[Physics] Newton's Two Gravitational Theorems

[Thomas Goodey]

On 12 Aug 2017 at 12:00, physics-request at tuks.nl wrote:

> I decided to bring up another old
> (twenty years) mathemetical I did.  Newton's "Shell Theorems
> used his new Integral Calculus to prove that INSIDE a large
> object (such as the Earth) there is often NO gravitational
> field since the Force Vectors often exactly cancel each
> other out. 

This is so confused in a number of ways... OFTEN? What 
planet does this come from? Theorems don't say "often".

Before publishing all his gravitational theories, Newton 
realized that he needed to prove two theorems, and he used 
his new "calculus of fluxions" to do it:

First: he proved that the M/R-squared attractive force of a 
solid uniform SPHERE of matter upon some external test 
mass, for which the attractions of all the little bits of 
the sphere must be taken together as a whole, is exactly 
equal to the force that it would be if all the mass were to 
be concentrated at the center of the sphere.

Second, he proved that, if you have a uniform HOLLOW 
SPHERICAL  shell of matter, a test mass internal to the 
hollow of the sphere (i.e. floating around inside it) 
experiences no attractive force due to the matter of the 
shell, because it all cancels out exactly.

> Since the Sun contains virtually all the mass in
> our Solar System, Kepler had been basically right in his
> calculations for the Solar System.

What calculations are you talking about? Kepler only 
observed relationships; he made no calculations as such.

> But ever since then, ALL astronomers ASSUME that is also
> true of the Milky Way Galaxy.

Of course they don't. Astronomers are not that naive or 
stupid. When they make calculations about the rotation of 
the galaxy and the forces acting upon the various stars of 
the galaxy due to to one another's attraction, they work 
out everything as exactly as they can based upon the data 
available.

You said:

> this all got me to thinking that we need to do massive
> numerical Integrations in the Galaxy, of Newton's
> gravitational Vector equation. 

You are not the first to think of that, by a long chalk. 
And you said:

> I spent many months in doing math regarding our TAPERED
> Spiral Arm..

Well, insofar as you got that right, you duplicated other 
people's results. People who have much more powerful 
calculating facilities than you do.

Thomas Goodey

*****************************
Anne's search for security 
holes in the localizer network 
software was close to 
impossible. Every year her 
zipheads pushed back their 
deadline for certainty another 
year or two. But the quagmire 
of Qeng Ho fleet software 
was almost eight thousand 
years deep.
--------- Vernor Vinge
----------'A Deepness in the Sky'