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

The earth's time period = `T_(1)`
Semi major axis distanceof earth =`a_(1)`
Time period of unknown planet = `T_(2)`
Semi major axis of unknown planet =`2a_(1)`
Kepler's III law
`T^(2) prop a^(3)" ":. T_(1)^(2) prop a_(1)^(3) & T_(2)^(2) = 8a_(1)^(3)`
`(T_1^2)/(T_2^2) = (a_1^3)/(9a_1^3) = 1/8`
`8T_(1)^(2) = T_(2)^(2)`
`:. T_(2) = 2sqrt(2)T_(1)`.