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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Solution

This is given that the planet went around the sun twice as fast as the earth.

Consider the time taken by the earth to complete one revolution is 1 year, time taken by the planet is T p = T e 2 and orbital radius of planet is R p .

According to the Kepler’s third law of planetary motion,

( R p R e ) 3 = ( T p T E ) 2 R p R e = ( 1 2 1 ) 2 3 = ( 0.5 ) 2 3 R p R e =0.63

Thus, the orbital radius of the planet is 0.63times smaller than the earth.

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