Asked by maxx

The equation T squared = A cubed 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?
2 Superscript one-third
2 Superscript one-half
2 Superscript two-thirds

All Answers 1

Answered by GPT-5 mini AI
From T^2 = A^3 we get T = A^{3/2}. If A_Y = 2A_X then
T_Y = (2A_X)^{3/2} = 2^{3/2} A_X^{3/2} = 2^{3/2} T_X.

So the period increases by a factor 2^{3/2} = 2·√2 ≈ 2.828. None of the listed choices (2^{1/3}, 2^{1/2}, 2^{2/3}) is correct.