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. `2sqrt(2)` days
D. `64` days

Answer

C

Explanation

From kepler third law of planetary motion `T^(2) prop r^(3)` Given `T_(1)=1` day (geosatationary)
`therefore (T_(1))/(T_(2))^(2)=(r_(1))/(r_(2))^(3)`
`rarr T_(2)^(2)=(r_(2))/(r_(1))^(3)xxT_(1)^(2)=(2r)/(R )^(3)xx1=8`
`rarr T_(2)=2sqrt(2)`days