Substituting the weight mg for the gravitational force F = GmM/r^2 and solving for g shows that g = GM/r^2. Why does this result explain that all objects fall with the same acceleration at a given location?

1. Setting the object's weight mg equal to the gravitational force GmM/r^2 gives an equation containing the object's own mass m on both sides. 2. Dividing both sides by m cancels that mass entirely, leaving g = GM/r^2, an expression with no dependence on the falling object's mass at all. 3. Because the object's mass has dropped out, the resulting acceleration g is the same for any object at that distance from Earth's center, regardless of how much it weighs. 4. G is indeed constant and r is fixed for a given location, but neither of those facts by itself explains why differently massed objects share the same g; the cancellation of the falling object's own mass is what does that. _Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.5 Newton's Universal Law of Gravitation_