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

The correct option is C 1.5 %

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