All bodies in the Earth's gravitational field are subject to a gravitational force that gives them the same gravitational acceleration g. If nothing obstructed the bodies when falling, they would all accelerate equally and therefore any pair of simultaneously dropped bodies would hit the ground at the same moment. Just as the feather and the hammer fell at the same moment on the moon.

On the moon, nothing else really prevents them from falling because there is no atmosphere. On Earth, we have to account for the influence of air. For a body to fall to the ground, it has to make its way through the atmosphere, which resists it. This resistance depends on, among other things, the shape of the body. A body shaped like a droplet passes through the air more easily than one shaped like a parachute.

If we consider two bodies in the shape of a ball, they will experience the same resistance. The same resistive force will act on both the lighter and the heavier ball. Although this force is of the same magnitude, its effect on each of the balls will be different.

Imagine a small, light golf ball rolling towards you. Using a little force, you can stop it. But if you apply the same amount of force to a rolling heavy basketball, you will not stop it. It's the same with our falling balls. The same amount of air resistance will slow down a light ball significantly more than a heavy ball. Therefore, the heavy ball will hit the ground sooner. But if they were falling in a vacuum, they would hit the ground at the same time.