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Question
A saturn year is 29.5 times the earth year how far is the saturn from the sun if the earth is away from the sun?
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Solution
“A Saturn year is 29.5 times the earth year”
It means time period of Saturn is 29.5 times that of earth
T’ = 29.5T
According to Kepler’s law
T^2 ∝ r^3
(T / T’)^2 = (r / r’)^3
(T / (29.5T))^2 = (1.5 × 10^8 / r)^3
1 / 870.25 = (1.5 × 10^8 / r)^3
r = 1.5 × 10^8 × (870.25)^(1/3)
r = 1.43 × 10^9 km
“A Saturn year is 29.5 times the earth year”
It means time period of Saturn is 29.5 times that of earth
T’ = 29.5T
According to Kepler’s law
T^2 ∝ r^3
(T / T’)^2 = (r / r’)^3
(T / (29.5T))^2 = (1.5 × 10^8 / r)^3
1 / 870.25 = (1.5 × 10^8 / r)^3
r = 1.5 × 10^8 × (870.25)^(1/3)
r = 1.43 × 10^9 km
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