Gravitation

Question : 14 of 25

Marks: +1, -0

A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the earth is

1.50 \times 10^{8}

km away from the sun?

Solution:

Using Kepler’s third law,

\frac{T_{S}^{2}}{R_{S}^{3}} = \frac{T_{E}^{2}}{R_{E}^{3}}

\Rightarrow R_{s}=R_{E} \left( \frac{T_{s}}{T_{E}} \right)^{\frac{2}{3}}

= 1.5 \times 10^{8} \left( \frac{29.5 T_{E}}{T_{E}} \right)^{\frac{2}{3}}

= 1.4 \times 10^{9} \text{ km}

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