Question

Imagine a geo-stationary satellite of earth which is used as an intercontinental telecast station. At what height will it have to be established

• A. ${10}^3\text{m}$
• B. $6.4\times {10}^3\text{m}$
• C. $35.94\times {10}^6\text{m}$
• D. Infinity

Answer 1

The correct option is C $35.94\times {10}^6\text{m}$

We know that the time period of a satellite in a circular orbit of radius $r$ is given by

$T^2=\frac{4{\pi }^2{r}^3}{GM}$

At height $h$ from surface,

$\Rightarrow T^2=\frac{4{\pi }^2(R+h{)}^3}{GM}$

$T=24\text{hrs};R=6400\text{km};G=6.67\times {10}^{-11}{\text{Nm}}^2{\text{/kg}}^2;M=6\times {10}^{24}\text{kg}$

Substituting the above, we get

$\Rightarrow (24\times 60\times 60{)}^2=\frac{4{\pi }^2(6.4\times {10}^6+h{)}^3}{6.67\times {10}^{-11}\times 6\times {10}^{24}}$

$\Rightarrow h=35,897\text{km}=35.89\times {10}^6\text{m}$

Hence, option $\left(c\right)$ is correct.

Why this question: It is important to remember that the distance of a geostationary satellite from the center of the earth is equal to $36000\text{km}$.