In a vacuum, all objects fall at the same rate due to the uniform acceleration caused by gravity, regardless of their mass.

This phenomenon stems from the principle of equivalence, which is a fundamental aspect of Einstein’s theory of general relativity. According to this principle, the effects of gravity on an object are indistinguishable from those experienced by an object in an accelerated frame of reference. Consequently, all objects, irrespective of their mass, will undergo the same acceleration when subjected to a gravitational field, such as that of the Earth.

In a vacuum, there are no external forces acting on the objects, such as air resistance, which could otherwise influence their rate of descent. Thus, the sole force acting on the objects is gravity. Near the Earth’s surface, the acceleration due to gravity is approximately $9.81 \, \text{m/s}^2$. For ease of calculation, this value is often rounded to $10 \, \text{m/s}^2$.

This concept was famously illustrated by Galileo, who is reputed to have dropped two spheres of differing masses from the Leaning Tower of Pisa to demonstrate that they would hit the ground simultaneously. Although this story is likely apocryphal, it effectively conveys the principle. Galileo’s experiments revealed that the acceleration of an object in free fall is independent of its mass.

This principle is also observable by astronauts in space. When they release objects of varying masses, they note that all objects fall toward the Earth at the same rate, irrespective of their mass. This uniformity occurs because, in the vacuum of space, there is no air resistance to decelerate the objects.

In summary, the reason objects in a vacuum fall at the same rate is due to the principle of equivalence and the absence of opposing forces such as air resistance. This results in a consistent acceleration caused by gravity, which is independent of the mass of the objects involved.