A satellite moves in a circle around the earth. The radius of this circle is equal to one half of the radius of the moon's orbit. The satellite completes one revolution is :

Options

A. `1//2` lunar month
B. `2//3` lunar month
C. `2^(-3//2)` lunar month
D. `2^(3//2)` lunar month

Answer

C

Explanation

According to kepler's law `T^(2) prop r^(3)` or `T prop r^(3//2)`
and as `r_(s) = (1)/(2) r_(m), (r_(s))/(r_(m)) = (1)/(2)`
`:. (T_(s))/(T_(m)) = ((r_(s))/(r_(m)))^(3//2) = ((1)/(2))^(3//2) = 2^(-3//2)`
`T_(s) = 2^(-3//2) T_(m)`