Question

when the masses are doubled and the separation is halved, what effect do they have in the gravitational force between the masses?

Answer 1

According to Universal Law of gravitation , the gravitational force of attrection between any two objects of mass
$M$ and $m$ is proportional to the product of their masses
and inversly proportional to the square of distance $r$ between them
So, force $F$ is given by
$F = G\frac{{M \times m}}{{{r^2}}}$
Now when the distance $r$ is reduced to half then force between two masses becomes
$F’=G\frac{M\times m}{\left ( \frac{r}{2} \right )^2}$
or,
$F’=4F$
Clearly , if distance between two objects is reduced to half then the gravitational force becomes four times larger than its previous value.