When the distance between two objects of masses m1 and m2 is doubled, the gravitational force between them decreases to one-fourth of its original value.

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. Mathematically:

F = G * (m1 * m2) / r²

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

* Doubling the Distance: If you double the distance (r becomes 2r), the denominator in the equation becomes (2r)². This means the force is divided by 2² = 4.

Therefore, doubling the distance between two objects reduces the gravitational force between them to one-fourth its original strength.