Question

A geostationary satellite is orbiting the earth at a height $6R$ above the earth's surface, where $R$ is radius of earth. The time period of another satellite at a height $2.5R$ from earth's surface would be:

• A. $24h$
• B. $\frac{6}{2.5}h$
• C. $\frac{25}{6}h$
• D. $6\sqrt{2}h$

Answer 1

The correct option is D $6\sqrt{2}h$

For geostationary satellite : $r_1=R+6R=7R$ $T_1=24$ $h$

For second satellite : $r_2=R+2.5R=3.5R$

Time period of satellite : $T=2\pi \sqrt{\frac{r^3}{GM}}$ where, $r$ is the radius of orbit

$⟹$ $\frac{T_2}{T_1}=\sqrt{\frac{r_2^3}{r_1^3}}$

$\therefore$ $\frac{T_2}{24}=\sqrt{\frac{(3.5R{)}^3}{(7R{)}^3}}=\frac{1}{2\sqrt{2}}$

$⟹$ $T_2=\frac{24}{2\sqrt{2}}=6\sqrt{2}$ $h$