Apollo astronaut David Scott dropped a hammer and a feather together on the Moon, and both reached the ground at the same time. What are the two distinct advantages that this experiment on the Moon had over the same kind of experiment as performed by Galileo on Earth?

As per the laws of gravity, acceleration due to gravity is independent of mass of an object. That means if you drop two objects of different mass form same height with zero initial speed, they will reach the ground at the same time.

Galileo had given this theory and proved it. But when you take one object as feather the presence of air makes it float and the law seems to fail. The law is correct but the only reason it fails is because the feather starts floating in the air.

To prove this we need a vacuum chamber with a great height to witness the free fall condition. Creating such a chamber on Earth is very difficult. David Scott had these advantages on the Moon. As Moon doesn't have any atmosphere so he got a natural vacuum environment.

Also, as the acceleration due to gravity on Moon is [tex]\frac{1}{6}th[/tex] of that on the Earth, it will take less time to touch the surface and one can easily observe the free fall without any aid of high speed camera.