Q. A satellite is launched into a circular orbit of radius $R$ around the earth. A second satellite is launched into an orbit of radius $4R$. The ratio of their respective periods is
A) 4:1
B) 1:8
C) 8:1
D) 1:4
Explanation
(b) We have
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T^{2} \propto R^{3}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ R_{1} = r$
$and\ \ \ \ \ \ \ \ \ \ \ R_{2} = 4r$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{T_{1}^{2}}{T_{2}^{2}} = \frac{(r)^{3}}{(4r)^{3}}$
$or\ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{T_{1}}{T_{2}} = \frac{1}{8}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.