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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 `1.50 xx 10^8 km` away from the sun ?

Text Solution

Verified by Experts

we are given:
`(T_("Saturn"))/(T_("Earth")) = 29.5, R_("Earth")= 1.50 xx 10^(8) Km`
We are to calculate, Distance of Saturn from the sun i.e., `R_("saturn")` From Kepler.s `3^(rd)` law
`(T_("Saturn")^(2))/(T_("Earth")^(2))= (R_("Saturn")^(3))/(R_("Earth")^(3)) rArr R_("Saturn") = R_("Earth") xx ((T_("Saturn"))/(T_("Earth")))^(2//3) = (1.5 xx 10^(8)) ((29.5)/(1))^(2//3)`
`=(1.5 xx 10^(8)) xx 9.547 = 14.32 xx 10^(8)km`
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