Bill Sheppard wrote:

snip
Non-Keplerian (or more unitary) rotation of galaxies
seems to present a quandary requiring 'dark matter' to account for. But
when you look at mass distribution in a typical spiral galaxy, why
should it display Keplerian rotation? That is to say, our solar system
has over 99% of its mass concentrated in the center, in the Sun. Whereas
the galaxy has much more of its mass spread out through the periphery.
This spread-out mass has to be under mutual gravitation, which would
force the rotation to be more unitary (less Keplerian).

I only know what I've read in popular accounts, but I understand
"Keplerian rotation" to refer not only to a situation like that in
the solar system, but to include all cases where the mass inside a
given orbit acts as if it's concentrated at the centre. Within the
part of the disc where the majority of the mass is located, it's true
that the motion tends to be somewhat unitary because the weaker
gravity in the regions more distant from the centre is partly
compensated for by the greater quantity of mass contained within the
larger orbits. Near the edge of the disk the Keplerian principle
dominates; once there's little additional mass to be 'taken up' by
orbits of increasing radius, their rotational velocity should drop
off quite quickly.

The "missing mass" problem appears when the rotational speeds of the
outer haloes of galaxies are measured: they don't seem to decline
nearly as much as the decrease in visibly radiating matter would
imply. Therefore they behave as if the observed disk were embedded in
a very much larger, invisible one. The quandary, then, is not that
non-Keplerian rotation occurs within the areas whose emissions of EMR
show them to be densely 'populated': that's entirely to be expected.
It's that the outlying regions behave much the same way, despite
their sparse appearance.

Painius counters that the galaxy *does* mirror the solar
system by having 99% of its mass in the central black hole, and
therefore *should* display Keplerian rotation, but doesn't.

I don't know where he that 99% comes from; it seems very exaggerated.
The figures I've seen bandied about for the "super-massive" black
hole in the hub of our Galaxy run from about two to five million
solar masses; IIRC the Milky Way's total mass is estimated to be
somewhere in the 100 to 150 *billion*-sun range, making the black
hole account for 0.005% of it at best!

To my uneducated perception, the 'missing mass' is
already present and accounted for in the galaxy's periphery, and 'dark
matter' is a solution without a problem.

The problem AIUI is that, in the periphery or not, we can't see the
stuff -- or conversely, what we *can* see is simply insufficient to
account for the observed effects. It's not a small discrepancy either
-- for some reason a food-related analogy occurs to me: must be
getting near dinnertime -- we're not talking about a few crumbs that
have fallen off the plate, but all five courses that should have
followed the appetizer.

This subthread started with the motions of galaxies within clusters.
Note that it was from observations of these that astronomers first
suspected missing mass, without being able to tell whether it
belonged to the individual members or was distributed in
intergalactic space. But we hear much more about the more recently
discovered galactic-rotation evidence, in part because modelling the
space-motions of galaxies solely on the basis of their red-shifts is
a very tricky and uncertain business, yielding little firm evidence,
while by looking at different parts of a rotating spiral (the closer
to edgewise, the better) one can get a pretty precise "rotation
curve", the red-shift of the centre serving to calibrate the other measurements.

--
Odysseus