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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)` away from the sun?

A

`1.2 xx 10^9 km`

B

`1.3 xx 10^9 km`

C

`1.4 xx 10^9 km`

D

`1.5 xx 10^9 km`

Text Solution

Verified by Experts

The correct Answer is:
C

Here `T_s = 29.5 T_e, R_e = 1.5 xx 10^8 km , R_s = ?`
According to kepler.s third law , `T^2 prop R^3`
` therefore (T_s^2)/(T_e^2) = (R_s^3)/(R_e^3)`
`R_s = R_e (T_s/T_e)^(2//3) = 1.5 xx 10^8 ((29.5 T_e)/(T_e))^(2//3) = 1.4 xx 10^9 km`
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