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?

Options

A. `1.4xx10^(6)` km
B. `1.4xx10^(7)` km
C. `1.4xx10^(8)` km
D. `1.4xx10^(9)` km

Answer

D

Explanation

(d) Here, `T_(S)=29.5 T_(E), R_(E)=1.5xx10^(8)` km,`R_(S)=?`
According to Kepler's third law, `T^(2) prop R^(3)`
`:. (T_(S)^(2))/(T_(E)^(2))=(R_(S)^(3))/(R_(E)^(3)),R_(S)=R_(E)((T_(S))/(T_(E)))^(2//3)`
`R_(S)=1.5xx10^(8)((29.5T_(E))/(T_(E)))=1.4xx10^(9)` km