An object starts falling back towards the center of gravity when the force of gravity acting on it becomes greater than any opposing forces or support that were previously preventing its downward motion. This typically occurs when the object has been lifted or displaced from its equilibrium position and is no longer being supported or held in place.
For example, if you lift a ball off the ground and then release it, the force of gravity will cause the ball to fall back towards the center of the Earth. The point at which the object transitions from an upward or stationary motion to falling back towards the center of gravity is often referred to as the "point of release" or the moment when the supporting force is removed.
It's important to note that this assumes no other significant forces, such as air resistance, are acting on the object. In reality, factors like air resistance can affect the behavior of falling objects, causing them to reach a terminal velocity or experience a different pattern of motion.