Question

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 the orbital period of planet Y is twice the orbital period of planet X, by what factor is the mean distance increased?
2 Superscript one-third
2 Superscript one-half
2 Superscript two-thirds
2 Superscript three-halves

Answer 1

Use A = T^(2/3). If T_Y = 2T_X then A_Y/A_X = (2)^(2/3).

Answer: 2^(2/3) (i.e., the cube root of 4).