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From: Luigi Fortunati <fortunati.luigi@gmail.com>
Newsgroups: sci.physics.research
Subject: Newton's Gravity
Date: Tue, 31 Dec 2024 14:03:32 +0100
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Newton's formula F=GmM/d^2 has been used to great advantage so far 
because it has proven to be valid and almost perfectly correct except 
for the small discrepancy in the perihelion calculation of Mercury's 
orbit, where Einstein's gravity formulas prove to be more precise.

So, Newton's formula is *almost* correct but not quite.

In this formula, the force is proportional to the product of the two 
masses (m*M).

Suppose that body A has mass M=1000 and body B has mass m=1, so that 
the force between the two bodies is proportional to 1000 (mM=1*1000).

If another unit mass 1 is added to body B, its mass doubles to m=2 and 
the force acting between the two bodies also doubles, because it will 
be proportional to 2000 (mM=2*1000).

But if the other unit mass is added to body A (instead of body B) the 
mass of A will become equal to M=1001 (remaining almost unchanged) just 
as the force between the two bodies remains practically unchanged and 
will be proportional to 1001 (mM=1*1001).

Why does the force acting between the two bodies double if we add the 
unit mass to body B and, substantially, does not change if we add it to 
the mass of body A?

Luigi Fortunati