Pioneer : Anomaly Still Anonymous

On 30 Jun 2006 01:29:54 -0700, "George Dishman"
wrote:

John C. Polasek wrote:
...
I may be misinterpreting what is in the model, but what I have tried
to represent in the upper model leg is a digital differential analyzer
doing numerical integration on data taken from the ephemeris and
double integrating it for range that would then update the ephemeris.
In so doing only the constant G is involved, and it's all
mathematical.

Then to produce anything resembling frequency, for later comparison
with the real hardware, from the point V(t), one must introduce the
multiplier -f0/c. In this regard I would expect that the multiplier is
a mathematic constant being 1/WL.sphone

If this is wrong, just say so and I can modify my model,

It is wrong. The model integrates a mathematical representation
of the initial location and motion of the craft with all subsequent
gravitational accelerations and specific manoeuvre effects to
model the velocity at any time which is pretty much what you
say in the first paragraph.

George, I appreciate your efforts to produce an ASCII style diagram,
but it defines in detail only the hardware that is the lower left half
of my diagram (I have improved the diagram; take a look at the
website). The hardware is 100%. In fact, I agree that aside from
A_radio, both model and hardware arrive at the same velocities.

But you are not addressing the frequency problem in the model , the
top right half of the diagram. It is this: if you checked with NIST in
1987 you would get a frequency 2.292......, and called NIST today you
would get exactly the same number 2.292....... I call this f87 in the
diagram. This is would be true if all atomic clocks, the station
clock, the maser standard, accelerated alike.
You can see how this would qualify f87 as a constant if it has the
same value that it was assigned 20 years earlier. So the original
numeric F87 is a constant in the model that has no way of tracking
acceleration.
And, unfortunately there is no accurate way of determining *true*
frequency, of if clock frequency is actually increasing, since the
easiest recourse is to cause the best possible atomic reference to
make a one second gate, whereupon the station clock counter would let
through 2.292.... cycles.


At that point, the relativistic Doppler equation is applied to the
recorded transmit frequency to predict the modelled receive
frequency for comparison against the actual receive frequency
recorded from the hardware.

but then tell
me how this coefficient -f0/c is brought up to date with the
transmitting clock. With an analog computer, yes, or using the station
clock to drive the DDA, but that looks like a nullity also.

I take back f0/c, the villain is f0.

The latter, the station clock is used to drive the exciter to
produce a frequency which is a known multiple of the clock
reference frequency. I suspect they would have used a
synthesiser just like the transponder on the craft so that the
exciter was locked to the station clock.

This is hardware

In th following, the capital "F" indicates a frequency which is
a number. The number on transmit is loaded into the hardware
and governs the ratio of the transmitted frequency to the station
clock. On receive the number fed into the synthesiser (DDS)
F_het is chosen to be slightly offset from the expected receive
frequency and the actaul signal shown as f_het is heterodyned
with the signal from the low noise amp (LNA). The difference is
then measured again using the station clock as a reference so
that the number F_rx written into the files is the ratio of the
actual receive frequency f_rx to the actual clock frequency f_ref.

Configuration during transmission

Exciter
_________________
f_ref / f_tx \
station -------- DDS -------- Amp -------- to dish
clock ^
|
F_tx -------- Written to data file




Configuration during reception

Exciter
_________________
f_ref / f_het \
station ---+---- DDS ---+---- Amp ... not used
clock | ^ |
| | | f_het
| F_het |
| |
| | f_rx
| mixer (*)-------- from dish / LNA
| |
| | f_if
| |
-------- counter
f_ref |
| F_if
|
v
Sum of measured value F_if
and F_het written to data
file: F_rx = F_het + F_if


f_* indicates the frequency of an electrical signal
F_* indicates a frequency in the form of a number




It is clear there is substantial misunderstanding somewhere.

The hardware on the Pioneer is 100%

Yes, you have a problem. Why don't you start to fix it by reading the
referred-to papers, or George or my previous posts, which you seem to
be conveniently ignoring?

You say "the station clock at the time of the tracking session is used
in the model". Please tell very specifically how this can be done.

The diagrams above attempt to do that.

Checking the frequency with NIST would be simplest. You can update an
atomic clock over the telephone.

Today we use GPS to lock our company clock to the
international standard. I don't know what method was in
use at the time of the Pioneer mission but there would
have been an equivalent. The station 'clock' was a
hydrogen maser which ran continuously producing a
10MHz reference frequency to which all the instruments
are locked.

It's hardware

Their site has a sample daily record
of a clock being checked, that shows infinitesimal *random* daily
changes about +-2e-13 which is nothing.
Remember that by hypothesis, NIST's masers have advanced by exactly
the same fraction as the statioin clock, so they all march together.

Yes.

But f0 in the model is stuck in the past.
We need to discuss f0 in the model.
No, f_tx must be derived from the station clock at the time
of transmission since it was an actual electrical signal.
Similatrly f_rx was compared against the station clock at
the time of reception to get the number F_rx. Both numbers
were written to the data files which we can now use.

but this is hardware, not model

Tell me how the number f0 is custom adjusted to the station clock's
frequency, when there is no way of determining its frequency in the
first place.

In the actual hardware, f0 (which I think corresponds to f_het
in my terminology, local oscillator for the heterodyne receiver)
is produced directly from the station clock by the synthesiser
in the exciter assembly.

still hardware

My argument is simply that f0 is set in stone, ...

You can make a battery that produces a reference voltage
for calibration purposes, but you cannot keep a sample of
a frequency in a bottle in that way and use it later. The
reference frequency signal is what is produced by the
maser at the time.

George
John P

"John C. Polasek" wrote in message
...
On 30 Jun 2006 01:29:54 -0700, "George Dishman"
wrote:

John C. Polasek wrote:
...
I may be misinterpreting what is in the model, but what I have tried
to represent in the upper model leg is a digital differential
analyzer
doing numerical integration on data taken from the ephemeris and
double integrating it for range that would then update the ephemeris.
In so doing only the constant G is involved, and it's all
mathematical.

