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A Saturn year is 29.5 times the earth ye...

A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is `1.5xx10^8` km away from the sun?

Text Solution

Verified by Experts

Given that `T_8 = 29.5 T_e` and `R_e = 1.5 xx 10^8 Km`
According to kepler.s third law , we can write `T^2 prop R^3`
` = (T_s/T_e)^2 = (R_s/R_e)^3 rArr R_s = R_e (T_s/T_e)^(2//3)`
` rArr R_s = 1.5 xx 10^8 ((19.5T_e)/(T_e))^(2//3) rArr R_s = 1.43 xx 10^9 km`
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