. The force of gravitational attraction (Fg) between two bodies is directly proportional to the product of the two masses (m1, m2) and inversely proportional to the square of the distance (d) separating the two masses is given by the formula below. What happens to the gravitational force ,Fg, if the distance, d, is quartered ? Everything else in the formula is constant.
Note: α is the centripetal acceleration and T is the period
Gm1 m2/d^2=Fg
If the distance, d, is quartered, it means that its value is divided by 4.
Using the formula, we can see that the gravitational force, Fg, is inversely proportional to the square of the distance. So, if the distance is divided by 4, the square of the distance is divided by 16 (4 squared).
Therefore, the gravitational force, Fg, would increase by a factor of 16.