Why does mass not matter on how quickly an object falls?

Question

I've seen all the mathematical proofs and physics demonstrations in vacuums. However, for example, if a hammer falls to the Earth it falls very quickly. But, it can be interpreted another way. The hammer doesn't fall to the Earth, the Earth falls to the hammer. Then, on the moon, (since the smaller gravitational acceleration) the moon falls a lot slower to the hammer than the Earth falls to the hammer.

Answer 1

that is because the gravitational force depends on mass o the earth and the object and the object which which fall like hammer have negligible mass as compared to the mass of the earth. therefore the force exerted is the same.