Question

A satellite is revolving around earth. If its radius of orbit is increased to 4 times that of a geostationary satellite, what will be its time period?

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

Answer 1

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

The relationship between the time period of revolution of a satellite and the radius of orbit is

$T^2\propto R^3$

$\therefore \frac{T_2}{T_1}={\left(\frac{r_2}{r_1}\right)}^{3/2}=(4{)}^{3/2}$

Since, the time period of geostationary satellite is equal to the time period of earth, i.e. $1\text{day}$

$\Rightarrow T_2=T_1(4{)}^{3/2}=8T_1=8\text{days}$

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

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 $24\text{hrs}$.