A body is orbiting around earth at a mean radius which is two times as greater as the parking orbit of a satellite, the period of body is

Options

A. 4 days
B. 16 days
C. `2 sqrt(2)` days
D. 64 days

Answer

C

Explanation

By Kepler's third law of planetary motion,
We have, `T^(2) prop a^(3)`
Given, `T_(1)=1` day (geostationary)
`a_(1)=a,a_(2)=2a` ltbegt `:. (T_(1)^(2))/(T_(2)^(2))=(a_(1)^(3))/(a_(2)^(3))rArrT_(2)^(2)=(a_(2)^(3))/(a_(1)^(3))T_(1)^(2)=((2a)^(3))/(a^(3))xx1=8`
`rArr T_(2) =2 sqrt(2)` days.