Question

The time period of a satellite in a circular orbit of radius $R$ is $T$. The period of another satellite in a circular orbit of radius $9R$ is:

• A. $3T$
• B. $9T$
• C. $27T$
• D. $12T$

Answer 1

The correct option is C $27T$

From kepler's law:$$T^2\propto R^3$$$\Rightarrow \frac{T_1}{T_2}={\left(\frac{R_1}{R_2}\right)}^{\frac{3}{2}}$

$\Rightarrow \frac{T_1}{T_2}={\left(\frac{R}{9R}\right)}^{\frac{3}{2}}$

$\Rightarrow \frac{T}{T_2}=\frac{1}{27}$

$\Rightarrow T_2=27T$