Question

The time period of an artificial satellite in a circular orbit of radius R is 2 days and its orbital velocity is $v_0$. If time period of another satellite in a circular orbit is 16 days then

• A. Its radius of orbit is 4R and orbit velocity is $v_0$
• B. Its radius of orbit is 4R and orbital velocity is $\frac{v_0}{2}$
• C. Its radius of orbit is 2R and orbital velocity is $v_0$
• D. Its radius of orbit is 2R and orbital velocity is $\frac{v_0}{2}$

Answer 1

The correct option is B

Its radius of orbit is 4R and orbital velocity is $\frac{v_0}{2}$

According to the Kepler's $3^{rd}$ Law

$T^2\propto R^3$
$\therefore R_2=4R$

Orbital velocity = $\sqrt{(}\frac{GM}{r})$