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 ?

A saturn year is 29.5 times the earth year. How far is the saturn from

1.	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 ?
Answer» Solution :`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`