Why massively change to a different topic?
Do you at least accept that there is a net force on each object?
The position of both Ma and Mc are located on the opposite sides of the globe of Mb as shown. The point e and f are the antipodal points.
Galileo and Newton say that both Ma and Mc fall at the same rate
No, they don't.
They discuss 2 objects dropped from the same location, not antipodal points.
When you have 2 objects dropped from antipodal points, you now have 3 objects in a straight line.
Each object is attracted to the other 2.
But in practice, on Earth that difference is negligible.
So the falling mass matter to g=GM/d^2 - Right
No, because what you actually have now when you consider object A falling is:
g=G*(Mb/dab^2 + Mc/dac^2).
And something similar for object B falling and object C falling, noting you also need to note the direction, where the object in the middle is pulled in 2 opposite directions so the overall acceleration is smaller.
You are also equating object B moving towards object A as making object A fall faster, rather than just it reducing the distance object A need to fall to collide with object B.
As another simple example, you have 4 trains.
Train A is travelling at 100 km/hr east towards a train moving at 50 km/hr to the east initially 150 km away.
Train B is travelling at 100 km/hr west towards a train moving at 50 km/hr to the east initially 150 km away.
Which is travelling faster? A or B?
The answer is that they are both travelling at 100 km/hr. It doesn't matter than with train A the other train is moving away from it, making it take 3 hours to collide while train B is heading towards the train making it take only 1 hour to collide.
Earth moving towards the object doesn't mean the object is accelerating faster.
Have you gone through my last reply where I showed that second mass m matter in the equation of acceleration due to gravity g=GM/d^2? This will answer your all questions.
You didn't.
You poorly showed the third mass matters.