Question

how does the force of gravitation between 2 objects change when the distance between them is doubled

Answer 1

According to the universal law of gravitation, gravitational force (F) acting between two objects is inversely proportional to the square of the distance (r) between them, i.e.,

$F\propto \frac{1}{r^2}$

If distance r becomes 2r, then the gravitational force will be proportional to
$$\begin{gathered} F\propto \frac{1}{(2r{)}^2} \\ \propto \frac{1}{4r^2} \end{gathered}$$
So if distance is doubled then gravitational force reduced to 4 time to that of original force.