Re: Galaxies without dark matter halos?

John Chandler <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]
> greywolf42 <[EMAIL PROTECTED]> wrote:

> : Differentiating between observations and theoretical calculation is
> : never "quibbling."  In this case, I was alluding to the fact that we
> : do not get orbital speeds from astrometry (observation) until we
> : include a theoretical calculation of distance (calculation).
>
> Unfortunately, that has nothing to do with our discussion.  I never
> used the word "speed" nor even "velocity," except in the phrase
> "angular velocity" or in responding to your other irrelevancies.  We
> do NOT need to know the distance to determine the angular velocity.

I have always been discussing physical orbital speeds.  See the statement
immediately below:

> : Your statement, to which I was replying was: "What's observed
> : astrometrically is the projected angular velocity."   We actually
> : observe an angular velocity (not projected) on the celestial sphere.
> : WE then include the assumption or calculation of distance, to
> : convert angular motions into projected angular velocity -- of the orbit.
> : I assumed the last three words, since we were discussing determinations
> : of orbital parameters.
>
> Wrong again.  The distance is irrelevant.  You can change the distance
> all you like, but the apparent (or the true) angular velocity of one
> star about the other remains the same.

Please note my attempt at clarification, using the words "of the orbit."
The physical orbit of the star.  I am not discussing the apparent
(projected) angular motion of the star.  I'm discussing the 'true' orbital
velocity of the star -- which requires knowing the inclination of the orbit
and the distance to the star.

We got into this discussion when you entered the thread with this exchange:

John Chandler:
"... the 3-D orbit can be determined directly [from] astrometry ... without
the help of radial velocities."

greywolf42:
"One cannot determine inclination of a stellar orbit just from astrometry --
even in the rare cases where you can watch and measure the describing of a
full ellipse by the orbiting body.  The projection of an ellipse is still an
ellipse."

Thus, I am discussing your claim that the 3-D, physical orbit of a star can
be determined in all respects through pure astrometry.  In your current
post, you admit that you'll also need the distance to the star, as I have
noted.


> : The key here is that we can't determine the true *orbital* angular
> : velocity from observation (which I thought was your original claim).
> : Because we don't know the inclination of the orbit.
>
> Wrong again.  We deduce the inclination from the astrometry, along
> with the rest of the orbital parameters, as I've said over and over.

And mere repetiton of the claim carries no weight.  Which is why I asked
for support of that claim over and over.

> : You've provided no explanations, but only unsupported claims.  I belive
> : you are incorrect.  However, I'll be happy to listen to an explanation.
> : How does the astrometry give you the orbital inclination?  Give
> : equations, please.
>
> Equations:
>
> M = nt
> M = E - e sinE
>
> x1 = a (cosE - e)
> x2 = a sqrt(1-e^2) sinE
> x3 = 0
>
> where n=mean motion, t=time from periapse, M = mean anomaly,
> e=eccentricity, E=eccentric anomaly, a=semimajor axis.
>
> Y = B X
>
> where X is the vector (x1,x2,x3) and B is the rotation matrix composed
> of the node, inclination, and periapse.  With astrometric data, you
> have observations of y1 and y2 as a function of time.  Do a weighted
> linearized least-squares fit to the data, and iterate to convergence.
> >From this solution, you get the six elliptic orbital elements.  If you
> happen to know the distance to the binary, you can express "a" in
> distance units; otherwise you have to use units of angle on the sky.
> As I mentioned before, the system of equations does have an ambiguity
> in the sign of the inclination, but the fit converges to whichever
> solution is "closer" to the starting conditions.

Here you obviously have a data-reduction procedure.  Presumably
peer-reviewed.  However, I was thinking more in lines of the actual physics
equations.  Would you be so kind as to provide a reference to the above,
that includes the underlying physical equations?  Thanks.

> : The same equation applies to astrometry (transverse velocity) as for
> : radial velocity.
>
> Wrong again.  The equation you copied is only for one-dimensional
> data.  Astrometry gives two dimensions at the same time.  That makes a
> crucial difference.  With radial velocity, the one-dimensional
> observable scales equally (and, thus, degenerately) with "a" and "i".
> With astrometry, one coordinate scales with "i", but the other (along
> the line of nodes) is independent of "i".

Sounds good.  I look forward to the reference.

[Mod. note: unnecessary quoted text deleted -- mjh]

Wouldn't it have been much easier, just to provide a suitable reference or
explanation earlier?  Instead of simply repeating the same claim over and
over?  That would have saved us both a fair amount of time.

greywolf42
ubi dubium ibi libertas