A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.50 ×10⁸ km away from the sun?

Distance of the Earth from the Sun, r_e = 1.5 × 10⁸ km 
                                                           = 1.5 × 10¹¹ m  
Time period of the Earth = T­_e 

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 = (4π²r³ / GM)^1/2 

For Saturn and Sun, 
r_s³ / r_e³  =  T_s² / T_e² 

         r_s = r_e(T_s / T_e)^2/3 

            = 1.5 × 10¹¹ (29.5 T_e / T_e)^2/3 

             = 1.5 × 10¹¹ (29.5)^2/3 

             = 14.32 × 10¹¹ m 
Hence, the distance between Saturn and the Sun is 1.43 × 10¹² m.