Question

The equation mc025-1.jpg 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

Kepler's law gives T^2 = A^3, so A = T^(2/3). If T_Y = 2 T_X then

A_Y / A_X = (T_Y / T_X)^(2/3) = 2^(2/3).

Answer: 2^(2/3).