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Old March 19th 17, 11:03 PM posted to sci.astro.research
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Default NET Angular Momentum of Globular cluster of stars

OK, so far great, close to zero net angular momentum in a globular or
elliptical. Please keep in mind I'm attempting to march down a Gedanken
path, and am not proposing anything that is likely.

Now, if I have an elliptical with zero angular momentum, this is not to
say there is no momentum. Clearly there is a lot of momentum and each
star contributes an angular momentum vector to the total sum, which is
zero.

If I establish a coordinate system X,Y,Z, then I can sum the angular
momentum about each axis with a SMBH at coordinate 0,0,0 at the origin
as a reference position.

As this has been decades since I've crunched these equations, perhaps my
terms need updating so please feel free to change my variables. I'll
use L for angular momentum. I can sum angular momentum about each of
the principle axis'.

For each axis, I get some number of objects moving around the axis with
one orientation, and another number of objects moving in the reverse
sense. So, I can sum them as total angular momentum L

L = aL_x + (-bL_x) + cL_y + (-dL_y) + eL_z + (-fL_z) = 0

So, a=b, c=d, and e=f.

And for a typical elliptical or globular, without oblateness, we can
probably go further and say that a=b=c=d=e=f.

In other words, objects are moving about the origin in all possible
orientations, they are thermalized, and there is no net angular
momentum.

But this does not mean there is no angular momentum. The stars possess
a lot of momentum, it's just all randomized.

[Moderator's note: This is not necessarily the case. It is also
possible---probable?---that each individual star has zero angular
momentum with respect to the SBH at the center, i.e. executes a
back-and-forth motion, passing through the centre of the galaxy. Stars
are few and far between, so this is possible without an appreciable
number of collisions. -P.H.]

If this seems about correct, then I'll move forward to the next step in
the Gedanken path, working with a galaxy that starts off with only

L = aL_x and with all of the rest of the components initially zero.

Have I made a mistake so far?

rt