If a small planet were discovered whose orbital period was twice that of

Earth, how many times farther from the Sun would this planet be?

1 answer

consider that T^2 = kr^3
That means that T^2/r^3 is constant

T^2/r^3 = (2T)^2/(xr)^3 = 4T^2/x^3r^3
So, 4/x^3 = 1, and x = ∛4

That is, our small planet's orbital radius is ∛4 times earth's.