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 distance of 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)" " therefore T_(1)^(2) prop a_(1)^(3) & T_(2)^(2)=8a_(1)^(3)`
`(T_(1)^(2))/(T_(2)^(2))=(a_(1)^(3))/(8a_(1)^(3))=(1)/(8), 8T_(1)^(2)=T_(2)^(2)`
`therefore T_(2)=2sqrt(2)T_(1)`