In a gravitational field, mass does not affect the acceleration of objects in free fall, as all objects accelerate at the same rate due to gravity, regardless of their mass. However, the mass of the gravitational source can influence the motion of falling objects. Vertical upward and downward motions are also governed by gravitational forces, but the effects of mass can vary depending on other factors like air resistance. The discussion highlights that while mass does not change the acceleration of falling objects, it plays a role in the overall gravitational interaction. Understanding these dynamics is crucial for analyzing motion in a gravitational field.