Gravitation NCERT Solutions Class 11 Physics - Solved Exercise Question 8.14

Question 8.14:

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?

Solution:

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, we have
T = (4π²r³ / GM)^1/2
For Saturn and Sun, we can write
r_s³ / r_e³  =  T_s² / T_e²
r_s = r_e(T_s / T_e)^2/3
= 1.5 X 10¹¹ (29.5 T_e / T_e)^2/3
= 1.5 X 10¹¹ (29.5)^2/3
= 14.32 X 10¹¹ m
Hence, the distance between Saturn and the Sun is 1.43 X 10¹² m