Then to produce anything resembling frequency, for later comparison
with the real hardware, from the point V(t), one must introduce the
multiplier -f0/c. In this regard I would expect that the multiplier
is
a mathematic constant being 1/WL.sphone

If this is wrong, just say so and I can modify my model,

It is wrong. The model integrates a mathematical representation
of the initial location and motion of the craft with all subsequent
gravitational accelerations and specific manoeuvre effects to
model the velocity at any time which is pretty much what you
say in the first paragraph.

George, I appreciate your efforts to produce an ASCII style diagram,
but it defines in detail only the hardware that is the lower left half
of my diagram (I have improved the diagram; take a look at the
website).

It is still lacking a clear description of what the symbols
mean and each stage of the process. It really isn't much use
at all at present but if you add some explanations it could
be very helpful. An example is:

The hardware is 100%. In fact, I agree that aside from
A_radio, both model and hardware arrive at the same velocities.

The term "A_radio" is not explained anywhere in the text
though it appears in your diagram. I would normally assume
the usual radio convention that "A" stands for Amplitude
so A_radio is the transmitter power of 250kW but that makes
no sense. Plaese explain your terms in the paper.

But you are not addressing the frequency problem in the model , the
top right half of the diagram. It is this: if you checked with NIST in
1987 you would get a frequency 2.292......, and called NIST today you
would get exactly the same number 2.292....... I call this f87 in the
diagram. This is would be true if all atomic clocks, the station
clock, the maser standard, accelerated alike.

Since the speed of the craft is determined from the ratio
F_rx/F_tx, only the clock change between the time of
transmission and time of reception matters. For example
consider a slight alternative where all terrestrial clocks
were stable in 1987 so the Tx signal was at 2.292GHz exactly
but the clocks doubled in frequency in the intervening years
so the Tx signal was stable but at 4.584GHz when a later
reading was taken. The returned frequency would also be
doubled (ignoring hardware limitations) so the ratio
F_rx/F_tx would be unaffected and the derived speed would
be correct. What that means is that your "f87" doesn't exist.

You can see how this would qualify f87 as a constant if it has the
same value that it was assigned 20 years earlier. So the original
numeric F87 is a constant in the model that has no way of tracking
acceleration.
And, unfortunately there is no accurate way of determining *true*
frequency,

You don't need to know the "true" frequency, the only
thing used is the ratio.

of if clock frequency is actually increasing, since the
easiest recourse is to cause the best possible atomic reference to
make a one second gate, whereupon the station clock counter would let
through 2.292.... cycles.


At that point, the relativistic Doppler equation is applied to the
recorded transmit frequency to predict the modelled receive
frequency for comparison against the actual receive frequency
recorded from the hardware.

but then tell
me how this coefficient -f0/c is brought up to date with the
transmitting clock. With an analog computer, yes, or using the
station
clock to drive the DDA, but that looks like a nullity also.

I take back f0/c, the villain is f0.

There is no such thing as "f0" in the model.

The latter, the station clock is used to drive the exciter to
produce a frequency which is a known multiple of the clock
reference frequency. I suspect they would have used a
synthesiser just like the transponder on the craft so that the
exciter was locked to the station clock.

This is hardware

Yes, but focus on the values written to the files, F_tx
and F_rx. Those are what must be used as the data input
to the model.

In th following, the capital "F" indicates a frequency which is
a number. The number on transmit is loaded into the hardware
and governs the ratio of the transmitted frequency to the station
clock. On receive the number fed into the synthesiser (DDS)
F_het is chosen to be slightly offset from the expected receive
frequency and the actaul signal shown as f_het is heterodyned
with the signal from the low noise amp (LNA). The difference is
then measured again using the station clock as a reference so
that the number F_rx written into the files is the ratio of the
actual receive frequency f_rx to the actual clock frequency f_ref.

Configuration during transmission

Exciter
_________________
f_ref / f_tx \
station -------- DDS -------- Amp -------- to dish
clock ^
|
F_tx -------- Written to data file




Configuration during reception

Exciter
_________________
f_ref / f_het \
station ---+---- DDS ---+---- Amp ... not used
clock | ^ |
| | | f_het
| F_het |
| |
| | f_rx
| mixer (*)-------- from dish / LNA
| |
| | f_if
| |
-------- counter
f_ref |
| F_if
|
v
Sum of measured value F_if
and F_het written to data
file: F_rx = F_het + F_if


f_* indicates the frequency of an electrical signal
F_* indicates a frequency in the form of a number




It is clear there is substantial misunderstanding somewhere.

The hardware on the Pioneer is 100%

The hardware on the Pioneer is not shown above, only
the ground segment, but I don't think the craft end
is contentious.

Checking the frequency with NIST would be simplest. You can update an
atomic clock over the telephone.

Today we use GPS to lock our company clock to the
international standard. I don't know what method was in
use at the time of the Pioneer mission but there would
have been an equivalent. The station 'clock' was a
hydrogen maser which ran continuously producing a
10MHz reference frequency to which all the instruments
are locked.

It's hardware

So here's the next stage:


F_tx(t1) \
V_dsn_t(t1) -- Doppler -- F_cr(t2)
V_cr(t2) /

where F_cr(t) is the frequency received at the craft
at time t (one can subsume the 240/221 fixed turnround
ratio), V_cr(t) is the velocity of the craft at time t
and V_dsn_t(t) is the velocity of the DSN transmit site
at time t which is known from the ephemeris and Earth
rotation data. Then:

F_cr(t2) \
V_dsn_r(t3) -- Doppler -- F_model(t3)
V_cr(t2) /

Where F_model(t) is the receive frequency predicted by
the model for reception at time t and V_dsn_r is the
velocity of the DSN receive site at time t. The times
a

t1: time of transmission
t2: time when the signal is transponded by the craft
t3: time of reception

t3 is as recorded in the data files but since the
propagation time depends on the range, t2 and then t1
have to be calculated using the modelled location at
time t2. The transmit frequency was generally constant
through any contact period but the times are needed to
apply the ephemeris and Earth rotation Doppler effects.

