Dan O. answered • 04/30/24
Mass actually plays no role in free fall as all objects, regardless of their mass, fall with the same acceleration when placed in the same gravitational field. This is known as the equivalence principle.
You might think intuitively that this seems untrue by considering, for example, dropping a feather and a bowling ball from the same height and asking which one will hit the ground first. On earth, the bowling ball will accelerate faster but this is only due to air resistance affecting the feather more than the ball. If one were to drop a feather and a bowling ball on the moon where there is no air, they would hit the ground at the same time if dropped from the same height. Even on earth if one did the experiment in a vacuum chamber, the result would be the same.
Another good example is zero g airplanes used for the training of astronauts. These planes go up to a great height and then proceed to free fall for 5-10 seconds before leveling out. When in free fall, all of the people and object in the plane look as though they are floating as they would be in outer space away from any gravitational source. This is because all the objects and people, regardless of mass, are accelerating at the same rate and so are not accelerating relative to any other object in free fall.
In Newtonian mechanics, the equivalence principle comes from the fact that the force of gravity is proportional to an object's mass and the gravitational field while Newton's second law of motion says that any force is proportional to an object's mass and it's acceleration. Therefore, when combining these equations, the mass cancels on either side and one finds the acceleration of an object is equal to the gravitational field and the mass of the object plays no role.
In Einstein's General Theory of Relativity, the equivalence principle is central to the identification of gravity as a manifestation of the geometry of spacetime but the details of that can be for another question :).