Question

The time period of a satellite very close to earth is $T$. The time period of geo-synchronous satellite will be

• A. $2\sqrt{2}\left(T\right)$
• B. $6\sqrt{6}\left(T\right)$
• C. $7\sqrt{7}\left(T\right)$
• D. $\frac{1}{7\sqrt{7}}\left(T\right)$

Answer 1

Answer: (C)

$7\sqrt{7}\left(T\right)$

A geo-synchronous satellite orbits at a height of $6R$ from the surface of the earth.
we have $T^2\propto r^3$
$\Rightarrow {\left(\frac{T_1}{T_2}\right)}^2={\left(\frac{r_1}{r_2}\right)}^3$
$\Rightarrow {\left(\frac{T_1}{T_2}\right)}^2={\left(\frac{R}{R+6R}\right)}^3$
$\Rightarrow {\left(\frac{T_1}{T_2}\right)}^2={\left(\frac{1}{7}\right)}^3$
$\Rightarrow \frac{T_1}{T_2}=\frac{1}{\sqrt{7^3}}$
$\Rightarrow T_2=T_1\sqrt{7^3}=7\sqrt{7}\left(T\right)$