The resulting receive frequency predictions are then
compared with the actual received values F_rx(t3) and
the model parameters adjusted to minimise the error.

Notice the key point, only the logged values F_tx and
F_rx are used and then only as a ratio, so any error
in the station clock which was common to both times
cancels out. The only discrepancy that gets through
is the amount the station clock drifted between time
t1 and time t3. Note also that clocks were at different
sites.

Bottom line: there is no "f0" or "f87" in the model,
the role is fulfilled by the recorded values of
F_tx(t).

George

On Sat, 1 Jul 2006 20:22:56 +0100, "George Dishman"
wrote:


"John C. Polasek" wrote in message
.. .
On 30 Jun 2006 01:29:54 -0700, "George Dishman"
wrote:

John C. Polasek wrote:
...
I may be misinterpreting what is in the model, but what I have tried
to represent in the upper model leg is a digital differential
analyzer
doing numerical integration on data taken from the ephemeris and
double integrating it for range that would then update the ephemeris.
In so doing only the constant G is involved, and it's all
mathematical.

Then to produce anything resembling frequency, for later comparison
with the real hardware, from the point V(t), one must introduce the
multiplier -f0/c. In this regard I would expect that the multiplier
is
a mathematic constant being 1/WL.sphone

If this is wrong, just say so and I can modify my model,

It is wrong. The model integrates a mathematical representation
of the initial location and motion of the craft with all subsequent
gravitational accelerations and specific manoeuvre effects to
model the velocity at any time which is pretty much what you
say in the first paragraph.

George, I appreciate your efforts to produce an ASCII style diagram,
but it defines in detail only the hardware that is the lower left half
of my diagram (I have improved the diagram; take a look at the
website).

It is still lacking a clear description of what the symbols
mean and each stage of the process. It really isn't much use
at all at present but if you add some explanations it could
be very helpful. An example is:

The hardware is 100%. In fact, I agree that aside from
A_radio, both model and hardware arrive at the same velocities.

The term "A_radio" is not explained anywhere in the text
though it appears in your diagram. I would normally assume
the usual radio convention that "A" stands for Amplitude
so A_radio is the transmitter power of 250kW but that makes
no sense. Plaese explain your terms in the paper.

Yes A_radio is the 1.1x10^-10m/ss given as the radiative effect of 8
watts continuously on, pushing us awayfrom the earth, which when
lumped with others for a bias of .9 units that make an observed 7.8
units go to 8.7 units.

But you are not addressing the frequency problem in the model , the
top right half of the diagram. It is this: if you checked with NIST in
1987 you would get a frequency 2.292......, and called NIST today you
would get exactly the same number 2.292....... I call this f87 in the
diagram. This is would be true if all atomic clocks, the station
clock, the maser standard, accelerated alike.

Since the speed of the craft is determined from the ratio
F_rx/F_tx, only the clock change between the time of
transmission and time of reception matters. For example
consider a slight alternative where all terrestrial clocks
were stable in 1987 so the Tx signal was at 2.292GHz exactly
but the clocks doubled in frequency in the intervening years
so the Tx signal was stable but at 4.584GHz when a later
reading was taken. The returned frequency would also be
doubled (ignoring hardware limitations) so the ratio
F_rx/F_tx would be unaffected and the derived speed would
be correct. What that means is that your "f87" doesn't exist.

You can see how this would qualify f87 as a constant if it has the
same value that it was assigned 20 years earlier. So the original
numeric F87 is a constant in the model that has no way of tracking
acceleration.
And, unfortunately there is no accurate way of determining *true*
frequency,

You don't need to know the "true" frequency, the only
thing used is the ratio.

of if clock frequency is actually increasing, since the
easiest recourse is to cause the best possible atomic reference to
make a one second gate, whereupon the station clock counter would let
through 2.292.... cycles.


At that point, the relativistic Doppler equation is applied to the
recorded transmit frequency to predict the modelled receive
frequency for comparison against the actual receive frequency
recorded from the hardware.

but then tell
me how this coefficient -f0/c is brought up to date with the
transmitting clock. With an analog computer, yes, or using the
station
clock to drive the DDA, but that looks like a nullity also.

I take back f0/c, the villain is f0.

There is no such thing as "f0" in the model.

The latter, the station clock is used to drive the exciter to
produce a frequency which is a known multiple of the clock
reference frequency. I suspect they would have used a
synthesiser just like the transponder on the craft so that the
exciter was locked to the station clock.

This is hardware

Yes, but focus on the values written to the files, F_tx
and F_rx. Those are what must be used as the data input
to the model.

In th following, the capital "F" indicates a frequency which is
a number. The number on transmit is loaded into the hardware
and governs the ratio of the transmitted frequency to the station
clock. On receive the number fed into the synthesiser (DDS)
F_het is chosen to be slightly offset from the expected receive
frequency and the actaul signal shown as f_het is heterodyned
with the signal from the low noise amp (LNA). The difference is
then measured again using the station clock as a reference so
that the number F_rx written into the files is the ratio of the
actual receive frequency f_rx to the actual clock frequency f_ref.

Configuration during transmission

Exciter
_________________
f_ref / f_tx \
station -------- DDS -------- Amp -------- to dish
clock ^
|
F_tx -------- Written to data file




Configuration during reception

Exciter
_________________
f_ref / f_het \
station ---+---- DDS ---+---- Amp ... not used
clock | ^ |
| | | f_het
| F_het |
| |
| | f_rx
| mixer (*)-------- from dish / LNA
| |
| | f_if
| |
-------- counter
f_ref |
| F_if
|
v
Sum of measured value F_if
and F_het written to data
file: F_rx = F_het + F_if


f_* indicates the frequency of an electrical signal
F_* indicates a frequency in the form of a number




It is clear there is substantial misunderstanding somewhere.

