r-r}{r}$
$=0.01=0.01 \times 100 \%=1 \%$
Hence, $\frac{\Delta T}{T}=\frac{3}{2} \times 1 \%=1.5 \%$