Here's why:
* Newton's Law of Universal Gravitation: This law states that the force of gravity between two objects is 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 states that the force acting on an object is equal to its mass times its acceleration (F = ma).
* Combining the Laws: When a body falls freely, the force acting on it is gravity. The force of gravity (Fg) is proportional to the mass of the falling body (m): Fg = Gm1m2/r², where G is the gravitational constant, m1 is the mass of the Earth, m2 is the mass of the falling body, and r is the distance between their centers.
* Canceling Mass: If we set the force of gravity equal to the mass of the falling body times its acceleration (Fg = ma), we get Gm1m2/r² = ma. The mass of the falling body (m2) cancels out on both sides, leaving us with acceleration (a) = Gm1/r².
Therefore, the acceleration due to gravity is only dependent on the mass of the Earth (m1) and the distance between the center of the Earth and the falling body (r).
Note: This is true only in a vacuum. Air resistance can affect the acceleration of falling objects, and its impact is more significant for lighter objects due to their larger surface area-to-mass ratio.