The hardware on the Pioneer is 100%

The hardware on the Pioneer is not shown above, only
the ground segment, but I don't think the craft end
is contentious.

Checking the frequency with NIST would be simplest. You can update an
atomic clock over the telephone.

Today we use GPS to lock our company clock to the
international standard. I don't know what method was in
use at the time of the Pioneer mission but there would
have been an equivalent. The station 'clock' was a
hydrogen maser which ran continuously producing a
10MHz reference frequency to which all the instruments
are locked.

It's hardware

So here's the next stage:


F_tx(t1) \
V_dsn_t(t1) -- Doppler -- F_cr(t2)
V_cr(t2) /

where F_cr(t) is the frequency received at the craft
at time t (one can subsume the 240/221 fixed turnround
ratio), V_cr(t) is the velocity of the craft at time t
and V_dsn_t(t) is the velocity of the DSN transmit site
at time t which is known from the ephemeris and Earth
rotation data. Then:

F_cr(t2) \
V_dsn_r(t3) -- Doppler -- F_model(t3)
V_cr(t2) /

Where F_model(t) is the receive frequency predicted by
the model for reception at time t and V_dsn_r is the
velocity of the DSN receive site at time t. The times
a

t1: time of transmission
t2: time when the signal is transponded by the craft
t3: time of reception

t3 is as recorded in the data files but since the
propagation time depends on the range, t2 and then t1
have to be calculated using the modelled location at
time t2. The transmit frequency was generally constant
through any contact period but the times are needed to
apply the ephemeris and Earth rotation Doppler effects.

The resulting receive frequency predictions are then
compared with the actual received values F_rx(t3) and
the model parameters adjusted to minimise the error.

Notice the key point, only the logged values F_tx and
F_rx are used and then only as a ratio, so any error
in the station clock which was common to both times
cancels out. The only discrepancy that gets through
is the amount the station clock drifted between time
t1 and time t3. Note also that clocks were at different
sites.

Bottom line: there is no "f0" or "f87" in the model,
the role is fulfilled by the recorded values of
F_tx(t).

George

George, look at it this way. The station and the model each have
"carrier" frequencies that are "modulated" additively by the craft
velocity as df = -dv/lambda. Each modulation is summed up as Df in the
diagram. Let's agree that the Df's are perfectly equal. Their
difference would therefore contribute zero to the output and the
entire left half of the graph including Df's would no longer be
interesting.

However, the velocities are modulating two different frequencies, f0
in the model and f0(1+Ht) in the real system. The output difference,
therefore, absent the modulation noise, is f0Ht.

If one were to conduct the Pioneer experiment today, one might
initialize by tinkering with velocities and ranges using the standard
f0, but now with prior knowledge, I would have them first increase f0
by about 4 hz if it was last set 20 years ago. (1.5Hz/8yrs) and then
tinker with velocity.

Would you agree, that just in general, if f0 really increased at
Hubble rate, while the copybook frequency f0 which obviously has no
aegis for alteration, that a comparison of some sort would yield the
linear plot we have today?

John P

"John C. Polasek" wrote in message
...
On Sat, 1 Jul 2006 20:22:56 +0100, "George Dishman"
wrote:

Much trimmed as not contentious:


The term "A_radio" is not explained anywhere in the text
though it appears in your diagram. I would normally assume
the usual radio convention that "A" stands for Amplitude
so A_radio is the transmitter power of 250kW but that makes
no sense. Plaese explain your terms in the paper.

Yes A_radio is the 1.1x10^-10m/ss given as the radiative effect of 8
watts continuously on, pushing us awayfrom the earth, which when
lumped with others for a bias of .9 units that make an observed 7.8
units go to 8.7 units.

OK, that's clear. There's no way I would have
guessed that from your paper.

So here's the next stage:


F_tx(t1) \
V_dsn_t(t1) -- Doppler -- F_cr(t2)
V_cr(t2) /

where F_cr(t) is the frequency received at the craft
at time t (one can subsume the 240/221 fixed turnround
ratio), V_cr(t) is the velocity of the craft at time t
and V_dsn_t(t) is the velocity of the DSN transmit site
at time t which is known from the ephemeris and Earth
rotation data. Then:

F_cr(t2) \
V_dsn_r(t3) -- Doppler -- F_model(t3)
V_cr(t2) /

Where F_model(t) is the receive frequency predicted by
the model for reception at time t and V_dsn_r is the
velocity of the DSN receive site at time t. The times
a

t1: time of transmission
t2: time when the signal is transponded by the craft
t3: time of reception

t3 is as recorded in the data files but since the
propagation time depends on the range, t2 and then t1
have to be calculated using the modelled location at
time t2. The transmit frequency was generally constant
through any contact period but the times are needed to
apply the ephemeris and Earth rotation Doppler effects.

The resulting receive frequency predictions are then
compared with the actual received values F_rx(t3) and
the model parameters adjusted to minimise the error.

Notice the key point, only the logged values F_tx and
F_rx are used and then only as a ratio, so any error
in the station clock which was common to both times
cancels out. The only discrepancy that gets through
is the amount the station clock drifted between time
t1 and time t3. Note also that clocks were at different
sites.

Bottom line: there is no "f0" or "f87" in the model,
the role is fulfilled by the recorded values of
F_tx(t).

George, look at it this way. The station and the model each have
"carrier" frequencies that are "modulated" additively by the craft
velocity as df = -dv/lambda.

I'm not sure what you mean by "additively", the effect
of Doppler is multiplicative. The received frequency
is the product of the transmitted frequency and the
speed-dependent factor. That is important. Anyway the
key point is that what is modulated is the carrier
that was sent to the craft a few hours before, not a
signal transmitted in 1987.

Each modulation is summed up as Df in the
diagram. Let's agree that the Df's are perfectly equal. Their
difference would therefore contribute zero to the output and the
entire left half of the graph including Df's would no longer be
interesting.

