Given that the
equation T^2=A^3 shows the relationship between a planet’s orbital
period, T, and the planet’s mean distance from the sun, A, in
astronomical units, AU.
i.e. [tex]T= \sqrt{A^3} [/tex]
If planet Y is twice the mean distance from the
sun as planet X,
i.e. [tex]A_Y=2A_X[/tex],
then,
[tex] \frac{T_Y}{T_X} = \frac{\sqrt{(2A_X)^3}}{\sqrt{(A_X)^3}} = \frac{(2A_X)^3}{(A_X)^3} = \frac{8(A_X)^3}{(A_X)^3} =8[/tex]
Therefore, the orbital period increased by a factor of 2^3/2
