N:dlzc D:aol T:com (dlzc) N: dlzc1 D:cox wrote in message
news:esB3d.207292$4o.155232@fed1read01...
Dear Mich:

"Mich" wrote in message
...

Then you should get a *current* book. Your use Groups.Google, because it
has been derived here also. I will refer you to a posting by Stephen
Speicher date 2002oct20:

QUOTE
The relativistic Doppler effect can be seen, albeit quite
loosely, as a combination of time dilation with a more classical
Doppler effect applied to light, considering the finite time of
travel of the light.

Assume we have two inertial frames which are receding from each
other with a radial velocity v, with the second (primed) frame
emitting a pulse which travels at light speed towards an observer
in the first frame. We ask ourselves: what is the time
difference between two pulses emitted by the source, as seen by
the observer. In the source frame the pulses are separated by
dt', the time between the first and second pulses. The observer
will see this time separation, but it will be modified due to the
motion of the source, i.e., the extra distance traveled by the
second pulse due to the velocity between the observer and source.
So, the time, dt, between pulses as seen by the observer will be

dt = dt' + dt'(v/c) (1)

or,

dt/dt' = 1 + (v/c) (2)

But, since wavelength is the velocity times the time separation,
(2) becomes

(lambda)/(lambda)' = 1 + (v/c) (3)


o.k, I believe I understand this part.



Equation (3) relates the ratio of the source and observer
determined wavelengths to the velocity between the two frames,
assuming the pulses travel at c. This would reflect a classical
Doppler shift of wavelength due to relative motion between the
source and observer. To arrive at the relativistic expression
for the Doppler effect, we note that source determined times are
subject to time dilation, such that the time between pulses, as
determined in the source frame, must be multiplied by a factor of
gamma, g = 1/sqrt(1 - v^2/c^2). So, equation (1) becomes,

dt = g(dt') + g(dt')(v/c) (4)

or, following the previous steps,

(lambda)/(lambda)' = g{1 + (v/c)}

= (1 + v/c)/sqrt(1 - v^2/c^2)

= (1 + v/c)/sqrt(1 + v/c)sqrt(1 - v/c)

= {(1 + v/c)/sqrt(1 + v/c)}/sqrt(1 - v/c)

= {(1 + v/c)sqrt(1 + v/c)/(1 + v/c)}/sqrt(1 - v/c)

= sqrt{(1 + v/c)/(1 - v/c),

which is the standard form of the relativistic Doppler effect on
the ratio of received and sending wavelengths. And here, indeed,
it matters if the source is moving away from or towards the
observer. If the source were approaching the observer, then the
{+ g(dt')(v/c)} in equ (4) would be {- g(dt')(v/c)}, and the
overall relativistic effect would be reversed.


The gamma multiplied to the equation takes care of the relativistic red
shift.
I believe that I understand this part as well.


If instead of observing in a direction directly towards or away
from the source, if observation is made perpendicular to its
motion, as would be considered for the situation where the source
circles the observer, then the relativistic effect is known as
the transverse Doppler effect, and it can be shown to be

(lambda)/(lambda)' = 1/sqrt(1 - v^2/c^2),


And the (1+v/c) is not inserted as there is no change of distances
separating
the observer and the light source. I think I understand this as well.


which is, just like time dilation, a relation involving just
gamma. There are, of course, much more rigorous derivations of
this relativistic Doppler effect -- one which is more general in
nature -- but this simple one illustrates how the effect is a
combination of time dilation with motion between source and
observer, when considering the emitted pulse traveling along
their line of motion.
END QUOTE

David A. Smith


I don't quite feel this explains the problem in question, though.
Let us say the source sends two pulses while traveling with the velocity of
v away from the observer. The time the two pulses will arrive at the
observer will be s/c.Relative to the source's frame of reference, the two
pulses were separated by dt', and relative to the observer the pulses ought
to be separated
by g(dt') + g(dt')(v/c) . Again, those two pulses travelled the distance
from where the pulses were released to the observer having this particular
"wavelenght",or "frequency" coming towards the observer.Now, just before the
pulses arrived at their destination, the observer changes frame of
reference, and now v must change in the equation due to this last change of
reference....but the velocity changes relative to what? The source may no
longer exist when the pulse hits the observer.

Andre

Dear Mich:

"Mich" wrote in message
...

