Two asteroids of mass $\backslash ($ M $\backslash )$ are in deep space far away from any other objects. The centers of the asteroids are a distance $\backslash ($ d $\backslash )$ apart where $\backslash ($ d $\backslash )$ is much larger than the size of the asteroids, and each asteroid exerts a force of magnitude $\backslash ($ F $\backslash )$ on the other. At a later time, the mass of each asteroid has increased to $\backslash (2$ M $\backslash )$ and they are a distance $\backslash (\backslash$frac$\{$d$\}\{2\}\backslash )$ apart. What is the magnitude of the force that each asteroid exerts on the other at this later time?

$($A$)\backslash (16$ F $\backslash )$

$8$F

$\backslash (4$ F $\backslash )$

$($D$)\backslash ($ F $\backslash )$