The planet Neptune travels around the sun with a period of 165 years. The ratio of its mean radius of the orbit to that of the earth is approximately

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The planet Neptune travels around the sun with a period of 165 years. The ratio of its mean radius of the orbit to that of the earth is approximately

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10 : 1

20 : 1

30 : 1

40 : 1

answer is C.

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Detailed Solution

We are given radius of earth

= r_{1}

Time period $= T_{1} = 1 year$

Radius of Neptune $= r_{2}$

Time period $= T_{2} = 165 year$

${(\frac{T_{1}}{T_{2}})}^{2} = {(\frac{r_{1}}{r_{2}})}^{3} \Rightarrow \frac{r_{1}}{r_{2}} = {(\frac{165}{1})}^{\frac{2}{3}}$

$= 30 : 1 (nearly)$

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