A Saturn year is 29.5 times that earth year. How far is the Saturn from the sun if the earth is `1.50xx10^(8)` km away from the sun ?

Explanation

distance of the earth from the sun, `r_e`=`1.5*10^8` km

`T_e`=Time period of the earth

Time period of Saturn, `T_s`=`29.5``T_e`

Distance of Saturn from the Sun= `r_s`

From Kepler's third law of planetary motion,

`T`=`sqrtfrac(4pi^2xxr^3)(GM)`

`impliesfrac((r_s)^3)((r_e)^3)=frac((T_s)^2)((T_e)^2)`

`r_s=r_e*((T_s)/(T_e))^(2/3)`

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