A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the earth is `1.50 xx 10^(8) Km` away from the sun ?

Explanation

Given that `T_(s) = 29.5 T_(e)` and `R_(e) = 1.5 xx 10^(8) Km`
According to Kepler.s third law,
we can write `T^(2) prop R^(3)`
`rArr ((T_(s))/(T_(e)))^(2) = ((R_(s))/(R_(e)))^(3) R_(s) = R_(2)((T_(s))/(T_(e)))^(2//3)`
`rArr R_(3) = 1.5 xx 10^(8)((29.5 T_(e))/(T_(e)))^(2//3) rArr R_(3) = 1.43 xx 10^(9)Km`