Question

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

• A. $8days$
• B. $4days$
• C. $2days$
• D. $16days$

Answer 1

The correct option is A $8days$

Given,

$r_1=r$

$r_2=4r$

$T_1=1day$

The time period of the geostationary satellite is given by

$T=2\pi \sqrt{\frac{r^3}{G{m}_E}}$. . . . . .(1)

where, $G=$ gravitational constant

From equation (1),

$T\propto \sqrt{r^3}$

$\frac{T_2}{T_1}=\sqrt{\frac{r_2^3}{r_1^3}}$

$T_2=T_1\sqrt{\frac{4r\times 4r\times 4r}{r^3}}=8T_{1}days$

$T_2=8\times 1=8days$

The correct option is A.