The mean distance increased by a factor of 2^(²/₃)
The given equation for the relationship between a planet's orbital period, T and the planet's mean distance from the sun, A is;
T² = A³.
Let the orbital period of planet X = T(X).
Let the orbital period of planet Y = T(Y).
Let the mean distance of planet X from the sun = A(X).
Let the mean distance of planet Y = A(Y).
Thus;
A(Y) = 2A(X)
Therefore;
[T(Y)]² = [A(Y)]³ = [2A(X)]^3
However, [T(X)]² = [A(X)]³
Thus;
[T(Y)]² = 2³[T(X)]² * [T(Y)]²/[T(X)]² = 2³T(Y)/T(X) = 2^(³/₂)
That's for orbital period but the mean distance will increase by 2^(²/₃)
Thus we conclude that, the mean distance increased by a factor of 2^(²/₃)
Read more about factor of increase at; https://brainly.com/question/1638294
#SPJ1
