Newton's Gravity

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