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? | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-8 Gravitation



Q.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?

 

 

Answer



Distance of the Earth from the Sun, re = 1.5 × 108 km = 1.5 × 1011 m
Time period of the Earth = e
Time period of Saturn, Ts = 29. 5 Te
Distance of Saturn from the Sun = rs
From Kepler’s third law of planetary motion, we have
T = (4π2r3 / GM)1/2
For Saturn and Sun, we can write
rs3 / re3  =  Ts2 / Te2
rs = re(Ts / Te)2/3
= 1.5 × 1011 (29.5 Te / Te)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.