The force increases by four times if each mass is doubled.

Here's why:

* Newton's Law of Universal Gravitation: The force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

* Formula: F = G * (m1 * m2) / r²

* F = Force of gravity

* G = Gravitational constant

* m1 = Mass of object 1

* m2 = Mass of object 2

* r = Distance between the centers of the objects

* Doubling the Masses: If you double both m1 and m2, the product (m1 * m2) becomes four times larger. Since the force is directly proportional to this product, the force also increases by a factor of four.

Example:

Let's say you have two objects with masses of 1 kg each. If you double their masses to 2 kg each, the force of gravity between them will quadruple.