In 1971, during the Apollo 15 mission, astronaut David Scott conducted Galileo’s famous “hammer and feather drop” experiment. Galileo had concluded that all objects, regardless of mass, would fall at the same rate of speed. Galileo theorized that a feather falls slower not because of its mass, but because of wind resistance. Hence, given that there is no atmosphere on the moon, a hammer and feather dropped at the same time on the moon should fall at the same speed and both objects should hit the ground simultaneously. Here is the video of the experiment as it was conducted during the Apollo 15 mission.
In Mission Controller John Allen’s Apollo 15 Science Report, he pointed out the importance of the theory’s validity to the moon mission itself:
During the final minutes of the third extravehicular activity, a short demonstration experiment was conducted. A heavy object (a 1.32-kg aluminum geological hammer) and a light object (a 0.03-kg falcon feather) were released simultaneously from approximately the same height (approximately 1.6 m) and were allowed to fall to the surface. Within the accuracy of the simultaneous release, the objects were observed to undergo the same acceleration and strike the lunar surface simultaneously, which was a result predicted by well-established theory, but a result nonetheless reassuring considering both the number of viewers that witnessed the experiment and the fact that the homeward journey was based critically on the validity of the particular theory being tested.
Joe Allen, NASA SP-289, Apollo 15 Preliminary Science Report, Summary of Scientific Results, p. 2-11