However, the velocities are modulating two different frequencies, f0
in the model and f0(1+Ht) in the real system.

No, f_tx(t1 + H*(t3-t1)) in reality and f_tx(t1) in
the model. See above for the definition of t1 and t3.

The output difference,
therefore, absent the modulation noise, is f0Ht.

Since Doppler is multiplicative, you need to consider
the error in the ratio, not the difference. The key
though is that it applies only over the propagation
time.

Would you agree, that just in general, if f0 really increased at
Hubble rate, while the copybook frequency f0 which obviously has no
aegis for alteration, that a comparison of some sort would yield the
linear plot we have today?

The plot would be nearly linear because the round trip
propagation time increased nearly linearly over the
mission period, but since the Hubble term only
applies for a few hours and not the 8 years you are
assuming, it would be about 10,000 times smaller
than is observed.

George

On Sat, 1 Jul 2006 22:35:39 +0100, "George Dishman"
wrote:


"John C. Polasek" wrote in message
.. .
On Sat, 1 Jul 2006 20:22:56 +0100, "George Dishman"
wrote:

Much trimmed as not contentious:


The term "A_radio" is not explained anywhere in the text
though it appears in your diagram. I would normally assume
the usual radio convention that "A" stands for Amplitude
so A_radio is the transmitter power of 250kW but that makes
no sense. Plaese explain your terms in the paper.

Yes A_radio is the 1.1x10^-10m/ss given as the radiative effect of 8
watts continuously on, pushing us awayfrom the earth, which when
lumped with others for a bias of .9 units that make an observed 7.8
units go to 8.7 units.

OK, that's clear. There's no way I would have
guessed that from your paper.

So here's the next stage:


F_tx(t1) \
V_dsn_t(t1) -- Doppler -- F_cr(t2)
V_cr(t2) /

where F_cr(t) is the frequency received at the craft
at time t (one can subsume the 240/221 fixed turnround
ratio), V_cr(t) is the velocity of the craft at time t
and V_dsn_t(t) is the velocity of the DSN transmit site
at time t which is known from the ephemeris and Earth
rotation data. Then:

F_cr(t2) \
V_dsn_r(t3) -- Doppler -- F_model(t3)
V_cr(t2) /

Where F_model(t) is the receive frequency predicted by
the model for reception at time t and V_dsn_r is the
velocity of the DSN receive site at time t. The times
a

t1: time of transmission
t2: time when the signal is transponded by the craft
t3: time of reception

t3 is as recorded in the data files but since the
propagation time depends on the range, t2 and then t1
have to be calculated using the modelled location at
time t2. The transmit frequency was generally constant
through any contact period but the times are needed to
apply the ephemeris and Earth rotation Doppler effects.

The resulting receive frequency predictions are then
compared with the actual received values F_rx(t3) and
the model parameters adjusted to minimise the error.

Notice the key point, only the logged values F_tx and
F_rx are used and then only as a ratio, so any error
in the station clock which was common to both times
cancels out. The only discrepancy that gets through
is the amount the station clock drifted between time
t1 and time t3. Note also that clocks were at different
sites.

Bottom line: there is no "f0" or "f87" in the model,
the role is fulfilled by the recorded values of
F_tx(t).

George, look at it this way. The station and the model each have
"carrier" frequencies that are "modulated" additively by the craft
velocity as df = -dv/lambda.

I'm not sure what you mean by "additively", the effect
of Doppler is multiplicative. The received frequency
is the product of the transmitted frequency and the
speed-dependent factor.
The velocity of the target produces df = -vf0/c and yes, that's
multiplicative. But that's the Doppler part which is down 25,000: 1 or
88db and is negligible and amounts to noise.
The chart itself is a plot of the difference between the "whole
frequencies" f0, a constant, and f0(1+Ht) over a substantial period
of years. I tried to "make it happen" during flight time and arrived
at the 1/25,000 ratio. It's all the difference in the carriers, f0
definitely constant, and freal very likely advancing, but no easy way
to prove it except for the Pioneer test.

Anyway the
key point is that what is modulated is the carrier
that was sent to the craft a few hours before, not a
signal transmitted in 1987.

Remember back ( in 1983 I think), it was decreed and "it is so
written" that the 133Cs maser delivers 9+ gigacycles in one second
which at once compromised both the frequency and the second. The
station clock will read today the same as 20 years ago, by comparison
with that clock. But that's not to say that it isn't running faster.
There is no way to assess whether the frequency has indeed increased,
certainly not with that method of comparison.

The frequency increase, which I put as only a hypothesis, is "proved"
in my theory: our universe is moving at the speed of light away from
its center of mass and the clocks are speeding up as is the speed of
light. I added a new term to Newton's
-g = MG/r^2 = cdc/dr (= Hc) etc. etc.
that shows the expansion effect.

Each modulation is summed up as Df in the
diagram. Let's agree that the Df's are perfectly equal. Their
difference would therefore contribute zero to the output and the
entire left half of the graph including Df's would no longer be
interesting.

However, the velocities are modulating two different frequencies, f0
in the model and f0(1+Ht) in the real system.

No, f_tx(t1 + H*(t3-t1)) in reality and f_tx(t1) in
the model. See above for the definition of t1 and t3.

The output difference,
therefore, absent the modulation noise, is f0Ht.

Since Doppler is multiplicative, you need to consider
the error in the ratio, not the difference. The key
though is that it applies only over the propagation
time.

Would you agree, that just in general, if f0 really increased at
Hubble rate, while the copybook frequency f0 which obviously has no
aegis for alteration, that a comparison of some sort would yield the
linear plot we have today?

The plot would be nearly linear because the round trip
propagation time increased nearly linearly over the
mission period, but since the Hubble term only
applies for a few hours and not the 8 years you are
assuming, it would be about 10,000 times smaller
than is observed.

