Question

A satellite can be in a geostationary orbit around the earth at a distance $r$ from the centre. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth if its distance from the center is

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

Answer 1

The correct option is C $\frac{r}{(4{)}^{1/3}}$

From Kepler's third law,

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

$[\omega =\frac{2\pi }{T}]$

$\omega \propto \frac{1}{r^{3/2}}$

Let the distance of satellite is $R$ from the centre.

$\therefore$ When the angular velocity is doubled,

$\left(\frac{\omega }{2\omega }\right)={\left(\frac{R}{r}\right)}^{3/2}$

$\frac{R}{r}=\frac{1}{(2{)}^{2/3}}$

$R=\frac{r}{(4{)}^{1/3}}$