Why are the 'Fixed Stars' so FIXED?

"Henri Wilson" HW@.... wrote in message
...
On 16 Feb 2007 00:30:15 -0800, "George Dishman"
wrote:

On 16 Feb, 03:17, HW@....(Henri Wilson) wrote:
On Thu, 15 Feb 2007 23:53:52 -0000, "George Dishman"

wrote:
"Henri Wilson" HW@.... wrote in message
.. .
On 15 Feb 2007 01:58:58 -0800, "George Dishman"

wrote:
....
There is a cyclic doppler shift.
That means pulses come closer together then move apart again every
orbit.
If that isn't 'bunching' (of the pulses) what is?

Ah, true. However that is a function of speed
alone, I was talking of the bunching due to
your variable speed which is in additional to
the conventional effect. Here's the bit snipped
from above:

-:-

Not quite, there is an interesting difference. The
bunching effect depends on the acceleration and if
you think of a circular orbit seen edge on, clearly
the acceleration will vary 90 degrees out of phase
with the velocity. For high speed and a short
extinction distance the velocity will predominate
while for low speed and long distance the
acceleration will produce the larger contribution.

George, you are refering to conventional doppler shift using constant
c.
This is not the same as bunching due to c+v changes.

No, I'm describing ballistic theory, there is
no acceleration term in conventional Doppler.

-:-

Yes...well I don't use equations anyway. I let the computer do the
simulation...and there is no acceleration term .. although it might be
present
indirectly.

Whatever, we both know qualitatively how the curves should
look so we can check if your code gives a credible answer.

Bottom line though is that previously I was not talking
about conventional theory, please take more care as I
understand very well what the consequences of your theory
will be.

The apparent maximum radial velocity using the
conventional formula (invariant c) is 27983 m/s
by my reckoning.

I will get the same answer for the maximum....but it will occur at a
slightly
different phase.

You should get the same as the conventional theory
if you enter a distance of zero, a simple check to
start. Then as you increase the distance the
acceleration term will introduce a quadrature
element which will change both the phase and
amplitude. To keep the match to the amplitude, you
can change the orbital inclination or the masses.

The orbital inclination is already included in the radial velocity
reading.

Yes, as we said before, your velocity figure is actually
v*sin(i). We both understand that.

I have tried to explain this to Androcles but he cannot get it.

There's lots he doesn't get but you and I understand it.

No matter how an orbit is tilted, you can always rotate your telescope
(and
head) so that there exists an axis in the orbit plane that is
perpendicular to
your LOS. From that viewpoint, the radial velocities around the whole
orbit are
The 'edge on ones' simply multiplied by the same (unknown) cos factor.

The measured radial velocities ARE those of the edge on orbit multiplied
by
cos(tilt)....so you cannot include it again.

For circular orbits like this, that's true.

For the purposes of predicting brightness curves, I only have to consider
edge
on orbits. My 'yaw angle' is that for an edge on orbit. It is not the
conventional definition....but it works and it makes the programming much
easier.

For elliptical orbits in general you have to consider
the angle between the major axis and the line of sight
which I guess is your yaw, but for J1909-3744 we can
ignore it.

It doesn't matter what it is.
If a circular orbit is tilted around an axis perpendicular to the LOS,
the
radial velocities around the whole orbit are multiplied by the same
factor
cos(tilt). That is already included in the observed velocity readings.

Yes, what your program really tells you is v*sin(i)
(using the standard convention for inclination)
rather than v itself.

It doesn't tell me anything about v.

I FEED IN the measured value of maximum observed velocity (If I can get
it).

I don't think you quite understand the principle involved George.

Trial and error Henry, you feed what you think is the
true value of v*sin(i) and see whether the curves match
the observations. If not you alter the value until you
get a match and then you have found the value of v*sin(i).
At that point the predicted velocity curve should match
the published curve and you have found the true velocity
which takes into account the effect of ballistic theory
on the Doppler. Isn't that how you use it?

However, consider the difference
between a low speed orbit seen edge on and a high
speed orbit at high inclination. Given that we know
the period is 1.5 days, the high speed orbit requires
either a higher mass companion or a smaller orbit.

However, we know from spectroscopic analysis that
the companion is a white dwarf with a surface
temperature around 8500 degrees and a magnitude
of about 21. That gives an indication of the mass
so you can combine that with your result to work
out limits for the inclination.

Like I said, if you redefine YAW you don't have to worry about
inclination.

Yaw angle is the angle the major axis of an edge on orbit makes with the
LOS.

Ah, I guessed correctly :-)

Anyway, put the numbers into your program and tell
me what you get and then we can discuss their
interpretation. Check the results for zero distance
first and make sure you get the right speed and
phase.

Naturally for zero distance I get no brightness variation. The observed
velocity is in phase with the true velocity.

You should still get a very small variation due to
the conventional bunching you reminded me of at the
top.

Then increase the distance to 3 light years
but keep everything else the same and tell me how
the amplitude and phase change. Those two checks
should just confirm your software is working, after
that we can try the more interesting questions of
mass etc. and see if we can put some limits on the
extinction distance.

My software works.

We'll see.

It predicts brightness curves. Orbit inclination does not affect curve
shape.

I can predict the brightness curve of the dwarf companion. Where can I
find the
observed one?

There is no observed brightness variation reported
but that can probably only be taken to say any
variation is less than 1 mag, the existing single
measurements are no more accurate than that.

I'm not sure what it is you are asking me to do.

OK, let's do it in small steps so that I can
give you clear questions.

Common to all: set the eccentricity to zero, yaw
becomes irrelevant. Set the orbital period to
1.5334494503 days.

Step 1. Set the distance to zero (your sim should
reproduce the conventional theory) and set the
actual velocity to 27983 m/s.

Check that the observed velocity curve you get
matches that and that the maximum velocity is
90 degrees after conjunction.

Step 2. Increase the distance until you just get
the velocity curves going to infinity and tell me
what distance you get.

I am guessing that the critical distance should be
around 4 light years but let's see what your program
says before we get on to the more interesting stuff.

George