George

John P

"John C. Polasek" wrote in message
...
On Sat, 1 Jul 2006 22:35:39 +0100, "George Dishman"
wrote:


"John C. Polasek" wrote in message
. ..
On Sat, 1 Jul 2006 20:22:56 +0100, "George Dishman"
wrote:

Much trimmed as not contentious:


The term "A_radio" is not explained anywhere in the text
though it appears in your diagram. I would normally assume
the usual radio convention that "A" stands for Amplitude
so A_radio is the transmitter power of 250kW but that makes
no sense. Plaese explain your terms in the paper.

Yes A_radio is the 1.1x10^-10m/ss given as the radiative effect of 8
watts continuously on, pushing us awayfrom the earth, which when
lumped with others for a bias of .9 units that make an observed 7.8
units go to 8.7 units.

OK, that's clear. There's no way I would have
guessed that from your paper.

So here's the next stage:


F_tx(t1) \
V_dsn_t(t1) -- Doppler -- F_cr(t2)
V_cr(t2) /

where F_cr(t) is the frequency received at the craft
at time t (one can subsume the 240/221 fixed turnround
ratio), V_cr(t) is the velocity of the craft at time t
and V_dsn_t(t) is the velocity of the DSN transmit site
at time t which is known from the ephemeris and Earth
rotation data. Then:

F_cr(t2) \
V_dsn_r(t3) -- Doppler -- F_model(t3)
V_cr(t2) /

Where F_model(t) is the receive frequency predicted by
the model for reception at time t and V_dsn_r is the
velocity of the DSN receive site at time t. The times
a

t1: time of transmission
t2: time when the signal is transponded by the craft
t3: time of reception

t3 is as recorded in the data files but since the
propagation time depends on the range, t2 and then t1
have to be calculated using the modelled location at
time t2. The transmit frequency was generally constant
through any contact period but the times are needed to
apply the ephemeris and Earth rotation Doppler effects.

The resulting receive frequency predictions are then
compared with the actual received values F_rx(t3) and
the model parameters adjusted to minimise the error.

Notice the key point, only the logged values F_tx and
F_rx are used and then only as a ratio, so any error
in the station clock which was common to both times
cancels out. The only discrepancy that gets through
is the amount the station clock drifted between time
t1 and time t3. Note also that clocks were at different
sites.

Bottom line: there is no "f0" or "f87" in the model,
the role is fulfilled by the recorded values of
F_tx(t).

George, look at it this way. The station and the model each have
"carrier" frequencies that are "modulated" additively by the craft
velocity as df = -dv/lambda.

I'm not sure what you mean by "additively", the effect
of Doppler is multiplicative. The received frequency
is the product of the transmitted frequency and the
speed-dependent factor.

The velocity of the target produces df = -vf0/c and yes, that's
multiplicative. But that's the Doppler part which is down 25,000: 1 or
88db and is negligible and amounts to noise.

It would also be multiplicative if applied to your
ficticious "f0" or "f87".

The chart itself is a plot of the difference between the "whole
frequencies" f0, a constant, and f0(1+Ht) over a substantial period
of years. I tried to "make it happen" during flight time and arrived
at the 1/25,000 ratio. It's all the difference in the carriers, f0
definitely constant, and freal very likely advancing, but no easy way
to prove it except for the Pioneer test.

Anyway the
key point is that what is modulated is the carrier
that was sent to the craft a few hours before, not a
signal transmitted in 1987.

Remember back ( in 1983 I think), it was decreed and "it is so
written" that the 133Cs maser delivers 9+ gigacycles in one second
which at once compromised both the frequency and the second. The
station clock will read today the same as 20 years ago, by comparison
with that clock. But that's not to say that it isn't running faster.
There is no way to assess whether the frequency has indeed increased,
certainly not with that method of comparison.

There is a method in theory. One could have sent a
signal in 1983 to a probe 11.5 light years away
which sent it back to Earth at the same frequency.
Neglecting Doppler efefcts, you would then have a
copy of that original frequency to compare with
the present clocks. In fact that is what your paper
assumes happened.

The frequency increase, which I put as only a hypothesis, is "proved"
in my theory: ...

No it isn't because in reality the signal was sent to
the craft only a few hours earlier, not in 1987.

As you say above, you "tried to 'make it happen' during
flight time and arrived at the 1/25,000 ratio" which is
the correct conclusion, this sort of simple drift doesn't
work. There is no place for an "f0" in the model and you
cannot just invent it because it suits your goal.

George

On Sun, 2 Jul 2006 19:13:14 +0100, "George Dishman"
wrote:


"John C. Polasek" wrote in message
.. .
On Sat, 1 Jul 2006 22:35:39 +0100, "George Dishman"
wrote:


"John C. Polasek" wrote in message
...
On Sat, 1 Jul 2006 20:22:56 +0100, "George Dishman"
wrote:

Much trimmed as not contentious:


The term "A_radio" is not explained anywhere in the text
though it appears in your diagram. I would normally assume
the usual radio convention that "A" stands for Amplitude
so A_radio is the transmitter power of 250kW but that makes
no sense. Plaese explain your terms in the paper.

Yes A_radio is the 1.1x10^-10m/ss given as the radiative effect of 8
watts continuously on, pushing us awayfrom the earth, which when
lumped with others for a bias of .9 units that make an observed 7.8
units go to 8.7 units.

OK, that's clear. There's no way I would have
guessed that from your paper.

So here's the next stage:


F_tx(t1) \
V_dsn_t(t1) -- Doppler -- F_cr(t2)
V_cr(t2) /

where F_cr(t) is the frequency received at the craft
at time t (one can subsume the 240/221 fixed turnround
ratio), V_cr(t) is the velocity of the craft at time t
and V_dsn_t(t) is the velocity of the DSN transmit site
at time t which is known from the ephemeris and Earth
rotation data. Then:

F_cr(t2) \
V_dsn_r(t3) -- Doppler -- F_model(t3)
V_cr(t2) /

Where F_model(t) is the receive frequency predicted by
the model for reception at time t and V_dsn_r is the
velocity of the DSN receive site at time t. The times
a

t1: time of transmission
t2: time when the signal is transponded by the craft
t3: time of reception

t3 is as recorded in the data files but since the
propagation time depends on the range, t2 and then t1
have to be calculated using the modelled location at
time t2. The transmit frequency was generally constant
through any contact period but the times are needed to
apply the ephemeris and Earth rotation Doppler effects.

