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 planet Y is twice the mean distance from the sun as planet X, by what factor is the orbital period increased?

Answer 1

The answer for your question is going to be. 2^((3)/(2)) I know this cause I just took a quiz with this question on it

Answer 2

Answer with explanation:

The Equation which is relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU.

 → $T^2=A^3$

For Planet , X

$A_{1}=x AU\\\\(T_{1})^2=x^3$

                                        --------------------------------------(1)

And, For Planet ,Y

$A_{2}=2 x AU\\\\(T_{2})^2=(2 x)^3$

                                       -----------------------------------------(2)

Dividing equation (1) by (2)

$\frac{(T_{1})^2}{(T_{2})^2}=\frac{x^3}{(2x)^3}$

$[\frac{(T_{1})}{(T_{2})}]^2=\frac{x^3}{8 x^3}\\\\\frac{(T_{1})}{(T_{2})}=\sqrt{\frac{1}{8}}\\\\ T_{2}={2\sqrt{2}}{T_{1}}$

→Orbital Period of Planet Y increases by, 2√2 times =2 ×1.414=2.828 times than planet X.