The force of gravitation between two objects is governed by Newton’s law of universal gravitation, which states that the force F between two objects is inversely proportional to the square of the distance r between them:
where:
- F is the gravitational force,
- G is the gravitational constant,
- m1 and m2 are the masses of the two objects,
- r is the distance between the centers of the two objects.
If the distance r between the objects is reduced to half, the new distance is r\2. The gravitational force at this new distance would be:
Thus, when the distance between the two objects is reduced to half, the gravitational force between them increases by a factor of 4.