The resulting receive frequency predictions are then
compared with the actual received values F_rx(t3) and
the model parameters adjusted to minimise the error.

Notice the key point, only the logged values F_tx and
F_rx are used and then only as a ratio, so any error
in the station clock which was common to both times
cancels out. The only discrepancy that gets through
is the amount the station clock drifted between time
t1 and time t3. Note also that clocks were at different
sites.

Bottom line: there is no "f0" or "f87" in the model,
the role is fulfilled by the recorded values of
F_tx(t).

George, look at it this way. The station and the model each have
"carrier" frequencies that are "modulated" additively by the craft
velocity as df = -dv/lambda.

I'm not sure what you mean by "additively", the effect
of Doppler is multiplicative. The received frequency
is the product of the transmitted frequency and the
speed-dependent factor.

The velocity of the target produces df = -vf0/c and yes, that's
multiplicative. But that's the Doppler part which is down 25,000: 1 or
88db and is negligible and amounts to noise.

It would also be multiplicative if applied to your
ficticious "f0" or "f87".

The chart itself is a plot of the difference between the "whole
frequencies" f0, a constant, and f0(1+Ht) over a substantial period
of years. I tried to "make it happen" during flight time and arrived
at the 1/25,000 ratio. It's all the difference in the carriers, f0
definitely constant, and freal very likely advancing, but no easy way
to prove it except for the Pioneer test.

Anyway the
key point is that what is modulated is the carrier
that was sent to the craft a few hours before, not a
signal transmitted in 1987.

Remember back ( in 1983 I think), it was decreed and "it is so
written" that the 133Cs maser delivers 9+ gigacycles in one second
which at once compromised both the frequency and the second. The
station clock will read today the same as 20 years ago, by comparison
with that clock. But that's not to say that it isn't running faster.
There is no way to assess whether the frequency has indeed increased,
certainly not with that method of comparison.

There is a method in theory. One could have sent a
signal in 1983 to a probe 11.5 light years away
which sent it back to Earth at the same frequency.
Neglecting Doppler efefcts, you would then have a
copy of that original frequency to compare with
the present clocks. In fact that is what your paper
assumes happened.

I did not have that in my paper, but let's agree that a transmitted
frequency will retain its same value. In the imaginary experiment you
cite, there would be a frequency difference corresponding to Hf0x23yr
as I see it either by frequency beat or Lissajou figure on a
scope(theoretically).

The curious thing is with the above, there would be a beat even
though we know the original transmitted signal had the frequency f0
(2.292 as painted on the side of the clock), and you just checked with
NIST and they assured you that your station was "dead-on" at 2.292
just like the marking. Yet you get a frequency difference that is not
Doppler. It's the cosmic effect of clocks moving up in a gravity well.
NIST has no way to keep track .

The frequency increase, which I put as only a hypothesis, is "proved"
in my theory: ...

No it isn't because in reality the signal was sent to
the craft only a few hours earlier, not in 1987.

As you say above, you "tried to 'make it happen' during
flight time and arrived at the 1/25,000 ratio" which is
the correct conclusion, this sort of simple drift doesn't
work. There is no place for an "f0" in the model and you
cannot just invent it because it suits your goal.

Yes George there has to be a place for f0 in the model. It's the only
way you can get to compare frequencies with the Pioneer. You have just
calculated the number v = 12km/s and now you need to multiply by
-1/lambda and then you need to add in the base frequency f0. You need
that in order to compare against Pioneer's f3.
The chart comes from "whole frequency" comparison. Don't bring up that
little Doppler effect; it only confuses the issue. For me, the two
doppler beats deltaf can be identical.

George

John P

"John C. Polasek" wrote in message
news
On Sun, 2 Jul 2006 19:13:14 +0100, "George Dishman"
wrote:
"John C. Polasek" wrote in message
. ..
On Sat, 1 Jul 2006 22:35:39 +0100, "George Dishman"
wrote:


"John C. Polasek" wrote in message
m...
On Sat, 1 Jul 2006 20:22:56 +0100, "George Dishman"
wrote:

big snip of background


... The times a

t1: time of transmission
t2: time when the signal is transponded by the craft
t3: time of reception

t3 is as recorded in the data files but since the
propagation time depends on the range, t2 and then t1
have to be calculated using the modelled location at
time t2. The transmit frequency was generally constant
through any contact period but the times are needed to
apply the ephemeris and Earth rotation Doppler effects.

....

Remember back ( in 1983 I think), it was decreed and "it is so
written" that the 133Cs maser delivers 9+ gigacycles in one second
which at once compromised both the frequency and the second. The
station clock will read today the same as 20 years ago, by comparison
with that clock. But that's not to say that it isn't running faster.
There is no way to assess whether the frequency has indeed increased,
certainly not with that method of comparison.

There is a method in theory. One could have sent a
signal in 1983 to a probe 11.5 light years away
which sent it back to Earth at the same frequency.
Neglecting Doppler efefcts, you would then have a
copy of that original frequency to compare with
the present clocks. In fact that is what your paper
assumes happened.

I did not have that in my paper, but let's agree that a transmitted
frequency will retain its same value. In the imaginary experiment you
cite, there would be a frequency difference corresponding to Hf0x23yr
as I see it either by frequency beat or Lissajou figure on a
scope(theoretically).

The curious thing is with the above, there would be a beat even
though we know the original transmitted signal had the frequency f0
(2.292 as painted on the side of the clock), and you just checked with
NIST and they assured you that your station was "dead-on" at 2.292
just like the marking. Yet you get a frequency difference that is not
Doppler. It's the cosmic effect of clocks moving up in a gravity well.
NIST has no way to keep track .

