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_(c)=1` year: `T_(p)=(T_(r))/(2)=(1)/(2)` year: `r_(c)=1A.U`.
Using kepler's third law, we have `r_(p)=r_(c)((T_(P))/(T_(c)))^(2//3)`
`rArr r_(p)=1((1//2)/(1))^(2//3)=0.63` AU