Question

how is the gravitational force between two masses affected if the separation between them is doubled

Answer 1

F = G m1 m2 / r^2
if r is doubled
then
F = G m1 m2 / (2r )^2
F = G m1 m2 /4r^2
F = 1/4 G m1 m2 / t^2
Force will be 1/4 of original force

Answer 2

So as the mass of either object increases, the force of gravitational attraction between them also increases. ... If the separation distance between two objects isdoubled (increased by a factor of 2), then the force of gravitational attraction is decreased by a factor of 4 (2 raised to the second power).


I am assuming you are asking gravitational force of attraction.

Gravitational force of attraction is given by

F =(G×M1×M2)
--------------
R²

The force of attraction is inversely proportional to the square of the distance between the bodies.

If we double the centre distance R, the force of attraction falls to 1/4thth the original value.