What assumption did Newton make when establishing the inverse square law for gravitational forces?

Newton used Kepler's third law, which relates the period of orbit (T) to the radius (r) of the orbit, to derive his law of universal gravitation. By assuming circular orbits and using the centripetal force formula, he was able to show that the gravitational force decreases with the square of the distance between two masses. This led to the formulation of the inverse-square law for gravitational force.