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

Explanation

`implies` Time period of earth = 1 yr
Time period of planet Saturn = 29.5 yr
Orbital radius of earth `R_E = 1.5 xx 10^(8)` km
Orbital radius of planet Saturn `= R_S`
According to Kepler.s third law,
`T^(2) prop r^3`
`:. ((T_E)/(T_s))^2 = (R_E/R_S)^3`
`:. (1/(29.5))^2 =((1.5xx10^8)/(R_s))^3`
`:. R_s^3 = (29.5)^2 (1.5 xx10^8)^3`
`= 2.947 xx 10^(27) km`
`:. R_s= 1.43 xx10^(9) km`
`= 1.43 xx10^(12) m`