Which manner the force of gravitation will change when the distance between them is made double () the distance between them is reduced to half?

When the distance between the two objects is halved, the gravitational force becomes four times.

Proof

According to the universal law of gravitation

The gravitational force F between the two bodies of masses M and m is kept at a distance d from each other such that:;

F = G (m1.m2/r2)

Where,

m1 and m2 are the masses of the two bodies.

G is the gravitational constant.

r is the distance between the two bodies.

Given that the distance is reduced to half then,

r = 1/2 r

While the force between the two bodies is inversely proportional to the square of the distance between them which is given as:

F = G (m1.m2/(r/2)2)

F= 4G m1.m2/ r2

Therefore, when the distance is halved, the gravitational between these two bodies becomes four times