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, re = 1.5 ×
108 km = 1.5 ×
1011 mTime period of the Earth = Te
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 X 1011 (29.5 Te / Te)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
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