Question

Why the gravitational force between two objects to the distance betwwen the object is doubled?

Answer 1

If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on. Since gravitational force is inversely proportional to the square of the separation distance between the twointeracting objects, more separation distancewill result in weaker gravitational forces

Answer 2

F = GmM/R^2
F=Force
m=mass 1
M=mass 2
R=Distance between the bodies
G=Gravitational constant

when distance is doubled
F= GmM/(2R)^2
F = GmM/4R^2
4F= GmM/R^2
this shows us that when the distance between two bodies is doubled then the force becomes 4 times the original force.