A planet year is 8 times the Earth year. How far is the planet from the Sun,
if the earth is 1.5x108 km away from the Sun ? *
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Answer:
Distance of Earth from Sun,r
e
=1.5×10
11
m
Time period of 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=
GM
4π
2
r
3
⟹r
s
3
/r
e
3
=T
s
2
/T
e
2
r
s
=r
e
(T
s
/T
e
)
2/3
=1.5×10
11
×29.5
2/3
=14.32×10
11
m
Therefore, the distance between Saturn and the Sun is 1.43×10
12
m.
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