Proving Ideas: Wikipedia vs. Reality

These results were important to Newton's analysis of planetary motion; they are not immediately obvious, but they can be proven with calculus. (Alternatively, Gauss's law for gravity offers a much simpler way to prove the same results.)Source: http://en.wikipedia.org/wiki/Shell_theorem The wikipedia entry is false, according to its own obvious premise.
Physical theories are not proven by calculus in any way.
They are proven (if at all) by accurate physical measurement.

The calculus, which by the way we fully provided in posts #10 and #13,
proves nothing at all, except that the demonstration
that mathematical reasoning follows well-understood rules.

The mistake made in the wikipedia article, and probably also made
in many 1st year Physics texts and popular science articles,
is that the successful completion of a math problem in integration,
proves anything at all for the science of physics, or the operation of
classical gravitational and electrostatic forces.
It doesn't and can't because the problems and their solution are
in entirely different categories of science.

Integration is used to 'prove' mathematical results, for the mathematical 'world',
in a very narrow and abstract mathematical sense.
Calculus is not any kind of tool that can bridge or connect the worlds of mathematics to the world of physics.
Those connections are made by axioms, premises, hypotheses, definitions,
and conventions, in conjunction with higher analytical theories of meaning.

A calculus result only has a tentative meaning and existence
in the mind of a mathematician. Its value is not based on 'truth-content'
in regard to the real world, but is rather based on 'consistency' results
through Group Theory and Theory of Algebra, such as Galois and the Lebesque field.

This misunderstanding in regard to the purpose and meaning of Calculus,
and indeed any mathematical result generally, i.e., its 'truth-content' in
regard to reality, is one of the most common logical and epistemological errors
in engineering, physics, and even amateur mathematics, and runs rampant in 'pop-science'.

Real physicists and mathematicians don't "prove" theorems
in the sense of their applicability to physical problems by using math.
The create rather a tentative 'plausibility' to mathematical tools,
based on their apparent usefulness in solving physical problems,
and accurately predicting results.

Feynman for instance, would never make any truth-claim whatever about QED.
He would only call it
"the most accurate predictor of experimental measurement we have,
good for about 8 digits of accuracy, in proper use."

Nor does Gauss' law prove anything at all, except in the mathematical realm.
Its an analysis and methodology which results from other mathematical theorems.