Re: Newton's Gravity

In article <vl0q35$28cau$1@dont-email.me> Luigi Fortunati wrote:

Suppose that body A has mass M=1000 and body B has mass m=1 [[...]]
 
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, [[...]]
 
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 [[...]]
 
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?

In article <ltkbcoF9g4cU1@mid.dfncis.de>, I replied
| Why not?  Why might we expect the effects of adding mass in one location
| (A) to be the same as those of adding mass in a different location (B)?

In article <vl3tv1$2sdba$1@dont-email.me>, Luigi replied

Yes, we *should* expect the same effects if we mean the same thing by
"effects."
 
I'm talking about masses (causes) and forces (effects): what effects
are you talking about?

Let's analyze a somewhat more general system:  Suppose we have a pair
of masses A and B, and consider the effects of adding a mass C at either
position #1 or position #2.
[Luigi's original question had position #1 = position
of A, position #2 = position of B, mass A = 1000, mass
B = 1, and mass C = 1, but I find it useful to consider
the more generic case.]

A+B+C1 and A+B+C2 are *physically different* systems (going from one to
the other involves moving the mass C from position #1 to position #2).
So why should we expect any of the following Newtonian gravitational
effects to be the same between these two *physically different* systems:
* Newtonian gravitational potential U at some test point X
* Newtonian gravitational acceleration "little-g" at some test point X
  (= - gradient of U)
* force between A+C1 and B versus force between A and B+C2

In fact, it's easy to see that all three of these "effects" differ...  as
we should expect, because (again) we're comparing *physically different*
systems.

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