N:dlzc D:aol T:com (dlzc) N: dlzc1 D:cox wrote in
message
news:esB3d.207292$4o.155232@fed1read01...
Dear Mich:

"Mich" wrote in message
...

Then you should get a *current* book. Your use Groups.Google, because
it
has been derived here also. I will refer you to a posting by Stephen
Speicher date 2002oct20:

QUOTE
The relativistic Doppler effect can be seen, albeit quite
loosely, as a combination of time dilation with a more classical
Doppler effect applied to light, considering the finite time of
travel of the light.

Assume we have two inertial frames which are receding from each
other with a radial velocity v, with the second (primed) frame
emitting a pulse which travels at light speed towards an observer
in the first frame. We ask ourselves: what is the time
difference between two pulses emitted by the source, as seen by
the observer. In the source frame the pulses are separated by
dt', the time between the first and second pulses. The observer
will see this time separation, but it will be modified due to the
motion of the source, i.e., the extra distance traveled by the
second pulse due to the velocity between the observer and source.
So, the time, dt, between pulses as seen by the observer will be

dt = dt' + dt'(v/c) (1)

or,

dt/dt' = 1 + (v/c) (2)

But, since wavelength is the velocity times the time separation,
(2) becomes

(lambda)/(lambda)' = 1 + (v/c) (3)


o.k, I believe I understand this part.



Equation (3) relates the ratio of the source and observer
determined wavelengths to the velocity between the two frames,
assuming the pulses travel at c. This would reflect a classical
Doppler shift of wavelength due to relative motion between the
source and observer. To arrive at the relativistic expression
for the Doppler effect, we note that source determined times are
subject to time dilation, such that the time between pulses, as
determined in the source frame, must be multiplied by a factor of
gamma, g = 1/sqrt(1 - v^2/c^2). So, equation (1) becomes,

dt = g(dt') + g(dt')(v/c) (4)

or, following the previous steps,

(lambda)/(lambda)' = g{1 + (v/c)}

= (1 + v/c)/sqrt(1 - v^2/c^2)

= (1 + v/c)/sqrt(1 + v/c)sqrt(1 - v/c)

= {(1 + v/c)/sqrt(1 + v/c)}/sqrt(1 - v/c)

= {(1 + v/c)sqrt(1 + v/c)/(1 + v/c)}/sqrt(1 - v/c)

= sqrt{(1 + v/c)/(1 - v/c),

which is the standard form of the relativistic Doppler effect on
the ratio of received and sending wavelengths. And here, indeed,
it matters if the source is moving away from or towards the
observer. If the source were approaching the observer, then the
{+ g(dt')(v/c)} in equ (4) would be {- g(dt')(v/c)}, and the
overall relativistic effect would be reversed.


The gamma multiplied to the equation takes care of the relativistic red
shift.
I believe that I understand this part as well.


If instead of observing in a direction directly towards or away
from the source, if observation is made perpendicular to its
motion, as would be considered for the situation where the source
circles the observer, then the relativistic effect is known as
the transverse Doppler effect, and it can be shown to be

(lambda)/(lambda)' = 1/sqrt(1 - v^2/c^2),


And the (1+v/c) is not inserted as there is no change of distances
separating
the observer and the light source. I think I understand this as well.


which is, just like time dilation, a relation involving just
gamma. There are, of course, much more rigorous derivations of
this relativistic Doppler effect -- one which is more general in
nature -- but this simple one illustrates how the effect is a
combination of time dilation with motion between source and
observer, when considering the emitted pulse traveling along
their line of motion.
END QUOTE


I don't quite feel this explains the problem in question, though.
Let us say the source sends two pulses while traveling with the velocity
of
v away from the observer. The time the two pulses will arrive at the
observer will be s/c.

s/c?

Relative to the source's frame of reference, the two
pulses were separated by dt', and relative to the observer the pulses
ought
to be separated
by g(dt') + g(dt')(v/c) . Again, those two pulses travelled the distance
from where the pulses were released to the observer having this
particular
"wavelenght",or "frequency" coming towards the observer.Now, just before
the
pulses arrived at their destination, the observer changes frame of
reference,

Why? The "v" is the relationship between the source and the observer. I
don't see where "changing frame of reference" is necessary.

and now v must change in the equation due to this last change of
reference....but the velocity changes relative to what? The source may no
longer exist when the pulse hits the observer.

