If the moon were twice as far from the earth as it is now, the gravitational force it
exerts on the earth would be

One-fourth of the original gravitational force.

Explanation:

The gravitational force between two objects of masses is given as:

Where,

Therefore, the gravitational force is inversely proportional to the square of the distance between the masses.

Now, if the distance is doubled, then the force has to be reduced by a factor of one by four or gravitational force will one-fourth of the original.

Let us verify it.

If , then new gravitational force is,

As seen above, new gravitational force is one-fourth of the original gravitational force between moon and Earth.