Question

A satellite orbiting the earth in a circular orbit of radius R completes one revolution in 3 h. If orbital radius of geostationary satellite is 36,000 km, orbital radius of earth is :

• A. 6000 km
• B. 9000 km
• C. 12000 km
• D. 15000 km

Answer 1

Answer: (B)

Time period, $T^2=\frac{4{\pi }^2}{GM}{r}^3$ or $T^2=\frac{4{\pi }^2}{g{R}^2}{r}^3$ or $T=\frac{2\pi }{R}\sqrt{\frac{r^3}{g}}$ or $T\propto r^{3/2}$ $\therefore$ $\frac{T_1}{T_2}={\left(\frac{r_1}{r_2}\right)}^{3/2}$ Given, $T_1=3h,T_2=24h$ (geostationarysatellite) $r_1=R,r_2=36000km$ $\therefore$ $\frac{3}{24}={\left(\frac{R}{36000}\right)}^{3/2}$ or $R={\left(\frac{1}{8}\right)}^{2/3}\times 36000$ or $R=\frac{1}{4}\times 36000=9000km$