All bodies fall with the same acceleration in the absence of air friction due to the fundamental principle that gravity exerts the same force on all objects, regardless of their mass.

Here's a breakdown of why:

* Newton's Law of Universal Gravitation: This law states that every object in the universe attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

* Force and Acceleration: Newton's second law of motion tells us that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma).

* Combining the Laws: When an object falls freely, the only force acting on it is gravity. The gravitational force on an object is directly proportional to its mass (F = Gm1m2/r²). However, when we look at the acceleration (a = F/m), the mass of the object cancels out!

Therefore, the acceleration due to gravity (g) depends only on the mass of the Earth (M) and the distance between the object and the Earth's center (r):

g = GM/r²

This means that regardless of the mass of the falling object, all objects will accelerate towards the Earth with the same acceleration, approximately 9.8 m/s² near the Earth's surface.

Important Note: This is true only in a vacuum, where air friction is absent. In reality, air resistance significantly affects the acceleration of falling objects, especially for objects with larger surface areas or lower densities.