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

Given: `a_(2)=2a_(1)`
To find: `T_(2)=??`
Formula: `T^(2)propa^(3)" "rArrTprop(a)^(3//2)`
`T_(2)prop(2a_1)^(3//2)`
`prop(2)^(3//2)(a_1)^(3//2)`
`T_(2)prop2sqrt(2)T_(1)`
`thereforeT_(2)=(2sqrt(2))T_(1)`