With same gravity constance everything fall down at the same speed, but only in a vacuum. In an atmosphere there count the air resistance of an object, even if they are made of the same material and weight, an iron sphere of 1 kg fall faster than a iron sheet of 1 kg.

Except if you could measure exactly the speed of objects falling in a vacuum, the heavier object would appear to fall faster due to the gravitational pull on the Earth. You’re forgetting the Earth falls toward the object too.

No, mass or weight of an object is irrelevant, in one of the jurney to the Moon, astronauts demostrate it with an hammer and a feather on the moon that both fellt at the same speed. It exist one gravity aceleration, on earth is 9,82 ms², which is the force of acceleration which experiment any object on Earth, the only difference which can slow it down is the resistant of air, this can be different in each object, but without atmosphere there is nothing which slow down the acceleration of the object, it’s irrelevant the material, weight, mass or form. Basic physic

www.youtube.com/watch?v=Oo8TaPVsn9Y

The difference is far too small to measure at these scales, the Earth would be falling toward the more massive object faster than the less massive object. Therefore the more massive object hits first.

Therefore the more massive object hits first.

Only technically. The effect you’re describing is so minute that it’s insignificant.

It’s like pointing out that the Great Pyramids of Giza are so massive that time moves 1 billionth slower for the surrounding objects. It’s neat that the effect is potentially measurable, but noone is going to be adjusting their clocks to account for it

Science is built on technicalities. In an exam, if a student considered the centre of m_1 as the centre of gravity instead of the weighed centre of m_1 and m_2 they would fail. This is no different

Your analogy doesn’t hold up, because factors get ignored in physics discussion all the time. Whem was the last time you’ve see a question in a dynamics class that didn’t ignore air resistance for the sake of simplicity?

The effect you’re describing is orders of magnitude smaller than that. I doubt the change would even register in a double floating-point variable if you did the calculations in Matlab