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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 × 108km 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 = r
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.

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