And? The two events that are observed could have been the arrival of a
photon topedo, and the detonation of the warp core. The v could have been
established either by observing characteristic wavelengths emitted as the
anti-matter impacted the ship, or by observations made of the ship passing
signature markers (say two planets). v can be determined by a number of
methods, none of which require the source to be anything except "existing"
when the light is emitted at the two events.

David A. Smith

N:dlzc D:aol T:com (dlzc) N: dlzc1 D:cox wrote in message
news:aDM3d.212134$4o.170337@fed1read01...
Dear Mich:

"Mich" wrote in message
...

N:dlzc D:aol T:com (dlzc) N: dlzc1 D:cox wrote in
message
news:esB3d.207292$4o.155232@fed1read01...
Dear Mich:

"Mich" wrote in message
...
Why? The "v" is the relationship between the source and the observer. I
don't see where "changing frame of reference" is necessary.

and now v must change in the equation due to this last change of
reference....but the velocity changes relative to what? The source may
no
longer exist when the pulse hits the observer.

And? The two events that are observed could have been the arrival of a
photon topedo, and the detonation of the warp core. The v could have been
established either by observing characteristic wavelengths emitted as the
anti-matter impacted the ship, or by observations made of the ship passing
signature markers (say two planets). v can be determined by a number of
methods, none of which require the source to be anything except "existing"
when the light is emitted at the two events.

David A. Smith


But that's just it; I "personally" have a hard time accepting the two
pulses as being inseparable from the source.Once the two pulses have been
sent from the source, the source not longer matters; that is,the source can
move however it will without affecting the outcome of the predicted
frequency the observer will receive. Once the two pulses have been sent from
the source,they have a velocity and a wavelength(distance separating the
pulse), relative to the observer and this doesn't change, eventhough the
source might change it's frame of reference after the pulses have been sent.
Now Once the two pulses are sent, if the observer moves, the predicted
frequency will have change proportionally to the change of relative velocity
between the observer and the pulses...not the source, since the source's
frame of reference relative to the observer no longer matters after the
pulses have been sent.
There are two ways that this can be achieved. Either the wavelength
distance between the two pulses) changes, or the relative velocity between
the pulses and the observer, which Relativity forbid.

Andre

Nothing is constant. Mass and energy are interchangeable. Gravity is a
by-product of this fact. Time is altered by mass, and vice versa. Atomic
vibration isn't a vibration at all. It is growth; except that the observers
are growing too. So all they witness is vibration. As mass increases, time
slows. This creates accelaration and therefore gravity. Can none of you see
this? It is the ultimate theory.

It's all there if you care to imagine.

Dear Mich:

"Mich" wrote in message
...

N:dlzc D:aol T:com (dlzc) N: dlzc1 D:cox wrote in
message
news:aDM3d.212134$4o.170337@fed1read01...
....
and now v must change in the equation due to this last
change of reference....but the velocity changes relative
to what? The source may no longer exist when the pulse
hits the observer.

And? The two events that are observed could have been the
arrival of a photon topedo, and the detonation of the warp
core. The v could have been established either by observing
characteristic wavelengths emitted as the anti-matter impacted
the ship, or by observations made of the ship passing signature
markers (say two planets). v can be determined by a number of
methods, none of which require the source to be anything
except "existing" when the light is emitted at the two events.

But that's just it; I "personally" have a hard time accepting the two
pulses as being inseparable from the source.Once the two pulses have
been
sent from the source, the source not longer matters; that is,the source
can
move however it will without affecting the outcome of the predicted
frequency the observer will receive. Once the two pulses have been sent
from
the source,they have a velocity and a wavelength(distance separating the
pulse), relative to the observer and this doesn't change, eventhough the
source might change it's frame of reference after the pulses have been
sent.

But *not* decoupled from the source-observer relative velocity until
*after* emission.

Now Once the two pulses are sent, if the observer moves, the predicted
frequency will have change proportionally to the change of relative
velocity
between the observer and the pulses...not the source, since the source's
frame of reference relative to the observer no longer matters after the
pulses have been sent.

References to source velocity are always to the source at the time of
emission. No other claim is made. Nor required.

There are two ways that this can be achieved. Either the wavelength
distance between the two pulses) changes, or the relative velocity
between
the pulses and the observer, which Relativity forbid.

The distance between pulses would correspond with length contraction, and
is in agreement with relativity.

And the relative velocity between the pulses and the observer would violate
Maxwell's relations, not relativity (directly). And would make
refraction-based optics untenable in a dynamic Universe, since the focal
point of a lens would therefore be a function of source velocity.

David A. Smith

N:dlzc D:aol T:com (dlzc) N: dlzc1 D:cox wrote in message
news:Lq34d.216255$4o.195007@fed1read01...
Dear Mich:

"Mich" wrote in message
...

But that's just it; I "personally" have a hard time accepting the two
pulses as being inseparable from the source.Once the two pulses have
been
sent from the source, the source not longer matters; that is,the source
can
move however it will without affecting the outcome of the predicted
frequency the observer will receive. Once the two pulses have been sent
from
the source,they have a velocity and a wavelength(distance separating the
pulse), relative to the observer and this doesn't change, eventhough the
source might change it's frame of reference after the pulses have been
sent.

But *not* decoupled from the source-observer relative velocity until
*after* emission.

True. The relative velocity existing between the source and observer
"before" the light pulse is released from the source will "determine" the
amount of doppler shift the observer will see. But, right after the pulse
have been released, then, the source's speed, or change thereof, no longer
is dependant to what the doppler shift will be seen as by the observer.

References to source velocity are always to the source at the time of
emission. No other claim is made. Nor required.

But the velocity must be between the source and the observer. The source
alone cannot be said to have a velocity; or am I not understanding what you
wrote?

There are two ways that this can be achieved. Either the wavelength
distance between the two pulses) changes, or the relative velocity
between
the pulses and the observer, which Relativity forbid.

The distance between pulses would correspond with length contraction, and
is in agreement with relativity.

This length contraction is almost nonexistant in low velocities. I'm having
proplems with the "classical doppler effect".In every instances, when it
concerns sound or water waves, when the observer changes it's frame of
reference, the change of wave frequency is always due to a change in
relative velocities between the observer and the waves. I don't understand
Relativity's
explanation on this.



And the relative velocity between the pulses and the observer would
violate
Maxwell's relations, not relativity (directly). And would make
refraction-based optics untenable in a dynamic Universe, since the focal
point of a lens would therefore be a function of source velocity.

But what if, unlike Maxwell we viewed the light pulses in turns of a
particle and not a wave in some medium?

Andre

David A. Smith

Dear Mich:

"Mich" wrote in message
...

N:dlzc D:aol T:com (dlzc) N: dlzc1 D:cox wrote in
message
news:Lq34d.216255$4o.195007@fed1read01...
Dear Mich:

"Mich" wrote in message
...

But that's just it; I "personally" have a hard time accepting the two
pulses as being inseparable from the source.Once the two pulses have
been
sent from the source, the source not longer matters; that is,the
source
can
move however it will without affecting the outcome of the predicted
frequency the observer will receive. Once the two pulses have been
sent
from
the source,they have a velocity and a wavelength(distance separating
the
pulse), relative to the observer and this doesn't change, eventhough
the
source might change it's frame of reference after the pulses have been
sent.

But *not* decoupled from the source-observer relative velocity until
*after* emission.

True. The relative velocity existing between the source and observer
"before" the light pulse is released from the source will "determine" the
amount of doppler shift the observer will see. But, right after the pulse
have been released, then, the source's speed, or change thereof, no
longer
is dependant to what the doppler shift will be seen as by the observer.

So there is one step: the relationship between the "Universe et al" and
the source, and the other step: the relationship between the "Universe et
al" and the observer? Is the is abstraction necessary/useful?

References to source velocity are always to the source at the time of
emission. No other claim is made. Nor required.

But the velocity must be between the source and the observer. The source
alone cannot be said to have a velocity; or am I not understanding what
you
wrote?

I'm not sure. We have a velocity wrt the Universe of about 300 km/sec.
What the observer sees is the relationship between himself and the source
at the time of the emission. There is no evidence of an intermediate step.

There are two ways that this can be achieved. Either the wavelength
distance between the two pulses) changes, or the relative velocity
between
the pulses and the observer, which Relativity forbid.

The distance between pulses would correspond with length contraction,
and
is in agreement with relativity.

This length contraction is almost nonexistant in low velocities. I'm
having
proplems with the "classical doppler effect".In every instances, when it
concerns sound or water waves, when the observer changes it's frame of
reference, the change of wave frequency is always due to a change in
relative velocities between the observer and the waves. I don't
understand
Relativity's
explanation on this.

It can be presented as two components: 1) the classical Doppler shift, 2)
time dilation of the source's "events".

The first you understand, because it is "perspective" based on geometry.
One could travel in certain directions and receive the wave pulses in
reverse order, or in unshifted frequency, as long as one stayed at or below
the celerity of the wave in the medium

As to the second, relativity simply "ties" time into the same cloth as
space, and time dialtion/length contraction are perspective effects in this
4D space.

And the relative velocity between the pulses and the observer would
violate
Maxwell's relations, not relativity (directly). And would make
refraction-based optics untenable in a dynamic Universe, since the focal
point of a lens would therefore be a function of source velocity.

But what if, unlike Maxwell we viewed the light pulses in turns of a
particle and not a wave in some medium?

Maxwell's description is valid physics, and makes useful and correct
predictions. So it is applicable to relativity, as one of its postulates.

Then we are faced with a massless particle that travels at a single speed
for all observers. In a Universe of "relatives", we have one constant.
Sort of.

David A. Smith

N:dlzc D:aol T:com (dlzc) N: dlzc1 D:cox wrote in message
news:lFo4d.223098$4o.99383@fed1read01...
Dear Mich:

"Mich" wrote in message
...

N:dlzc D:aol T:com (dlzc) N: dlzc1 D:cox wrote in
message
news:Lq34d.216255$4o.195007@fed1read01...
Dear Mich:

"Mich" wrote in message
...

True. The relative velocity existing between the source and observer
"before" the light pulse is released from the source will "determine"
the
amount of doppler shift the observer will see. But, right after the
pulse
have been released, then, the source's speed, or change thereof, no
longer
is dependant to what the doppler shift will be seen as by the observer.

So there is one step: the relationship between the "Universe et al" and
the source, and the other step: the relationship between the "Universe et
al" and the observer? Is the is abstraction necessary/useful?

I'm not sure what you mean, here, Dave. I've tried to restrict the
frequencies ( distance between the pulses) as viewed from the frames of the
observer and that of the source only.


But the velocity must be between the source and the observer. The source
alone cannot be said to have a velocity; or am I not understanding what
you
wrote?

I'm not sure. We have a velocity wrt the Universe of about 300 km/sec.
What the observer sees is the relationship between himself and the source
at the time of the emission. There is no evidence of an intermediate
step.

The relationship between the universe and the observer(earth orbiting the
sun at 300 km/sec) can be disregarded in this case.
At the time of emission, the observer sees a distance x separating itself
from the source, as well as a velocity v existing between it and the source.
....Or if this is a trick question, the observer sees nothing until it
receives a light pulse from the source. However we can assume that such
observations had already taken place with light signals prior to the light
pulses being emitted for the purpose of studying the doppler effect.

It can be presented as two components: 1) the classical Doppler shift, 2)
time dilation of the source's "events".

I understand this.


The first you understand, because it is "perspective" based on geometry.
One could travel in certain directions and receive the wave pulses in
reverse order, or in unshifted frequency, as long as one stayed at or
below
the celerity of the wave in the medium

ok

As to the second, relativity simply "ties" time into the same cloth as
space, and time dialtion/length contraction are perspective effects in
this
4D space.

I believe I understand this.

But what if, unlike Maxwell we viewed the light pulses in turns of a
particle and not a wave in some medium?

Maxwell's description is valid physics, and makes useful and correct
predictions. So it is applicable to relativity, as one of its postulates.

I do believe that Maxwell's equations has been interpretated in terms of
particle
theory without any problems.

Then we are faced with a massless particle that travels at a single speed
for all observers. In a Universe of "relatives", we have one constant.
Sort of.

In my opinion, Maxwell intergrated his equation into a theory of light in
terms of waves moving through a medium. Therefore, the constant c which came
out of his equation,was a great surprise....since the earth was to travel
with great velocity through it. But within the particle theory of light,
Maxwell's constant c does indeed make sense since the emitter and receiver
are on the same frame of reference. The same can be said with the Michelson
and Morley experiment.

Andre

Dear Mich:

"Mich" wrote in message
...

N:dlzc D:aol T:com (dlzc) N: dlzc1 D:cox wrote in
message
news:lFo4d.223098$4o.99383@fed1read01...
....
True. The relative velocity existing between the source and
observer "before" the light pulse is released from the source
will "determine" the amount of doppler shift the observer
will see. But, right after the pulse have been released, then,
the source's speed, or change thereof, no longer is
dependant to what the doppler shift will be seen as by the
observer.

So there is one step: the relationship between the "Universe et al"
and the source, and the other step: the relationship between the
"Universe et al" and the observer? Is the is abstraction necessary/
useful?

I'm not sure what you mean, here, Dave. I've tried to restrict the
frequencies ( distance between the pulses) as viewed from the frames
of the observer and that of the source only.

OK. But you brought up "velocity between the observer and the signal" at
one point.

But the velocity must be between the source and the observer.
The source alone cannot be said to have a velocity; or am I not
understanding what you wrote?

I'm not sure. We have a velocity wrt the Universe of about 300
km/sec. What the observer sees is the relationship between himself
and the source at the time of the emission. There is no evidence of
an intermediate step.

The relationship between the universe and the observer(earth orbiting the
sun at 300 km/sec) can be disregarded in this case.

The 300 km/sec has more components than just orbiting the Sun, FWIW.
Motion of the Sun about the Milky Way's center, motion of the Milky Way in
the Virgo Supercluster, and motion of the Virgo cluster wrt the "Universe
et al". Just FYI.

At the time of emission, the observer sees a distance x separating
itself from the source, as well as a velocity v existing between it and
the source.
...Or if this is a trick question, the observer sees nothing until it
receives a light pulse from the source.

The observer could see some object of known distance, briefly light the
source up. "Tricky" perhaps, but not "trick".

However we can assume that such
observations had already taken place with light signals prior to
the light pulses being emitted for the purpose of studying the
doppler effect.

It can be presented as two components: 1) the classical
Doppler shift, 2) time dilation of the source's "events".

I understand this.

The first you understand, because it is "perspective" based
on geometry. One could travel in certain directions and receive
the wave pulses in reverse order, or in unshifted frequency, as
long as one stayed at or below the celerity of the wave in the
medium

ok

As to the second, relativity simply "ties" time into the same
cloth as space, and time dialtion/length contraction are
perspective effects in this 4D space.

I believe I understand this.

But what if, unlike Maxwell we viewed the light pulses in
turns of a particle and not a wave in some medium?

Maxwell's description is valid physics, and makes useful and
correct predictions. So it is applicable to relativity, as one of
its postulates.

I do believe that Maxwell's equations has been interpretated in
terms of particle theory without any problems.

Most likely. ;)

Then we are faced with a massless particle that travels at a single
speed for all observers. In a Universe of "relatives", we have one
constant. Sort of.

In my opinion, Maxwell intergrated his equation into a theory of light
in terms of waves moving through a medium. Therefore, the constant
c which came out of his equation,was a great surprise....since the
earth was to travel with great velocity through it. But within the
particle
theory of light, Maxwell's constant c does indeed make sense since
the emitter and receiver are on the same frame of reference.

But they don't have to be. In fact the value of "v" separates the emitter
and receiver frames. Yet TWLS always returns an average of c.

The same
can be said with the Michelson and Morley experiment.

OK.

David A. Smith

Thank you for the info, Dave.

N:dlzc D:aol T:com (dlzc) N: dlzc1 D:cox wrote in message
news:HAq4d.223821$4o.151168@fed1read01...
Dear Mich:

"Mich" wrote in message
...

N:dlzc D:aol T:com (dlzc) N: dlzc1 D:cox wrote in
message
news:lFo4d.223098$4o.99383@fed1read01...
...
I'm not sure what you mean, here, Dave. I've tried to restrict the
frequencies ( distance between the pulses) as viewed from the frames
of the observer and that of the source only.

OK. But you brought up "velocity between the observer and the signal" at
one point.

True...but the velocity between the ought to be, and I believe it to be c.
However this brought me to the question as to how can the doppler effect be
explained when the observer changes frame.That is the reason why I brought
up
the velocity relationship between the observer and the pulse signal.

The 300 km/sec has more components than just orbiting the Sun, FWIW.
Motion of the Sun about the Milky Way's center, motion of the Milky Way in
the Virgo Supercluster, and motion of the Virgo cluster wrt the "Universe
et al". Just FYI.

Very interesting.... I didn't know that.

But they don't have to be. In fact the value of "v" separates the emitter
and receiver frames. Yet TWLS always returns an average of c
David A. Smith

This is an important point to the problem that I have. Do you know some
links which would explain the observation to this?

Thanks for your time

Andre