On 24 Aug 2006 11:12:59 -0700, "Aluminium Holocene Holodeck Zoroaster"
<QncyMI@netscape.net> wrote:

[. . .]

I had a curious and irreverant thought the other night prompted by an
interview with the "discoverer" of dark matter to explain a supposedly
anomalous constant velocity of rotation for matter in the Andromeda
galaxy regardless of radius from the center. It seems according to her
explanation that velocities should fall with increasing radius because
gravitation is an inverse square force whose effect should decrease in
proportion.

So my thinking wandered to the question of whether a flat disk should
also produce such an effect. Obviously it would where gravitationally
attractive matter is concentrated at the center as in the case of the
sun or planets considered as attractive centers because the amount of
gravitationally attractive matter would not increase as a function of
distance from the attractive body.

However this would not be true for flat disks of uniform density
gravitationally attractive matter. The amount of gravitationally
attractive matter would increase as the square of radius from the
center just offsetting the inverse square decrease in the strength of
gravitational attraction leading to a constant velocity overall.

The effect is analogous for mechanical explanations for why inverse
square gravitationally contracted spheres such as the earth by and
large rotate as a single object. For in this case the amount of matter
increases as the cube of distance from the center. And since the force
of gravitational attraction falls in inverse square proportion to that
distance, the ratio between matter and force becomes a linear function
of radius or distance from the center of rotation. Thus the velocity
of rotation increases roughly in linear proportion to the radius and
all matter thus constrained rotates more or less in unison.

Now this isn't to suggest that matter in the Andromeda or any other
galaxy is in fact distributed in a flat disk of uniform density.But in
point of fact the analysis presented by the discoverer of dark matter
treated the problem as if the entirety of gravitationally attractive
matter were concentrated at the center of the galaxy instead of
distributed in some considerable proportion throughout the galaxy.

It seems absurd that this kind of mistake could happen in physics. Yet
this is exactly what analysis of the issue requiring the existence of
"dark" matter suggested. Basically the velocity of matter at some
distance from the center of the galaxy should be expected to fall in
proportion to the square of distance since gravitation is an inverse
square force. However velocity remains roughly constant. Therefore
some kind of "dark" matter must exist to make up for the discrepancy.

Maybe I'm misreading the situation on the basis of an uncritical
popular documentary and maybe such considerations have already been
acknowledged and discounted. However it is very tempting to see the
supposed demand for "dark" matter to compensate for the inverse square
decrease in gravitational attraction as nothing more than the effect
of a more or less uniform density galactic disk instead.

~v~~