Re: Do dark matter calculations make the stupid assumption that all mass is at the center of the galaxy?
- From: franklinhu@xxxxxxxxx
- Date: Sat, 23 May 2009 21:28:32 -0700 (PDT)
On May 23, 12:31 pm, Lofty Goat <rlwatk...@xxxxxxxxx> wrote:
On Fri, 22 May 2009 22:20:25 -0700, franklinhu wrote:
I was wondering if someone could confirm or deny the assumption that the
expected galaxy rotation speed curves that show that there must be dark
mass in the galaxy make the assumption that all of the mass of the
galaxy can be considered to exist at the center of the galaxy?
I read an article which attempted to confirm the galaxy rotational curve
speeds and it did use this assumption and came up with answers that
matched the mainstream science results.
Quite frankly, I can't see how any scientist could possibly make such a
stupid assumption that you could calculate the rotational speed of an
orbiting body by presuming all the mass is at the center of the galaxy.
Certainly for systems like the solar system where there is very little
mass outside of the sun, this makes a perfectly good assumption, but if
you look at a galaxy, I would think that the mass is more or less evenly
distributed along the entire disk such that more than half of the mass
exists on the outer half of the galaxy which would greatly skew the
rotational calculation.
So, someone in the know, please tell me they weren't so stupid as to put
all the mass at the center of the galaxy and please provide some
references on what they think the actual mass distribution is that they
used to calculate rotational speeds.
fhudarkmatter
Actually the whole thing isn't quite so dumb as one might think. Here's
the sort of thing you'd find in a good astronomy textbook:
Let's say you want to figure the orbit of a star around the center of a
galaxy, and that the visible matter in said galaxy is uniformly
distributed and in the shape of a disc.
As long as you're in the plane of your galaxy, the matter outside your
star's orbit you can more or less ignore. Its gravity pulls your star
equally in all directions, so within the galactic plane it has no effect.
The matter inside your star's orbit is what determines its orbital
period. It works out exactly the same whether the matter inside the
orbit is uniformly distributed, or is concentrated at a point at its
center.
As for the example you used of the Solar system, the Earth's orbit around
the Sun wouldn't change if the entire mass of the Sun were concentrated
in a black hole, or if the Sun were 180 million miles across, with the
Earth orbiting just above its surface.
For figuring Earth's orbit around the Sun all that matters is its mass
and how far Earth is from its center of mass. Its mass matters, but as
long as it is uniformly distributed its density doesn't. The same goes
for the matter in a galaxy around which a star orbits, to wit, the matter
inside the star's orbit.
While the matter in a real galaxy isn't *exactly* uniformly distributed,
it's close enough for a very good approximation.
Now, as for that purported dark matter....
Because the visible matter in most big galaxies is confined to a disc, if
the star wanders above or below the galactic plane, the gravity of the
material both inside and outside its orbit will tend to pull it back into
the plane.
The dark matter, on the other hand, is supposed to be distributed more
spherically. So, the dark matter inside the star's orbit will provide
gravity that will speed that orbit up; the dark matter outside its orbit
will pull equally in all directions and change nothing.
The biggest difference between the visible and dark matter, because of
their differing distribution, is that the dark matter doesn't do much to
keep stars in the galactic plane.
So, the whole line of reasoning really isn't that loony after all, so
long as one knows the rules the stuff has been observed to follow.
And if you don't have room on your shelves for another textbook, you can
find the details and the math on the Web: the formula for gravitational
force, that for calculating orbital periods, the derivation of the
formula for gravity inside a uniformly dense, ring or hollow sphere.
It's all out there.
(That last formula is simple enough even for me to remember: F=0.)
-- RLW- Hide quoted text -
- Show quoted text -
So, you are saying that they DO assume all mass is effectively
concentrated at the center and that any matter outside of a stars
orbit is inconsequential.
It would appear that the force of gravity within a ring of matter is
zero:
http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/GravField.htm
However, this does not excuse you from determining the amount of mass
within the orbit of any star. To do a precision calculation, you must
make a determination of the density of the galaxy at every point along
the radius and calculate the expected rotational speed at each point
based upon the accumulated mass.
So, can anyone find a chart showing a chart of matter density for a
galaxy based upon radius and the expected orbital velocities at those
points? Then you could convincingly show that the expected velocities
do not match the measured ones.
.
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