An unknown planet orbits the sun with distance twice the semi major axis distance of the Earth's orbit. It the Earths time period is `T_(1)` , what is the time period of this period is planet?

Explanation

By Kepler.s 3rd law `T^(2)prop a^(3)`
Time period of unknown planet = `T_(2)`
Time period of Earth =`T_(1)`
Distance of unknown planet from the Sun = `a_(2)`
`(T_(1)^(2))/(T_(2)^(2)) = (a_(1)^(2))/(a_(2)^(3))`
`T_(2) = ((a_(2))/(a_(1)))^(3/2)T_(1)" "a_(2)=2a`
`T_(2) = ((2a_(1))/(a_(1)))^(3/2)T_(1) rArrT_(2) =2sqrt(2)T_(1)`