Here's why:

* Newton's Law of Universal Gravitation: This law states that 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.

* The Formula: The formula for gravitational force is:

F = (G * m1 * m2) / r^2

Where:

* F = gravitational force

* G = gravitational constant

* m1 and m2 = masses of the objects

* r = distance between their centers (radius in this case)

* Doubling the Radius: If you double the radius (r), you are essentially squaring the denominator in the formula (r^2). This means the denominator becomes four times larger.

* The Result: Since the force is inversely proportional to the square of the radius, doubling the radius will decrease the gravitational force to one-fourth of its original value.