Free fall: Heavier vs. Lighter objects

Earlier days, people believed that Heavier objects fall faster than Lighter objects during their free fall based on casual observations. They even took an example of feather and ball. As a feather is lighter it falls at a slower rate as compared to a ball and they concluded their theory saying Heavier objects fall faster than Lighter objects during their free fall. That observation seems correct but it is not. They considered free fall but it wasn't actually free fall. I mean they were supposed to consider only gravitational force(free fall) but they had two forces acting on feather and ball. Those are gravity and air resistance. Since feather has less density w.r.t air than a ball, feather reaches the ground at a slower rate than a ball. Now if you drop same, both feather and ball from same height(let them free fall) but this time in the vacuum. Now they both fall at the same rate. This experiment was conducted on the moon(they say so), where there is no air. And observations proved that objects fall at same rates regardless of their masses.

Now, some people say, mathematically, that according to the equation of gravitation,

Where:

* F(Fg) is Force of attraction, Gravity;

* G is Universal Gravitational constant and it's value in SI unit is 6.67x10^(-11) N-(m/kg)^2;

* M1(Me) and M2(mm) are Masses of two bodies of which gravitational force has to be measured     between;

* r is the distance between two masses. Distance is measured as if masses are compressed at the centers of each bodies.

When the mass is high, that gives a higher value of F making attractive force stronger. that means higher gravitational pull and hence, heavier objects get higher acceleration than lighter objects. So, Heavier objects fall faster than Lighter objects.

But even this theory is false according to me. Because considering Newton's law of inertia, heavier objects have the greater inertia of rest than lighter objects. So the fact which makes F higher is the same factor which makes object stay in Inertia of rest, making objects fall at the same rate, always, regardless of their masses.

Some people did not understand this and they replied to my explanation: "What if I drop moon and a small ball on earth, will they reach at the same time?" that too with attitude.

Anyway, the answer is, yes! They do reach earth's surface at the same time after their free fall from same height. This is because, the moon is heavier compared to a ball and since its very heavy, it tries to stay in its rest, conserving its rest(stable state). Hence, even though mass is greater and attractive force is high but inertia cancels out that acceleration and maintains constant acceleration.
THat's it.