What principle explains why all objects fall at the same rate in a vacuum?

The principle that explains why all objects fall at the same rate in a vacuum is based on equal acceleration due to gravity. In a vacuum, there is no air resistance to affect the motion of falling objects. This means that regardless of their masses, all objects experience the same gravitational acceleration, which on Earth is approximately 9.81 m/s².

This phenomenon was famously demonstrated by Galileo, who showed that a heavier object does not fall faster than a lighter one when air resistance is eliminated. In a vacuum, the absence of air means that there are no external forces to act differently on objects of different weights. Therefore, they all fall at the same rate, demonstrating that the acceleration due to gravity is constant for all objects in the absence of air resistance.

This fundamental concept is pivotal in understanding motion under gravity and forms the basis for many principles in physics regarding the behavior of objects in free fall.