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?

2^1/3

2^1/2

2^2/3

2^3/2

you!

2^3/2

Step-by-step explanation:

The question is on formulae variation

Given T²=A³the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A

Making T subject of the formulae

T²=A³square root both sides

T= √A³ OR    (A³)^1/2

if  the orbital period of planet Y is twice the orbital period of planet X then,

Y=2T

Y=2× √A³

Y=2×(A³)^1/2

Applying the laws of indices

Y=2×(A)^(3×1/2)

Y=2×(A)^3/2

Compare

A^3/2 and 2A^3/2

The mean distance increased by 2^3/2

i believe it's a.

i'm not sure on this one, most likely correct.