How Galileo explained that heavy objects fall at the same speed as light ones 

Galileo Galilei  proved it by dropping two objects from the  Leaning Tower of Pisa . But this wasn't enough to convince contemporary academics. He had to use  Symmetry (physics)
If we drop three objects of the same shape and mass at the same time, do they arrive at the ground at the same time? They agreed. 
What if we move the objects horizontally closer or farther away before dropping them? They agreed that they would hit the ground at the same time. 
What if two of the objects are so close that touch before dropping them? They accepted the result wouldn't change. 
So, if the two objects that touch have double the mass that the third object, what difference does it make? Then, they finally believed that heavy objects fall at the same speed as light ones. 
Cumrun Vafa  explained this in  Lex Friedman  Podcast: 
 
 
This got ~300 votes on  Reddit  Physics:  https://www.reddit.com/r/Physics/comments/pkyad9/h...
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