If the masses remain the same but the distance of separation is decreased to one half of the original distance, the gravitational force between them will increase by a factor of four.

Here's why:

* Newton's Law of Universal Gravitation: This law states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

* Mathematical Representation: F = G * (m1 * m2) / r^2, where:

* F is the gravitational force

* G is the gravitational constant

* m1 and m2 are the masses of the objects

* r is the distance between their centers

The Impact of Distance:

* If you halve the distance (r/2), you're essentially squaring the denominator in the equation: (1/ (r/2)^2) = (1/(r^2/4)) = 4/r^2.

* This means the force becomes four times stronger.

In conclusion, decreasing the distance between two objects with constant mass will significantly increase the gravitational force between them.