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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 ?

Q:8.3  Suppose there existed a planet that went around the sun was twice as fast as the earth. What would be its orbital size as compared to that of the earth?

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Time taken by planet to complete a revolution around sun  =       \frac{1}{2}T_e

Using Kepler's law of planetary motion we can write :

                                                  \left ( \frac{R_p}{R_e} \right )^3\ =\ \left ( \frac{T_p}{T_e} \right )^2

or                                                 \frac{R_p}{R_e}\ =\ \left ( \frac{\frac{1}{2}}{1} \right )^\frac{2}{3}

or                                                  \frac{R_p}{R_e}\ =\ 0.63

Thus the planet is 0.63 times smaller than earth.

Posted by

Devendra Khairwa

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