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Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth ?

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a

Greater by a factor 0.63

b

Greater by a factor 2

c

Lesser by a factor 2

d

Lesser by a factor of 0.63

answer is C.

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Detailed Solution

$\begin{array}{l} T^{2} \propto R^{3}; T^{2 / 3} \propto R \\ {(\frac{T}{T_{2}})}^{2 / 3} = \frac{R}{R_{2}}; \\ \Rightarrow {(\frac{T}{T / 2})}^{2 / 3} = \frac{R}{R_{2}} \\ \Rightarrow R_{2} = \frac{R}{2^{2 / 3}} = \frac{R}{4^{1 / 3}} = 0 .63 R \end{array}$

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Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth ?