Why are the 'Fixed Stars' so FIXED?

On Sun, 18 Feb 2007 10:59:26 -0000, "George Dishman"
wrote:


"Henri Wilson" HW@.... wrote in message
.. .
On Sat, 17 Feb 2007 14:22:20 -0000, "George Dishman"



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?

Not exactly.
Unless I have access to a reliable figure for the maximum radial velocity
I
cannot really come to a firm conclusion about distance or unification
rate.

But you cannot ever get that because the variable
speed messes up the Doppler equation. As with any
modelling technique, you put in your initial guess
of the actual parameters, the program caclulates
the observed signals and then you iterate until
the predicted observables match that actuals.

Ah, but I only need a value for the MAXIMUM orbital speed. The BaTh and SR
doppler equations are effectively the same.
I feed in the max value and then try to match the brightness curve. In doing so
I obtain velocity curves at both the source and the observer.

George, the latest upgrade of my program is now on my website if you would like
to use it. www.users.bigpond.com/hewn/variables.exe
I have removed most of the bugs although it doesn't have comprehensive
instructions as yet. Extinction doesn't work for circular orbits.

I really need three quantities, Vmax, distance and magnitude change. I can
determine yaw angle and orbit eccentricity when matching the basic SHAPE
of a
brightness curve ....if I have such a curve.

All that can ever be observed are the spectral shift
and brightness for normal stars or the PRF for pulsars.
none of your results are valid unless you are working
back from those.

Like I said, all I need is period, distance and a value for the maximum radial
velocity.
For elliptical orbits, this has to be corrected for yaw angle, which I can
determine from curve shape.



Not if the observer is at the orbit centre.

George, I think you are refering to the pulses emitted by the pulsar
itself.
These will be observed to have a cyclic doppler shift.

The 'bunching of pulses' I refer to is not the same.

I will explain for the case of an orbiting star.

The program assumes the star emits identical pulses of light towards the
observer at regular intervals as it moves around its orbit...I can use
20000,
33000 or 60000 points per orbit. 30000 is usually enough to produce a
smooth
curve.

The pulses are assumed to move at (c+v)cos(a) towards a distant observer,
where
a is the angle between the orbit tangent and the LOS.

Rats! I assumed you would ignore the cos(a) term because
the orbit radius is much smaller than the distance to
the system so cos(a) ~ 1.


Sorry that should have been c + v.cos(a) where v is the tangential speed at any
point and a a function of time.
This merely describes the radial velocities towards the observer from all
points around the orbit.

Setting the distance to zero is
then equivalent to finding the rate that the pulses hit
a flat plane perpendicular to the line of sight say just
beyond the orbital radius and before any bunching can take
place, or having the right orbital speed but zero radius.

The program then
calculates the arrival times of all the pulses emitted over a number of
orbits
at the observer distance.
At any instant the pulse positions form a regular spatial pattern. As this
pattern moves past the observer, it gives the impression of brightness
variation. (dn/dt = dn/dx.dx/dt)

Thus, a bunching of pulses shows up as a brightness increase.

That's what I expected. At the distance where the
pulses first overlap (the fast ones catch the slow
ones) you get zero time between pulse arrivals hence
the inverse is an infinite number per second or
infinite brightness. It isn't really infinite as
there are only a finite number of pulses in the
stream but the calculation will go to very high
levels.

That's right. It does....but I have realised that this never happens, probably
becasue of extinction. This is why DeSitter was wrong...and his argument has
always been the only 'evidence' against the BaTh.


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.

Most variations are around 1.5 mag or less.
...and yes, I don't have much faith in the accuracies of many published
figures.

It's not a question of faith, numbers are accurate
but in this case there have only been two measurements
made AFAICS by different groups at different times.
It doesn't really matter, your brightness increase
would just be the number of pulses per second because
each pulse essentially carries the same energy other
than a random variation from pulse to pulse due to
the nature of the source.

If I produce a 'brightness curve' for the pulsar, its height will reflect the
number of pulses arriving per unit time...not its 'brightness'. Pulsars are
constant.


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.

That wont work.
'Zero distance' means 'at the orbit centre'. Radial velocity is zero...so
is
brightness variation.

....So I'm not with you at all, here.

Understandable, I made an assumption about your
software that wasn't correct. The orbital radius
is 1.9 light seconds so if you set the distance
to one light hour, there should be minimal
bunching as the critical distance (below) is
8 light years and cos(a) = 0.999999861. You
should get the conventional curves to 1 part
in 10^7.

What curve are you talking about George?
Not the pulsar curve I hope. I don't claim that is a result of the BaTh at all.
It's a spinning neutron star.

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

I assume you mean the 'brightness curves'.

Effectively yes. I should have said the speed goes
to c, not to infinity.

Consider the pulsar at four points in the orbit
round the barycentre '+':

D

A + C Earth

B

The diagram assumes the motion is anti-clockwise.

The highest acceleration towards Earth occurs at
point A. Look closer at two consecutive pulses
assuming they occur equally either side of A:

v - * ~ -- slow, c-v
A-(
* - v ~ -- fast, c+v

At the critical distance, the fast pulse just
catches the slow pulse after 8 light years so
they arrive simultaneously for an observer at
that distance.

Compare that with the conventional view. It says
the maximum Doppler would be at point B. For the
pulses to arrive simultanseously, the pulsar would
have to be moving at c to keep up with the first
pulse and emit the second alongside.

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.

Period = 0.0042 years
Velocity = 0.0000933c

Critical distance = ~ 8 LYs.

See: http://www.users.bigpond.com/hewn/J1909-3744.jpg

Note that the observed velocity curve (red) is very different from the
real
curve (blue) at that distance.

I asked and you answered:

2) Have you corrected your program to show the velocity curve
that would be derived from the ballistic Doppler shift?[*]

Yes.

At the point where the brightness goes to infinity,
the time between pulses goes to zero and the velocity
curve (red I think) should peak at c.

That is correct.

That should be
coincident with point A which should be where your
blue line crosses the white axis and is rising.

No it's more subtle than that. the point varies with distance. There is second
order term involving the 'rate of change of acceleration'. You have omitted it.

(I'm having some trouble producing the right colours with Vbasic on
windowsXP).

The colours are distinguishable on the jpeg so I that's
fine. The real concern is with the phase shift between
the blue and others. I'll have to give a little more
thought to the effect of propagation speed on arrival
time but have a think about what I'm saying and see if
you think your program is producing what I expect.

I have looked closely at this myself before.

The point of maximum brightness moves in phase wrt the source velocity curve as
distance in varied.

You might like to run the 'lightfronts' section of my program. It shows just
how the pulses move away from the source. Increase the time scale to about 20.

George

"Henri Wilson" HW@.... wrote in message
...
On Sun, 18 Feb 2007 10:59:26 -0000, "George Dishman"

wrote:


"Henri Wilson" HW@.... wrote in message
. ..
On Sat, 17 Feb 2007 14:22:20 -0000, "George Dishman"



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?

Not exactly.
Unless I have access to a reliable figure for the maximum radial
velocity
I
cannot really come to a firm conclusion about distance or unification
rate.

But you cannot ever get that because the variable
speed messes up the Doppler equation. As with any
modelling technique, you put in your initial guess
of the actual parameters, the program caclulates
the observed signals and then you iterate until
the predicted observables match that actuals.

Ah, but I only need a value for the MAXIMUM orbital speed.

Ah, but you cannot know that, all you know is the
maximum Doppler shift.

The BaTh and SR
doppler equations are effectively the same.

No they aren't, that's the whole point. Look at the
bottom of your reply where you agree the _apparent_
speed should reach c at the critical distance!

I feed in the max value and then try to match the brightness curve. In
doing so
I obtain velocity curves at both the source and the observer.

George, the latest upgrade of my program is now on my website if you would
like
to use it. www.users.bigpond.com/hewn/variables.exe
I have removed most of the bugs although it doesn't have comprehensive
instructions as yet. Extinction doesn't work for circular orbits.

That's OK, your existing distance factor can be
essentially used as the extinction factor as long
as we are observing from a much greater distance.

I really need three quantities, Vmax, distance and magnitude change. I
can
determine yaw angle and orbit eccentricity when matching the basic SHAPE
of a
brightness curve ....if I have such a curve.

All that can ever be observed are the spectral shift
and brightness for normal stars or the PRF for pulsars.
none of your results are valid unless you are working
back from those.

Like I said, all I need is period, distance and a value for the maximum
radial
velocity.

Like I said, what you have is maximum Doppler shift.

For elliptical orbits, this has to be corrected for yaw angle, which I can
determine from curve shape.

Not a problem, this one is circular (you snipped the
figure of ~10^-7 for eccentricity earlier).


The pulses are assumed to move at (c+v)cos(a) towards a distant
observer,
where
a is the angle between the orbit tangent and the LOS.

Rats! I assumed you would ignore the cos(a) term because
the orbit radius is much smaller than the distance to
the system so cos(a) ~ 1.


Sorry that should have been c + v.cos(a) where v is the tangential speed
at any
point and a a function of time.
This merely describes the radial velocities towards the observer from all
points around the orbit.

The point stands, I assumed something incorrect so
my comment was wrong and I understand why you were
confused by it. Anyway it's easy to get round as
I say later, just use 1 light hour for the distance.

Setting the distance to zero is
then equivalent to finding the rate that the pulses hit
a flat plane perpendicular to the line of sight say just
beyond the orbital radius and before any bunching can take
place, or having the right orbital speed but zero radius.

The program then
calculates the arrival times of all the pulses emitted over a number of
orbits
at the observer distance.
At any instant the pulse positions form a regular spatial pattern. As
this
pattern moves past the observer, it gives the impression of brightness
variation. (dn/dt = dn/dx.dx/dt)

Thus, a bunching of pulses shows up as a brightness increase.

That's what I expected. At the distance where the
pulses first overlap (the fast ones catch the slow
ones) you get zero time between pulse arrivals hence
the inverse is an infinite number per second or
infinite brightness. It isn't really infinite as
there are only a finite number of pulses in the
stream but the calculation will go to very high
levels.

That's right. It does....but I have realised that this never happens,
probably
becasue of extinction.

That's why it sets an upper limit to the extinction
distance, the whole point of this excercise.

This is why DeSitter was wrong...and his argument has
always been the only 'evidence' against the BaTh.

No, the Sagnac experiment rules it out, this is only
every going to be a hypothetical curiousity.

Most variations are around 1.5 mag or less.
...and yes, I don't have much faith in the accuracies of many published
figures.

It's not a question of faith, numbers are accurate
but in this case there have only been two measurements
made AFAICS by different groups at different times.
It doesn't really matter, your brightness increase
would just be the number of pulses per second because
each pulse essentially carries the same energy other
than a random variation from pulse to pulse due to
the nature of the source.

If I produce a 'brightness curve' for the pulsar, its height will reflect
the
number of pulses arriving per unit time...not its 'brightness'. Pulsars
are
constant.

Yes, that's why I said I wasn't really interested in
the brightness as such, but it has been helpful in
finding the critical distance.

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.

That wont work.
'Zero distance' means 'at the orbit centre'. Radial velocity is
zero...so
is
brightness variation.

....So I'm not with you at all, here.

Understandable, I made an assumption about your
software that wasn't correct. The orbital radius
is 1.9 light seconds so if you set the distance
to one light hour, there should be minimal
bunching as the critical distance (below) is
8 light years and cos(a) = 0.999999861. You
should get the conventional curves to 1 part
in 10^7.

What curve are you talking about George?

The red curve for the apparent speed. If you enter
27km/s the red curve should show that deviation
above and below the white axis. It would help if
you added a vertical scale or we cannot confirm
that. I'm presuming the value in the table on the
left called "Max. Vel." is your assumption for the
actual speed which you entered rather than the
highest point on the red curve.

Not the pulsar curve I hope. I don't claim that is a result of the BaTh at
all.
It's a spinning neutron star.

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

I assume you mean the 'brightness curves'.

Effectively yes. I should have said the speed goes
to c, not to infinity.

Consider the pulsar at four points in the orbit
round the barycentre '+':

D

A + C Earth

B

The diagram assumes the motion is anti-clockwise.

The highest acceleration towards Earth occurs at
point A. Look closer at two consecutive pulses
assuming they occur equally either side of A:

v - * ~ -- slow, c-v
A-(
* - v ~ -- fast, c+v

At the critical distance, the fast pulse just
catches the slow pulse after 8 light years so
they arrive simultaneously for an observer at
that distance.

Compare that with the conventional view. It says
the maximum Doppler would be at point B. For the
pulses to arrive simultanseously, the pulsar would
have to be moving at c to keep up with the first
pulse and emit the second alongside.

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.

Period = 0.0042 years
Velocity = 0.0000933c

Critical distance = ~ 8 LYs.

See: http://www.users.bigpond.com/hewn/J1909-3744.jpg

Note that the observed velocity curve (red) is very different from the
real
curve (blue) at that distance.

I asked and you answered:

2) Have you corrected your program to show the velocity curve
that would be derived from the ballistic Doppler shift?[*]

Yes.

At the point where the brightness goes to infinity,
the time between pulses goes to zero and the velocity
curve (red I think) should peak at c.

That is correct.

That should be
coincident with point A which should be where your
blue line crosses the white axis and is rising.

No it's more subtle than that. the point varies with distance.

I'm assuming you have related the phase back to the
source system. In other words you subtract the mean
time from the barycentre to the observer from the
actual time. Otherwise a few light hours change to
distance would create a major apparent phase shift.

There is second
order term involving the 'rate of change of acceleration'. You have
omitted it.

I don't believe there is such a term but that's why
I want to do the short distance test first.

(I'm having some trouble producing the right colours with Vbasic on
windowsXP).

The colours are distinguishable on the jpeg so I that's
fine. The real concern is with the phase shift between
the blue and others. I'll have to give a little more
thought to the effect of propagation speed on arrival
time but have a think about what I'm saying and see if
you think your program is producing what I expect.

I have looked closely at this myself before.

The point of maximum brightness moves in phase wrt the source velocity
curve as
distance in varied.

You might like to run the 'lightfronts' section of my program. It shows
just
how the pulses move away from the source. Increase the time scale to about
20.

What I might do is try to produce my own version so
I can check what I expect. Your GUI is very unfriendly
or at least it was last time I tried to use it.

In the meantime, we will need to know the speed for
the peak of the red curve in comparison to the number
you enter so perhaps you could consider adding either
a speed scale or a box with the value at the peak like
the max/min brightness box.

George

On Mon, 19 Feb 2007 00:36:42 -0000, "George Dishman"
wrote:


"Henri Wilson" HW@.... wrote in message
.. .
On Sun, 18 Feb 2007 10:59:26 -0000, "George Dishman"

But you cannot ever get that because the variable
speed messes up the Doppler equation. As with any
modelling technique, you put in your initial guess
of the actual parameters, the program caclulates
the observed signals and then you iterate until
the predicted observables match that actuals.

Ah, but I only need a value for the MAXIMUM orbital speed.

Ah, but you cannot know that, all you know is the
maximum Doppler shift.

That's all I need.

The BaTh and SR
doppler equations are effectively the same.

No they aren't, that's the whole point. Look at the
bottom of your reply where you agree the _apparent_
speed should reach c at the critical distance!

Yes.... but during extinction, the wavelength contracts or expands, so as to
still maintain the correct details of source velocity.

I feed in the max value and then try to match the brightness curve. In
doing so
I obtain velocity curves at both the source and the observer.

George, the latest upgrade of my program is now on my website if you would
like
to use it. www.users.bigpond.com/hewn/variables.exe
I have removed most of the bugs although it doesn't have comprehensive
instructions as yet. Extinction doesn't work for circular orbits.

That's OK, your existing distance factor can be
essentially used as the extinction factor as long
as we are observing from a much greater distance.

It can. ..or you can set eccentricity at 0.01

I really need three quantities, Vmax, distance and magnitude change. I
can
determine yaw angle and orbit eccentricity when matching the basic SHAPE
of a
brightness curve ....if I have such a curve.

All that can ever be observed are the spectral shift
and brightness for normal stars or the PRF for pulsars.
none of your results are valid unless you are working
back from those.

Like I said, all I need is period, distance and a value for the maximum
radial
velocity.

Like I said, what you have is maximum Doppler shift.

No problem.

For elliptical orbits, this has to be corrected for yaw angle, which I can
determine from curve shape.

Not a problem, this one is circular (you snipped the
figure of ~10^-7 for eccentricity earlier).


The pulses are assumed to move at (c+v)cos(a) towards a distant
observer,
where
a is the angle between the orbit tangent and the LOS.

Rats! I assumed you would ignore the cos(a) term because
the orbit radius is much smaller than the distance to
the system so cos(a) ~ 1.


Sorry that should have been c + v.cos(a) where v is the tangential speed
at any
point and a a function of time.
This merely describes the radial velocities towards the observer from all
points around the orbit.

The point stands, I assumed something incorrect so
my comment was wrong and I understand why you were
confused by it. Anyway it's easy to get round as
I say later, just use 1 light hour for the distance.

Setting the distance to zero is
then equivalent to finding the rate that the pulses hit
a flat plane perpendicular to the line of sight say just
beyond the orbital radius and before any bunching can take
place, or having the right orbital speed but zero radius.

The program then
calculates the arrival times of all the pulses emitted over a number of
orbits
at the observer distance.
At any instant the pulse positions form a regular spatial pattern. As
this
pattern moves past the observer, it gives the impression of brightness
variation. (dn/dt = dn/dx.dx/dt)

Thus, a bunching of pulses shows up as a brightness increase.

That's what I expected. At the distance where the
pulses first overlap (the fast ones catch the slow
ones) you get zero time between pulse arrivals hence
the inverse is an infinite number per second or
infinite brightness. It isn't really infinite as
there are only a finite number of pulses in the
stream but the calculation will go to very high
levels.

That's right. It does....but I have realised that this never happens,
probably
becasue of extinction.

That's why it sets an upper limit to the extinction
distance, the whole point of this excercise.

This is why DeSitter was wrong...and his argument has
always been the only 'evidence' against the BaTh.

No, the Sagnac experiment rules it out, this is only
every going to be a hypothetical curiousity.

I'm not going to debate sagnac again.
You rely too much on the rotating frame...which can be very confusing.


If I produce a 'brightness curve' for the pulsar, its height will reflect
the
number of pulses arriving per unit time...not its 'brightness'. Pulsars
are
constant.

Yes, that's why I said I wasn't really interested in
the brightness as such, but it has been helpful in
finding the critical distance.

It could be, yes.



....So I'm not with you at all, here.

Understandable, I made an assumption about your
software that wasn't correct. The orbital radius
is 1.9 light seconds so if you set the distance
to one light hour, there should be minimal
bunching as the critical distance (below) is
8 light years and cos(a) = 0.999999861. You
should get the conventional curves to 1 part
in 10^7.

What curve are you talking about George?

The red curve for the apparent speed. If you enter
27km/s the red curve should show that deviation
above and below the white axis. It would help if
you added a vertical scale or we cannot confirm
that. I'm presuming the value in the table on the
left called "Max. Vel." is your assumption for the
actual speed which you entered rather than the
highest point on the red curve.

The velocity curves are set to always have the same size on the screen. The
scale is linear and yes, the maximum is that shown in the velocity box. Ity
should be the saem fro both rd and blue curves.

I have realised though that when using ellitical orbits I have to compensate
for Yaw angle because the maximum observed velocity is not necessarily the
velocity at periastron.

Not the pulsar curve I hope. I don't claim that is a result of the BaTh at
all.
It's a spinning neutron star.

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

I assume you mean the 'brightness curves'.

Effectively yes. I should have said the speed goes
to c, not to infinity.

Consider the pulsar at four points in the orbit
round the barycentre '+':

D

A + C Earth

B

The diagram assumes the motion is anti-clockwise.

The highest acceleration towards Earth occurs at
point A. Look closer at two consecutive pulses
assuming they occur equally either side of A:

v - * ~ -- slow, c-v
A-(
* - v ~ -- fast, c+v

At the critical distance, the fast pulse just
catches the slow pulse after 8 light years so
they arrive simultaneously for an observer at
that distance.

Compare that with the conventional view. It says
the maximum Doppler would be at point B. For the
pulses to arrive simultanseously, the pulsar would
have to be moving at c to keep up with the first
pulse and emit the second alongside.

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.

Period = 0.0042 years
Velocity = 0.0000933c

Critical distance = ~ 8 LYs.

See: http://www.users.bigpond.com/hewn/J1909-3744.jpg

Note that the observed velocity curve (red) is very different from the
real
curve (blue) at that distance.

I asked and you answered:

2) Have you corrected your program to show the velocity curve
that would be derived from the ballistic Doppler shift?[*]

Yes.

At the point where the brightness goes to infinity,
the time between pulses goes to zero and the velocity
curve (red I think) should peak at c.

That is correct.

That should be
coincident with point A which should be where your
blue line crosses the white axis and is rising.

No it's more subtle than that. the point varies with distance.

I'm assuming you have related the phase back to the
source system. In other words you subtract the mean
time from the barycentre to the observer from the
actual time. Otherwise a few light hours change to
distance would create a major apparent phase shift.

There is second
order term involving the 'rate of change of acceleration'. You have
omitted it.

I don't believe there is such a term but that's why
I want to do the short distance test first.

No, I was wrong there, although not entirely. The main reason the point moves
is due solely to the difference in emission times. For short distances, a half
period is quite significant.

(I'm having some trouble producing the right colours with Vbasic on
windowsXP).

The colours are distinguishable on the jpeg so I that's
fine. The real concern is with the phase shift between
the blue and others. I'll have to give a little more
thought to the effect of propagation speed on arrival
time but have a think about what I'm saying and see if
you think your program is producing what I expect.

I have looked closely at this myself before.

The point of maximum brightness moves in phase wrt the source velocity
curve as
distance in varied.

You might like to run the 'lightfronts' section of my program. It shows
just
how the pulses move away from the source. Increase the time scale to about
20.

What I might do is try to produce my own version so
I can check what I expect. Your GUI is very unfriendly
or at least it was last time I tried to use it.

It is much improved now.

Good luck if you try to write a program.
Mine has taken about six years to perfect, on and off.
There is some tricky programming.

In the meantime, we will need to know the speed for
the peak of the red curve in comparison to the number
you enter so perhaps you could consider adding either
a speed scale or a box with the value at the peak like
the max/min brightness box.

No, both peaks have the same value.
Unification doesn't affect the interpretation of doppler shift. I explained
why..
When light enters a glass plate, it slows and its wavelength decreases. The
number of wavecrests passing a point per second is the same as it was outside
the glass.

When starlight moving at c+v reaches the Earth's EM reference frame, it slows
to c wrt Earth. Its absolute wavelength decreases to Lc/(c+v). That's exactly
what you would expect using constant c. (actually its L(c-v)/c, virtually the
same for all practical speeds)

Unification in interstellar gas converts all light from the star to near c wrt
the source but the ABSOLUTE wavelengths of the c+v and c-v light are shifted
oppositely in the process.

So measured doppler shift on Earth should still be a true indicator of the
source's relative speed.





George

On 19 Feb, 04:44, HW@....(Henri Wilson) wrote:
On Mon, 19 Feb 2007 00:36:42 -0000, "George Dishman"
wrote:
"Henri Wilson" HW@.... wrote in message
.. .
On Sun, 18 Feb 2007 10:59:26 -0000, "George Dishman"
But you cannot ever get that because the variable
speed messes up the Doppler equation. As with any
modelling technique, you put in your initial guess
of the actual parameters, the program caclulates
the observed signals and then you iterate until
the predicted observables match that actuals.

Ah, but I only need a value for the MAXIMUM orbital speed.

Ah, but you cannot know that, all you know is the
maximum Doppler shift.

That's all I need.

Yes but you have to process it appropriately. Your
program is not doing that at present.

The BaTh and SR
doppler equations are effectively the same.

No they aren't, that's the whole point. Look at the
bottom of your reply where you agree the _apparent_
speed should reach c at the critical distance!

Yes.... but during extinction, the wavelength contracts or expands, so as to
still maintain the correct details of source velocity.

No, the speed matching causes the 'wavelength',
which in this case is the distance between pulses,
to eventually settle down to a constant value but
it will not be the original. The extreme test
example here is for viewing at 8 light years with
negligible extinction, or equivalently at infinity
with an exponential extinction distance of 8 light
years, and the wavelength is zero. Your software
still gives v/c=0.00009 when it should be v/c=1.

I have removed most of the bugs although it doesn't have comprehensive
instructions as yet. Extinction doesn't work for circular orbits.

That's OK, your existing distance factor can be
essentially used as the extinction factor as long
as we are observing from a much greater distance.

It can. ..or you can set eccentricity at 0.01

No, set it to 2.3*10^-7 if anything, but you
don't need an explicit extinction term. Just
treat your program as an observer at infinity
and distance is the characteristic extinction
length.

Like I said, all I need is period, distance and a value for the maximum
radial
velocity.

Like I said, what you have is maximum Doppler shift.

No problem.

Indeed, but you need to fix the bug in the
software to convert from the shift to the
speed correctly.

This is why DeSitter was wrong...and his argument has
always been the only 'evidence' against the BaTh.

No, the Sagnac experiment rules it out, this is only
every going to be a hypothetical curiousity.

I'm not going to debate sagnac again.
You rely too much on the rotating frame...which can be very confusing.

We discussed that in conceptual terms but the
proof we worked through was in the lab frame.
Anyway, let's not get diverted.


....So I'm not with you at all, here.

Understandable, I made an assumption about your
software that wasn't correct. The orbital radius
is 1.9 light seconds so if you set the distance
to one light hour, there should be minimal
bunching as the critical distance (below) is
8 light years and cos(a) = 0.999999861. You
should get the conventional curves to 1 part
in 10^7.

What curve are you talking about George?

The red curve for the apparent speed. If you enter
27km/s the red curve should show that deviation
above and below the white axis. It would help if
you added a vertical scale or we cannot confirm
that. I'm presuming the value in the table on the
left called "Max. Vel." is your assumption for the
actual speed which you entered rather than the
highest point on the red curve.

The velocity curves are set to always have the same size on the screen. The
scale is linear and yes, the maximum is that shown in the velocity box. Ity
should be the saem fro both rd and blue curves.

No, it should be 0.00009c for the blue curve
at 8 light years and 1.0c for the red curve.
The 'wavelength' at that distance is zero.

I have realised though that when using ellitical orbits I have to compensate
for Yaw angle because the maximum observed velocity is not necessarily the
velocity at periastron.

That could be the cause of your extra phase
change.

There is second
order term involving the 'rate of change of acceleration'. You have
omitted it.

I don't believe there is such a term but that's why
I want to do the short distance test first.

No, I was wrong there, although not entirely. The main reason the point moves
is due solely to the difference in emission times. For short distances, a half
period is quite significant.

Getting the correct location for the maximum speed
will matter too, but for our circular orbit it
shouldn't matter.

Anyway, bottom line at the moment is that you are
not calculating the apparent velocity correctly
from the pulse period so let's get that fixed
before worrying about the effects of eccentricity.

George

On 19 Feb 2007 00:41:06 -0800, "George Dishman"
wrote:

On 19 Feb, 04:44, HW@....(Henri Wilson) wrote:
On Mon, 19 Feb 2007 00:36:42 -0000, "George Dishman"
wrote:
"Henri Wilson" HW@.... wrote in message
.. .
On Sun, 18 Feb 2007 10:59:26 -0000, "George Dishman"
But you cannot ever get that because the variable
speed messes up the Doppler equation. As with any
modelling technique, you put in your initial guess
of the actual parameters, the program caclulates
the observed signals and then you iterate until
the predicted observables match that actuals.

Ah, but I only need a value for the MAXIMUM orbital speed.

Ah, but you cannot know that, all you know is the
maximum Doppler shift.

That's all I need.

Yes but you have to process it appropriately. Your
program is not doing that at present.

It's near enough to do what I want at present.... although I will have to take
Yaw angle into acount eventually..
All I am doing now is matching curves. The value of (distance x max velocity)
is rather arbitrary because I dont really know the unification distance and it
is not easy to obtain velocity diagrams.

The BaTh and SR
doppler equations are effectively the same.

No they aren't, that's the whole point. Look at the
bottom of your reply where you agree the _apparent_
speed should reach c at the critical distance!

Yes.... but during extinction, the wavelength contracts or expands, so as to
still maintain the correct details of source velocity.

No, the speed matching causes the 'wavelength',
which in this case is the distance between pulses,
to eventually settle down to a constant value but
it will not be the original.

Not according to me.
The final distance between adjacent pulses will vary according to their initial
velocity relative to the barycentre. Some will move closer together, others
further apart.

The extreme test
example here is for viewing at 8 light years with
negligible extinction, or equivalently at infinity
with an exponential extinction distance of 8 light
years, and the wavelength is zero. Your software
still gives v/c=0.00009 when it should be v/c=1.

George, unless I have access to a curve showing variation in pulse arrival
times I cannot help you much.

Reading the papers about this pulsar is quite confusing for me because the
authors make such a big issue of Shapiro delay. (They even admit light is
slowed by gravity). The BaTh interpretation would be quite different from
theirs.

I have removed most of the bugs although it doesn't have comprehensive
instructions as yet. Extinction doesn't work for circular orbits.

That's OK, your existing distance factor can be
essentially used as the extinction factor as long
as we are observing from a much greater distance.

It can. ..or you can set eccentricity at 0.01

No, set it to 2.3*10^-7 if anything, but you
don't need an explicit extinction term. Just
treat your program as an observer at infinity
and distance is the characteristic extinction
length.

Yes I can do that.
I only introduced the 'extinction' facility in order to try to obtain a value
for its rate.

Like I said, all I need is period, distance and a value for the maximum
radial
velocity.

Like I said, what you have is maximum Doppler shift.

No problem.

Indeed, but you need to fix the bug in the
software to convert from the shift to the
speed correctly.

George, this is a circular orbit and there is no difference between my and your
value of maximum velocity. I have tried to explain that extinction will not
affect measured doppler and its interpretation.


The red curve for the apparent speed. If you enter
27km/s the red curve should show that deviation
above and below the white axis. It would help if
you added a vertical scale or we cannot confirm
that. I'm presuming the value in the table on the
left called "Max. Vel." is your assumption for the
actual speed which you entered rather than the
highest point on the red curve.

The velocity curves are set to always have the same size on the screen. The
scale is linear and yes, the maximum is that shown in the velocity box. Ity
should be the same fro both red and blue curves.

No, it should be 0.00009c for the blue curve
at 8 light years and 1.0c for the red curve.
The 'wavelength' at that distance is zero.

George, I don't think we're taking about the same things here.
The blue curve is the true radial velocity curve towards the observer.
The red curve is generated in this way:

For the purpose of counting the arrival of pulses, the orbit period is divided
into 500 divisions, which form the elements of an array. The program adds all
the pulses that arrive in that division to make up the value of that array
element. It also follows each pulse individually so that it records the speed
at which the pulse left the source barycentre. It averages the velocities of
all the pulse that are placed into each array element.

Introducing extinction doesn't really change anything.

I have realised though that when using ellitical orbits I have to compensate
for Yaw angle because the maximum observed velocity is not necessarily the
velocity at periastron.

That could be the cause of your extra phase
change.

It shouldn't make much difference at low eccentricities and doesn't affect
brightness curve shape anyway. ..just the distance.


There is second
order term involving the 'rate of change of acceleration'. You have
omitted it.

I don't believe there is such a term but that's why
I want to do the short distance test first.

No, I was wrong there, although not entirely. The main reason the point moves
is due solely to the difference in emission times. For short distances, a half
period is quite significant.

Getting the correct location for the maximum speed
will matter too, but for our circular orbit it
shouldn't matter.

Anyway, bottom line at the moment is that you are
not calculating the apparent velocity correctly
from the pulse period so let's get that fixed
before worrying about the effects of eccentricity.

George you have it all back to front.

I don't want to calculate the velocity. I want to read about it in a table or
graph.
Can you provide that info for me?


George

On Feb 19, 2:56 pm, HW@....(Henri Wilson) wrote:

[snip all]


I don't want to calculate the velocity. I want to read about it in a table or
graph.
Can you provide that info for me?

Why should he do your research for you?




George

On 19 Feb, 23:56, HW@....(Henri Wilson) wrote:
On 19 Feb 2007 00:41:06 -0800, "George Dishman" wrote:
On 19 Feb, 04:44, HW@....(Henri Wilson) wrote:
On Mon, 19 Feb 2007 00:36:42 -0000, "George Dishman"
wrote:
"Henri Wilson" HW@.... wrote in message
.. .
On Sun, 18 Feb 2007 10:59:26 -0000, "George Dishman"
But you cannot ever get that because the variable
speed messes up the Doppler equation. As with any
modelling technique, you put in your initial guess
of the actual parameters, the program caclulates
the observed signals and then you iterate until
the predicted observables match that actuals.

Ah, but I only need a value for the MAXIMUM orbital speed.

Ah, but you cannot know that, all you know is the
maximum Doppler shift.

That's all I need.

Yes but you have to process it appropriately. Your
program is not doing that at present.

It's near enough to do what I want at present..

No, it is wrong by a factor of 11000 at 8 light years.
Of course that's only a test but the number is going
to be badly wrong at any range of interest.

.. although I will have to take
Yaw angle into acount eventually..

Does that matter at the moment for a circular
orbit?

All I am doing now is matching curves. The value of (distance x max velocity)
is rather arbitrary because I dont really know the unification distance and it
is not easy to obtain velocity diagrams.

The BaTh and SR
doppler equations are effectively the same.

No they aren't, that's the whole point. Look at the
bottom of your reply where you agree the _apparent_
speed should reach c at the critical distance!

Yes.... but during extinction, the wavelength contracts or expands, so as to
still maintain the correct details of source velocity.

No, the speed matching causes the 'wavelength',
which in this case is the distance between pulses,
to eventually settle down to a constant value but
it will not be the original.

Not according to me.

They do according to the theory, you don't have
a choice.

The final distance between adjacent pulses will vary according to their initial
velocity relative to the barycentre. Some will move closer together, others
further apart.

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

The extreme test
example here is for viewing at 8 light years with
negligible extinction, or equivalently at infinity
with an exponential extinction distance of 8 light
years, and the wavelength is zero. Your software
still gives v/c=0.00009 when it should be v/c=1.

George, unless I have access to a curve showing variation in pulse arrival
times I cannot help you much.

I've given you that repeatedly. The frequency varies by
30.5 mHz either side of 339 Hz.

Reading the papers about this pulsar is quite confusing for me

Indeed, but the basic information you need is trivial
for me. Some of the more specialised terms are less
clear but the basic orbit is simple.

because the
authors make such a big issue of Shapiro delay. (They even admit light is
slowed by gravity).

The Shapiro delay is what makes the system special.
It allows the inclination to be determined which
leads to highly accurate determination of a lot
of other parameters.

The BaTh interpretation would be quite different from
theirs.

It would, so stop looking for excuses and let's see what
your program says.

It can. ..or you can set eccentricity at 0.01

No, set it to 2.3*10^-7 if anything, but you
don't need an explicit extinction term. Just
treat your program as an observer at infinity
and distance is the characteristic extinction
length.

Yes I can do that.
I only introduced the 'extinction' facility in order to try to obtain a value
for its rate.

Essentially your distance parameter is already that.

Like I said, all I need is period, distance and a value for the maximum
radial velocity.

Like I said, what you have is maximum Doppler shift.

No problem.

Indeed, but you need to fix the bug in the
software to convert from the shift to the
speed correctly.

George, this is a circular orbit and there is no difference between my and your
value of maximum velocity. I have tried to explain that extinction will not
affect measured doppler and its interpretation.

Extinction in itself wouldn't but the initial speed
difference does affect the Dopppler. Faster pulses
catch up to slower ones for a while before extinction
matches their speeds. That means the pulses are closer
together giving the _false_ impression of a higher
speed. Your blue curve is the true speed, the red
curve should be the _apparent_ speed deduced from
the closed-up pulses. It should be _higher_ than the
blue curve.

The red curve for the apparent speed. If you enter
27km/s the red curve should show that deviation
above and below the white axis. It would help if
you added a vertical scale or we cannot confirm
that. I'm presuming the value in the table on the
left called "Max. Vel." is your assumption for the
actual speed which you entered rather than the
highest point on the red curve.

The velocity curves are set to always have the same size on the screen. The
scale is linear and yes, the maximum is that shown in the velocity box. Ity
should be the same fro both red and blue curves.

No, it should be 0.00009c for the blue curve
at 8 light years and 1.0c for the red curve.
The 'wavelength' at that distance is zero.

George, I don't think we're taking about the same things here.

I might occassionally get the red and blue transposed
but I don't think I have so far.

The blue curve is the true radial velocity curve towards the observer.

Yes.

The red curve is generated in this way:

For the purpose of counting the arrival of pulses, the orbit period is divided
into 500 divisions, which form the elements of an array. The program adds all
the pulses that arrive in that division to make up the value of that array
element. It also follows each pulse individually so that it records the speed
at which the pulse left the source barycentre. It averages the velocities of
all the pulse that are placed into each array element.

That will give the wrong answer. The pubilished velocity
data uses the conventional Doppler formula so the speed is

v = c * (df / f)

where df is the frequency shift

To find that, you can use the time between arrivals which
is just the period, or the inverse of the frequency.

Introducing extinction doesn't really change anything.

It stops the period changing after some distance, the
way you have it at the moment is fine. Just calculate
the Doppler shift from your pulse arrival times and you
will get the right answer.

I have realised though that when using ellitical orbits I have to compensate
for Yaw angle because the maximum observed velocity is not necessarily the
velocity at periastron.

That could be the cause of your extra phase
change.

It shouldn't make much difference at low eccentricities and doesn't affect
brightness curve shape anyway. ..just the distance.

It will have a small effect but for our circular
orbit, it is irrelevant. Can I ask that you lay
that aside on your to-do list until we finish
looking at J1909-3744.

There is second
order term involving the 'rate of change of acceleration'. You have
omitted it.

I don't believe there is such a term but that's why
I want to do the short distance test first.

No, I was wrong there, although not entirely. The main reason the point moves
is due solely to the difference in emission times. For short distances, a half
period is quite significant.

Getting the correct location for the maximum speed
will matter too, but for our circular orbit it
shouldn't matter.

Anyway, bottom line at the moment is that you are
not calculating the apparent velocity correctly
from the pulse period so let's get that fixed
before worrying about the effects of eccentricity.

George you have it all back to front.

I don't want to calculate the velocity. I want to read about it in a table or
graph.

Little children learn they don't always get what they
want. The published tables give the period and time
difference and I have done the calculation to turn that
into frequencies for you. All you need to do is fix the
bug in your program and then find the orbital parameters
and extinction that matches the observation.

Can you provide that info for me?

I have done many times Henry, stop trying to invent excuses.

George

On 20 Feb 2007 03:10:39 -0800, "George Dishman"
wrote:

On 19 Feb, 23:56, HW@....(Henri Wilson) wrote:
On 19 Feb 2007 00:41:06 -0800, "George Dishman" wrote:
On 19 Feb, 04:44, HW@....(Henri Wilson) wrote:
On Mon, 19 Feb 2007 00:36:42 -0000, "George Dishman"
wrote:
"Henri Wilson" HW@.... wrote in message
.. .
On Sun, 18 Feb 2007 10:59:26 -0000, "George Dishman"
But you cannot ever get that because the variable
speed messes up the Doppler equation. As with any
modelling technique, you put in your initial guess
of the actual parameters, the program caclulates
the observed signals and then you iterate until
the predicted observables match that actuals.

Ah, but I only need a value for the MAXIMUM orbital speed.

Ah, but you cannot know that, all you know is the
maximum Doppler shift.

That's all I need.

Yes but you have to process it appropriately. Your
program is not doing that at present.

It's near enough to do what I want at present..

No, it is wrong by a factor of 11000 at 8 light years.
Of course that's only a test but the number is going
to be badly wrong at any range of interest.

George, velocity and distance are conjugate.

If the velocity is 10% high then my distance will be10% low.
This is no big deal. I don't know where you are getting your figures.


.. although I will have to take
Yaw angle into acount eventually..

Does that matter at the moment for a circular
orbit?

No there is no error in a circular orbit.
However as I have shown, this is NOT a circular orbit according to BaTh. It has
an e ~ 0.06 with periastron furthest from observer.

The maximum OBSERVED radial velocity will differ only slighly from the maximum
PERIPHERAL velocity. However the phasing will be nearly 90 out!!!! So I'm going
to have to compensate for this when I compare phases.
I can do this fairly easily..and will do so soon.

I think this might explain why my curves for RT Aur were a fair way out in
phase.
Thakyou for your help George. You might have added another nail in Albert's
coffin.

All I am doing now is matching curves. The value of (distance x max velocity)
is rather arbitrary because I dont really know the unification distance and it
is not easy to obtain velocity diagrams.

The BaTh and SR
doppler equations are effectively the same.

No they aren't, that's the whole point. Look at the
bottom of your reply where you agree the _apparent_
speed should reach c at the critical distance!

Yes.... but during extinction, the wavelength contracts or expands, so as to
still maintain the correct details of source velocity.

No, the speed matching causes the 'wavelength',
which in this case is the distance between pulses,
to eventually settle down to a constant value but
it will not be the original.

Not according to me.

They do according to the theory, you don't have
a choice.

The final distance between adjacent pulses will vary according to their initial
velocity relative to the barycentre. Some will move closer together, others
further apart.

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.

The extreme test
example here is for viewing at 8 light years with
negligible extinction, or equivalently at infinity
with an exponential extinction distance of 8 light
years, and the wavelength is zero. Your software
still gives v/c=0.00009 when it should be v/c=1.

George, unless I have access to a curve showing variation in pulse arrival
times I cannot help you much.

I've given you that repeatedly. The frequency varies by
30.5 mHz either side of 339 Hz.

OK.


Reading the papers about this pulsar is quite confusing for me

Indeed, but the basic information you need is trivial
for me. Some of the more specialised terms are less
clear but the basic orbit is simple.

It turns out that this might not be true.

because the
authors make such a big issue of Shapiro delay. (They even admit light is
slowed by gravity).

The Shapiro delay is what makes the system special.
It allows the inclination to be determined which
leads to highly accurate determination of a lot
of other parameters.

Well the whole picture changes when you use c+v....as it does with most of
astrophysics. It becomes more simple and logical.

The BaTh interpretation would be quite different from
theirs.

It would, so stop looking for excuses and let's see what
your program says.

It is done.

It can. ..or you can set eccentricity at 0.01

No, set it to 2.3*10^-7 if anything, but you
don't need an explicit extinction term. Just
treat your program as an observer at infinity
and distance is the characteristic extinction
length.

Hahaha!
See, your claim that the orbit is circular is based on a perfectly sinelike
'red curve'. The BaTh shows that the OBSERVED sinewave velocity curve requires
an orbit with e ~ 0.6 or more depending on observer distance.

Yes I can do that.
I only introduced the 'extinction' facility in order to try to obtain a value
for its rate.

Essentially your distance parameter is already that.

Yes. For a mag change of 0.2, I get a distance of about 0.7 LY


Like I said, all I need is period, distance and a value for the maximum
radial velocity.

Like I said, what you have is maximum Doppler shift.

No problem.

Indeed, but you need to fix the bug in the
software to convert from the shift to the
speed correctly.

George, this is a circular orbit and there is no difference between my and your
value of maximum velocity. I have tried to explain that extinction will not
affect measured doppler and its interpretation.

Extinction in itself wouldn't but the initial speed
difference does affect the Dopppler. Faster pulses
catch up to slower ones for a while before extinction
matches their speeds. That means the pulses are closer
together giving the _false_ impression of a higher
speed. Your blue curve is the true speed, the red
curve should be the _apparent_ speed deduced from
the closed-up pulses. It should be _higher_ than the
blue curve.

No. The program averages the ORIGINAL pulse speeds that arrive in set time
intervals. It should oscillate between 'higher' and 'lower'.

The red curve for the apparent speed. If you enter
27km/s the red curve should show that deviation
above and below the white axis. It would help if
you added a vertical scale or we cannot confirm
that. I'm presuming the value in the table on the
left called "Max. Vel." is your assumption for the
actual speed which you entered rather than the
highest point on the red curve.

The velocity curves are set to always have the same size on the screen. The
scale is linear and yes, the maximum is that shown in the velocity box. Ity
should be the same fro both red and blue curves.

No, it should be 0.00009c for the blue curve
at 8 light years and 1.0c for the red curve.
The 'wavelength' at that distance is zero.

George, I don't think we're taking about the same things here.

I might occassionally get the red and blue transposed
but I don't think I have so far.

The blue curve is the true radial velocity curve towards the observer.

Yes.

The red curve is generated in this way:

For the purpose of counting the arrival of pulses, the orbit period is divided
into 500 divisions, which form the elements of an array. The program adds all
the pulses that arrive in that division to make up the value of that array
element. It also follows each pulse individually so that it records the speed
at which the pulse left the source barycentre. It averages the velocities of
all the pulse that are placed into each array element.

That will give the wrong answer. The pubilished velocity
data uses the conventional Doppler formula so the speed is

v = c * (df / f)

where df is the frequency shift

To find that, you can use the time between arrivals which
is just the period, or the inverse of the frequency.

But you are using constant 'c'!!!. I'm using c+v...Naturally I will get a
different answer.

Introducing extinction doesn't really change anything.

It stops the period changing after some distance, the
way you have it at the moment is fine.

That's not good way to put it.
Nothing happens to the period no matter how extinction operates.

Just calculate
the Doppler shift from your pulse arrival times and you
will get the right answer.

Just stick c+v into your formula George and YOU will get right answer.
...Oh, and you might need a computer program to do it because v varies with
time.

I have realised though that when using ellitical orbits I have to compensate
for Yaw angle because the maximum observed velocity is not necessarily the
velocity at periastron.

That could be the cause of your extra phase
change.

It shouldn't make much difference at low eccentricities and doesn't affect
brightness curve shape anyway. ..just the distance.

It will have a small effect but for our circular
orbit, it is irrelevant. Can I ask that you lay
that aside on your to-do list until we finish
looking at J1909-3744.

It is done.
It supports the BaTh observation that extinction distance is inversely velocity
dependent...which is odd when you think about it.

There is second
order term involving the 'rate of change of acceleration'. You have
omitted it.

I don't believe there is such a term but that's why
I want to do the short distance test first.

No, I was wrong there, although not entirely. The main reason the point moves
is due solely to the difference in emission times. For short distances, a half
period is quite significant.

Getting the correct location for the maximum speed
will matter too, but for our circular orbit it
shouldn't matter.

Anyway, bottom line at the moment is that you are
not calculating the apparent velocity correctly
from the pulse period so let's get that fixed
before worrying about the effects of eccentricity.

George you have it all back to front.

I don't want to calculate the velocity. I want to read about it in a table or
graph.

Little children learn they don't always get what they
want. The published tables give the period and time
difference and I have done the calculation to turn that
into frequencies for you. All you need to do is fix the
bug in your program and then find the orbital parameters
and extinction that matches the observation.

you are using constant c.
I'm using c+v.

Can you provide that info for me?

I have done many times Henry, stop trying to invent excuses.

George

"Henri Wilson" HW@.... wrote in message
...
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