If the distance between two objects is increased to four times the original distance, how will that increase change the force of attraction between the objects?

The formula for gravitational force F is equal to the gravitational constant multiplied by the respective masses of both objects, all over the square of the distance between the two. In mathematical form:

Let:

G = gravitational constant
M = mass of one object
m = mass of the other object
d = distance between the two objects
F = gravitational force

F = (G * M * m) / d^2

As seen in the formula, the gravitational force or force of attraction is inversely proportional to the square of the distance. If we were to increase the distance by 4 times as much, this would reduce the force of attraction by 16 times.