Re: Newton's Gravity

Luigi Fortunati il 11/01/2025 08:53:59 ha scritto:

In my animation https://www.geogebra.org/m/ntefhssz I have visualized
the two bodies A and B with their respective decreasing gravitational
fields.
>
Body B (smaller) is entirely immersed in the strong red ring of force
10 of the gravitational field of A, while body A (whose center of
gravity is far from body B) is only marginally touched by the weak
gravitational force of body B.
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If we reduce body B even further to the minimum of its mass (with the
appropriate slider), the gravitational force that B experiences from
body A is at its maximum, while (on the contrary) the gravitational
force of body B becomes practically non-existent and also acts only in
one point and not on the whole of body A (more or less like the
gravitational force of my body acts very weakly on only one point of
the Earth (my room at most)) and not on the whole Earth.
>
Instead, if we increase the mass of body B to the maximum, it becomes
equal to that of body A and, only at this point, the two opposing
gravitational forces (A towards B and B towards A) become totally
equal, adding their mutual attractive effects.

The consequence of all this is that the gravitational force of the
larger body of mass M acts on the entire mass <m> of the smaller body
and this justifies the product m*M of Newton's formula, which
corresponds to the force exerted by the larger mass M on the entire
mass <m>.

Instead, the gravitational force of the smaller body of mass <m> cannot
act on the entire body of mass M because M is larger and therefore acts
only on a part of body A of size compatible with <m> and, therefore,
the force of body B on body A is not proportional to m*M but to m*m.

Consequently, the total gravitational force is proportional to the sum
of m*M plus m*m (mM+mm=m(M+m)).

Newton's formula should contain this small change: from F=GmM/d^2 to
F=Gm(m+M)/d^2 (with m<=M) which returns to being equal to the previous
one when the mass <m> is negligible (as happens here on Earth to any
body with respect to the entire Earth).

In fact, when <m> is negligible, m+M (for all practical purposes) is
equal to M.

Is it possible to carry out an experiment to verify which of the two
formulas (F=GmM/d^2 and F=Gm(m+M)/d^2 with m<=M) is more adherent to
reality?

Luigi Fortunati

Ps. If the formula F=Gm(m+M)/d^2 (with m<=M) turns out to be more
correct, the masses of the planets and stars (calculated with the
formula F=GmM/d^2) will have to be recalculated.