Galileo determined that all objects in free fall near the surface of the Earth accelerate at the same rate, regardless of their mass. This is a fundamental principle of physics and is often summarized as:

* All objects fall at the same rate in a vacuum.

Let me clarify a few things:

* Free fall: This means the only force acting on the object is gravity.

* Near the surface of the Earth: This means we are ignoring air resistance and other factors that might affect the acceleration.

* Same rate: This means that objects of different masses will fall with the same acceleration.

Galileo's experiments, though not performed in a perfect vacuum, demonstrated this principle remarkably well. He showed that a heavy object and a light object, dropped from the same height, would reach the ground at the same time (ignoring air resistance). This was a revolutionary idea at the time, as people believed heavier objects fell faster.

Important note: While all objects fall at the same rate in a vacuum, air resistance can significantly impact the rate at which objects fall in the real world. This is why a feather and a bowling ball fall at very different rates in the air.