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?

An unknown planet orbits the sun with distance twice the semi major ax

1.	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?
Answer» Solution :By Kepler.s 3rd LAW`T^(2)prop a^(3)` TIME periodof unknownplanet = `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)`