Answer:
e) Be four times greater
Explanation:
Here we have to use Newton's gravitational law that relates the gravitational force between two objects with their masses ([tex]m_{1} [/tex] & [tex]m_{2} [/tex]) and the distance between them ([tex]r[/tex]) in the next way:
[tex] F=G\frac{m_{1}m_{2}}{r^{2}}[/tex] (2)
Now if distance between asteroids is halved:
[tex]F_{2}=G\frac{m_{1}m_{2}}{(\frac{r}{2})^{2}} [/tex]
[tex]F_{2}=G\frac{m_{1}m_{2}}{\frac{r^{2}}{4}} [/tex]
[tex]F_{2}=G\frac{4m_{1}m_{2}}{r^{2}}=4G\frac{m_{1}m_{2}}{r^{2}} [/tex]
Note that [tex] G\frac{m_{1}m_{2}}{r^{2}} [/tex] because (1) is F so:
[tex]F_{2}=4F [/tex]
It's four times greater!
