A certain planet's year is `8` times the earth's year. Find the distance of this planet from the sun if the distance of the earth is `1 AU` from the sun.

Explanation

Let `T_(P), T_(E)` be the period of revolution of planet and earth around the sun. Given,
`T_(P) = 8 T_(E), r_(E) = 1 AU = 1.5 xx 10^(11) m, r_(P) = ?`
As `(T_(P)^(2))/(T_(E)^(2)) = (r_(P)^(3))/(r_(E)^(3)) `or `r_(P) =e_(E)((T_(P))/(T_(E)))^(2//3)`
`= (15 xx 10^(11))(8)^(2//3)`
`= (1.5 xx 10^(11)) xx 4`
`6.0 xx 10^(11) m`