Answer:B
Explanation:
Given
Distance of astronaut From asteroid x is [tex]r_x=140 km[/tex]
Distance of astronaut From asteroid Y is [tex]r_y=581 km[/tex]
Suppose M,M_x,M_y be the masses of Astronaut , asteroid X and Y
If the astronaut is in equilibrium then net gravitational force on it is zero
[tex]F_x=F_y[/tex]
[tex]\frac{GMM_x}{r_x^2}=\frac{GMM_y}{r_y^2}[/tex]
cancel out the common terms we get
[tex]\frac{M_x}{r_x^2}=\frac{M_y}{r_y^2}[/tex]
[tex]\frac{M_x}{M_y}=(\frac{r_x}{r_y})^2[/tex]
[tex]\frac{M_x}{M_y}=(\frac{140}{581})^2[/tex]
[tex]\frac{M_x}{M_y}=0.05806\approx 0.0581[/tex]
