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

Explanation

Here, `T_(e)` year , `T_(p) = (T_(e))/(2) = (1)/(2)` year , `r_(e) = 1 A.U., r_(p) = ?`
Using kepler's third law, we have `r_(p) = r_(e) (T_(p)/(T_(e)))^(2//3) = 1 ((1//2)/(1))^(2//3) = 0.63 AU`