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. If planet Y is twice the mean distance from the sun as planet X, by what factor is the orbital period increased?

Given the relationship T^2 = A^3, to compare the values of the orbital periods of X and Y, it would be easier to assign values. Since the Planet Y's distance A is twice that of Planet X's distance A, this can be shown below:

For Planet X (where A = 2):

T^2 = 2^3

T = 2.828

For Planet Y (where A = 4)

T^2 = 4^3

T = 8

Therefore, planet Y's orbital period is larger by (8/2.828) = 2.83 times.