Q. A satellite moves round the earth in a circular orbit of radius $R$ making 1 rev/day. A second satellite moving in a circular orbit, moves round the earth ones in 8 days. The radius of the orbit of the second satellite is
A) 8 R
B) 4 R
C) 2 R
D) R
Explanation
(b) From Kepler’s third law of planetary motion
$\ \ \ \ \ \ \ \ \ \ \ \ \ T^{2} \propto R^{3}$
$Given,\ T_{1} = 1,\ T_{2} = 8,\ R_{1} = R$
$\therefore\ \ \ \ \ \ \ \frac{T_{1}^{2}}{T_{2}^{2}} = \frac{R_{1}^{3}}{R_{2}^{3}}$
$\ \ \ \ \ \ \ \ \ R_{2}^{3} = R_{1}^{3}\frac{{\ \ T}_{2}^{2}}{T_{1}^{2}}\ \ \ $
$\ \ \ \ \ \ \ \ \ R_{2}^{3} = R_{1}^{3} \times (8)^{2}$
$\ \ \ \ \ \ \ \ \ R_{2}^{3} = R^{3} \times \left( 2^{3} \right)^{2}$
$\Rightarrow \ \ \ R_{2} = R \times 4 = 4R$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.