Question

A satellite $X$ is launched into a circular orbit of radius $R$ around the earth while a second satellite $Y$ is launched into an orbit of radius $4R$. The ratio of the time periods of $Y$ to $X$ is ______.

• A. $1$
• B. $4$
• C. $8$
• D. $16$

Answer 1

The correct option is C

$8$

Given:
Radius of orbit of $X$ is $R_1=R$
Radius of orbit of $Y$ is$R_2=4R$
Time period of orbit of $X$ be $T_1$
Time period of orbit of $Y$ be $T_2$

According to Kepler's Third Law,
Time period $T\propto R^{\frac{3}{2}}$
where R : Radius of the orbit.

$⟹\frac{T_2}{T_1}=\frac{R_2^{3/2}}{R_1^{3/2}}$
$\frac{T_2}{T_1}={\left(\frac{4R}{R}\right)}^{3/2}=8$