Question

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
2 Superscript three-halves

Answer 1

T = A^(3/2). If A doubles, T' = (2A)^(3/2) = 2^(3/2) A^(3/2) = 2^(3/2) T.

Answer: 2^(3/2) (i.e., 2·√2).