$8$ Multiple Choice

$1$ point

For the following situation there are:

Two astronauts with mass $m_{a,1}$ and $m_{a,2}.$

They are on two planets with mass $m_{p,1}$ and $m_{p,2}.$

These planets are orbiting stars with mass $m_{s,1}$ and $m_{s,2}.$

The radius of the planets are $R_{p,1}$ and $R_{p,2}.$

The radius of the orbits of the planets are $R_{o,1}$ and $R_{o,2}.$

Below you are given the relationship between each of the stated variables. What is the ratio of the planets orbits $\frac{T_2}{T_1}?m_{a,2}=2m_{a,1},m_{p,2}=2m_{p,1},m_{s,2}=m_{s,1},R_{p,2}=R_{p,1}$ and $R_{o,2}=2R_{o,1}$

$\sqrt[\phantom{2}]{\frac{1}{8}}$

$\sqrt[\phantom{2}]{\frac{1}{4}}$

$\sqrt[\phantom{2}]{\frac{1}{2}}$

$\sqrt[\phantom{2}]{1}$

$\sqrt[\phantom{2}]{2}$

$\sqrt[\phantom{2}]{4}$

$\sqrt[\phantom{2}]{8}$