Ah Science, it works everywhere. Galileo can make predictions about objects falling in a (near) vacuum under a gravitational field and hundreds of years later, he is verified by men on the moon.
Galileo conducted several experiments and concluded that the effect of gravity on earthly objects is the same, regardless of the mass of those objects. He argued that in the absence of other forces such as air resistance, all falling objects accelerate toward Earth at the same rate. In the absence of any (significant) resistance to free-fall on the Moon, any two objects should fall at the same rate regardless of mass.
However, when there are resistances to free-fall, like air resistance, the weight of the object (mass*force due to gravity) does influence the rate of free-fall. This is because the air surrounding the object exerts a drag force on the object while falling. This force, when balanced by the weight of the object, limits the falling speed of the object, i.e. its terminal velocity. This is why a ping-pong ball will fall slower than a golf ball here on Earth. The ping-pong ball’s weight is quickly equaled by the drag force (dependent on velocity), while the golf ball reaches a higher speed (due to gravity) before the drag force can equal the weight. The terminal velocity of an object, which determines the speed of free-fall, is dependent on mass, relative surface area, drag coefficient, and altitude.
Without such resistances, any object on Earth would fall at approximately 9.81 meters per second per second. In the video below, “true” free fall was demonstrated on the moon by astronaut David Scott on August 2, 1971. He simultaneously released a hammer and a feather from the same height above the moon’s surface. The hammer and the feather both fell at the same rate and hit the ground at the same time. This demonstrated Galileo’s discovery that in the absence of air resistance, all objects experience the same acceleration due to gravity. (On the Moon, the gravitational acceleration is much less than on Earth, approximately 1.6 m/s2).
At the end of the last Apollo 15 moon walk, Commander David Scott (pictured above) performed a live demonstration for the television cameras. He held out a geologic hammer and a feather and dropped them at the same time. Because they were essentially in a vacuum, there was no air resistance and the feather fell at the same rate as the hammer, as Galileo had concluded hundreds of years before – all objects released together fall at the same rate regardless of mass. Mission Controller Joe Allen described the demonstration in the “Apollo 15 Preliminary Science Report”:
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