$6$

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 weight felt by the astronauts due to the planets $\frac{F_{g,2}}{F_{g,1}}?m_{a,2}=2m_{a,1},m_{p,2}=m_{p,1},m_{s,2}=2m_{s,1},R_{p,2}=R_{p,1}$ and $R_{o,2}=R_{o,1}$

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{1}{2}$

$1$

$2$

$4$

$8$