Question

Satellite is revolving around earth. If its radius of orbit is increased to $4$ times of the radius of geostationary satellite, what will be its time period?

• A. $2\text{days}$
• B. $8\text{days}$
• C. $16\text{days}$
• D. $4\text{days}$

Answer 1

The correct option is B $8\text{days}$

The relationship between the time period of revolution of a satellite and the radius of orbit is $$T\propto r^{3/2}$$Let, $r_1$ be the radius of orbit of a geostationary satellite and $r_2$ be the radius of the given satellite.

$\therefore \frac{T_2}{T_1}={\left(\frac{r_2}{r_1}\right)}^{3/2}$

Given,
Time period of geostationary satellite, $T_1=24\text{hours}$,
$r_2=4r_1$

$\Rightarrow T_2=24\times {\left(\frac{4r_1}{r_1}\right)}^{3/2}$

$\therefore T_2=8\text{days}$.

Hence, option (a) is the correct answer.

Why this question: It is important to remember that the time period of a geostationary satellite is the same as the earth which is equal to $24\text{hrs}$.