Question

A satellite can be in a geostationary orbit around earth in an orbit of radius r. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth of radius

• A. $\frac{r}{2}$
• B. $\frac{r}{2\sqrt{2}}$
• C. $\frac{r}{(4{)}^{1/3}}$
• D. $\frac{r}{(2{)}^{1/3}}$

Answer 1

Answer: (C)

Angular speed of earth = angular speed of geostationary satellite

$T\propto \frac{1}{\omega }$

$\Rightarrow \frac{T_2}{T_1}=\frac{{\omega }_1}{{\omega }_2}=\frac{1}{2}$

$\Rightarrow T_2=\frac{T_1}{2}$

Also, $T\propto r^{3/2}$

$\therefore {\left(\frac{r_2}{r_1}\right)}^{3/2}=\frac{T_2}{T_1}=\frac{1}{2}$

$\frac{r_2}{r_1}={\left(\frac{1}{2}\right)}^{2/3}=\frac{1}{4^{1/3}}$

$r_2=\frac{r_1}{4^{1/3}}$