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 (decreased by a factor of 1/4), the gravitational force, Fg, will increase by a factor of (1/4)^2 = 1/16.
This is because the formula shows that the gravitational force is inversely proportional to the square of the distance (d^2). When the distance is quartered, the denominator in the formula becomes (1/4)^2 = 1/16, resulting in an increase in the gravitational force by a factor of 1/16.