Most of our views on this are now in accord, I only
address the speed issue here and maybe pick up some
other minor points separately later.

First I'll take one paragraph from later on;


Your method doesn't take the effect of
the initial speed difference into account.

Don't be silly George, Of course it does. That's the whole basis of the
calculation.
The radial speed at each point around the orbit is c + vcos(A)

I said before you could treat cos(A) as being always 1.
I was thinking there of the angle between the line of
sight and the line between the barycentres. Your angle
is between to have used the line of sight and the
velocity which of course is essential but if you make
it the angle between the velocity and a line joining
the barycentres then there will be a negligible error,
essentially the view from infinity, and it will work
at zero distance to allow comparison with the conventional
model.

Thanks to Jeff Root for pointing out my misunderstanding
of your definition.


"Henri Wilson" HW@.... wrote in message
...
On Wed, 21 Feb 2007 18:35:50 -0000, "George Dishman"
wrote:
....
I did explain Henry, at the critical distance the
gap between pulses is zero so your program should
report a value of c for the observed velocity curve
but the peak is the same height as the true value
which you entered as 0.0009. That's wrong by a
factor of 11000.

I think I know what you are trying to say here George.

At the critical distance, SOME pulses arrive together not ALL of them.
that is
because a cincave section of the orbit is such tat a large group of pulses
will
arrive at a distant point over a very short time interval.
They will have started out with a range of speeds; that's why some catch
up
with the others.

Yes.

After extinction, they will all be traveling at about c wrt the source BUT
their wavelengths will have changed so that their source speeds will still
appear to be the correct ones, when measured with a grating at the
observer
distance..

No. We are not using a grating. Individual pulses have
their time of arrival noted against an atomic clock.
Remember they are 2.95 ms apart so the 'wavelength' is
885 km.

The inverse of the time between arrivals is the pulse
repetion frequency. That frequency is what is turned
into the published orbital parameters and is what give
the 339 Hz +/- 30 mHz values.

So my graph shows the 'no extinction' case...because I say extinction
makes no
difference to the measured doppler shift.
....
There is no significant error...none at all for circular orbits.
Please explain why you think there is an error..
....
Yes, that's the error. The _published_ speed curve
will be based on the inverse period, the time
between pulse arrivals so that's what you need
to put into the simulation to make the curve
comparable.

George, the velocity will range from ~27000 +/-~0.01% m/s
Do you agree?

I am saying that, for any significant extinction
distance, the red line should have a greater
variation than the blue line. To find the true
speed, you adjust the velocity parameter until the
red line matches the published velocity curve. What
we need to sort out is why I think the red should
be higher than the blue.

They will also move closer and farther due to their
initially different speeds but that part will become
constant as the speeds equalise.

Yes..but their spacing overall will retain a periodic bunching.
It is not CONSTANT all the way along.

I think that's what I just said. It isn't constant
and reduces or grows until the speeds equalise
after which they remain unchanged regardless of
distance.

OK we agree on that.

Consider two pulses transmitted just before and just
after the neutron star passes behind the dwarf as seen
from Earth. This is the point of highest acceleration
and the second catches the first at the maximum rate.

First consider no extinction. The diagram shows the
earlier pulse 'a' already ahead of 'b' at the time
when b is emitted:

b a
b a
b a
*
a b
a b

The time between pulses goes to zero at the critical
distance. Now add extinction:

b a
b a
b a
b a
b a
b a
b a

The 'wavelength' settles down to a constant value but
it is less than the original. Note that this effect
is in addition to the normal Doppler change due to
velocity alone (but at the location we are considering
the radial speed is zero).

It is only that final pulse separation that we can
measure and which has been used to calculate the
27km/s value, and of course the published values assume
invariant speed. That means that if you want to compare
your program's output, specifically the blue line, with
published curves, you need to convert the received PRF
to a velocity _as_if_ the speed were always c, not
because of the physics but (if you like to think of it
this way) because that is the publishing convention.

In a nutshell, the shortened inter-pulse gap due to c+v
catch-up tricks us into thinking the orbital velocity
is higher than it really is. The red curve is the real
value and the blue curve is the "constant c" value
inferred from that shortened gap between pulses.

Does that make it clearer Henry?

If you follow that, you should appreciate that instead
of saying the extinction is 6 light hours, you could
keep your 0.7 light year figure but drop the orbital
speed to 27 m/s. Of course that's not tenable for a
variety of other reasons but it might illustrate the
point, almost all the apparent "Doppler" shift would
actually be due to the pulse catch-up effect.

For those parameters, the red curve would be 27983 m/s
but the blue curve would be only 27 m/s, and because
most of the red curve is due to the acceleration at
the time of emission, there would be a 90 degree phase
difference.

George