Right, that is the effect you are describing.

The frequency increase, which I put as only a hypothesis, is "proved"
in my theory: ...

No it isn't because in reality the signal was sent to
the craft only a few hours earlier, not in 1987.

As you say above, you "tried to 'make it happen' during
flight time and arrived at the 1/25,000 ratio" which is
the correct conclusion, this sort of simple drift doesn't
work. There is no place for an "f0" in the model and you
cannot just invent it because it suits your goal.

Yes George there has to be a place for f0 in the model. It's the only
way you can get to compare frequencies with the Pioneer. You have just
calculated the number v = 12km/s and now you need to multiply by
-1/lambda and then you need to add in the base frequency f0. You need
that in order to compare against Pioneer's f3.

Nope, they apply the speed to the Tx frequency
at time t1 as recorded in the file in the "ramp"
records. Those are a comparison of the actual
transmitted frequency with the station clock at
time t1, not what it was in 1987.

The chart comes from "whole frequency" comparison.

I know, but the hardware doesn't have any way to
reproduce the clock signal as it was years earlier.
Only the current clock can be used.

Don't bring up that
little Doppler effect; it only confuses the issue. For me, the two
doppler beats deltaf can be identical.

Doppler is a separate issue and I think we both
understand that, what you are missing is that
only the clock rate at time t1 versus t3 matters.

George

On Sun, 2 Jul 2006 23:49:28 +0100, "George Dishman"
wrote:


"John C. Polasek" wrote in message
news
On Sun, 2 Jul 2006 19:13:14 +0100, "George Dishman"
wrote:
"John C. Polasek" wrote in message
...
On Sat, 1 Jul 2006 22:35:39 +0100, "George Dishman"
wrote:


"John C. Polasek" wrote in message
om...
On Sat, 1 Jul 2006 20:22:56 +0100, "George Dishman"
wrote:

big snip of background


... The times a

t1: time of transmission
t2: time when the signal is transponded by the craft
t3: time of reception

t3 is as recorded in the data files but since the
propagation time depends on the range, t2 and then t1
have to be calculated using the modelled location at
time t2. The transmit frequency was generally constant
through any contact period but the times are needed to
apply the ephemeris and Earth rotation Doppler effects.

...

Remember back ( in 1983 I think), it was decreed and "it is so
written" that the 133Cs maser delivers 9+ gigacycles in one second
which at once compromised both the frequency and the second. The
station clock will read today the same as 20 years ago, by comparison
with that clock. But that's not to say that it isn't running faster.
There is no way to assess whether the frequency has indeed increased,
certainly not with that method of comparison.

There is a method in theory. One could have sent a
signal in 1983 to a probe 11.5 light years away
which sent it back to Earth at the same frequency.
Neglecting Doppler efefcts, you would then have a
copy of that original frequency to compare with
the present clocks. In fact that is what your paper
assumes happened.

I did not have that in my paper, but let's agree that a transmitted
frequency will retain its same value. In the imaginary experiment you
cite, there would be a frequency difference corresponding to Hf0x23yr
as I see it either by frequency beat or Lissajou figure on a
scope(theoretically).

The curious thing is with the above, there would be a beat even
though we know the original transmitted signal had the frequency f0
(2.292 as painted on the side of the clock), and you just checked with
NIST and they assured you that your station was "dead-on" at 2.292
just like the marking. Yet you get a frequency difference that is not
Doppler. It's the cosmic effect of clocks moving up in a gravity well.
NIST has no way to keep track .

Right, that is the effect you are describing.

The frequency increase, which I put as only a hypothesis, is "proved"
in my theory: ...

No it isn't because in reality the signal was sent to
the craft only a few hours earlier, not in 1987.

As you say above, you "tried to 'make it happen' during
flight time and arrived at the 1/25,000 ratio" which is
the correct conclusion, this sort of simple drift doesn't
work. There is no place for an "f0" in the model and you
cannot just invent it because it suits your goal.

Yes George there has to be a place for f0 in the model. It's the only
way you can get to compare frequencies with the Pioneer. You have just
calculated the number v = 12km/s and now you need to multiply by
-1/lambda and then you need to add in the base frequency f0. You need
that in order to compare against Pioneer's f3.

Nope, they apply the speed to the Tx frequency
at time t1 as recorded in the file in the "ramp"
records.

Could you clarify this mathematically, applying the speed to the TX
frequency? You mean adjusting the model? How specifically? You have a
way to modernize the coefficients in the model?

Those are a comparison of the actual
transmitted frequency with the station clock at
time t1, not what it was in 1987.

Can this actual transmitted frequency be brought into the model as a
numeric factor? Why would it not be the standard 2.292?Or is there a
wasy to transfuse it into the model even without knowing its value? If
you had reason to think it might be different, then some new questions
need to be raised.
The chart comes from "whole frequency" comparison.

I know, but the hardware doesn't have any way to
reproduce the clock signal as it was years earlier.
Only the current clock can be used.

Well of course everything is done currently in the station and always
rechecked for conformance to 2.292Ghz. The model must likewise have
that same 2.292 imprimatur. And it must use it some way to produce the
total frequency fmod = f0 - vf0/c, of which the 2d term is
negligible. f0 is added to the converted velocity stream in the model
(f87 in my diagram).

But meanwhile the real clock frequencies have theoretically moved on
up by f0Ht with no one able to prove otherwise, right from clocks that
are currently certified as 2.292. NIST nor any one else can decide.
The declaration of 133Cs being 9,192,631,770 cycles to equal 1
second, with c *declared* as 299,792,458 m/s merely locks the
wavelength of the Cesium transition to 0.0326xxx m.

Don't bring up that
little Doppler effect; it only confuses the issue. For me, the two
doppler beats deltaf can be identical.

Doppler is a separate issue and I think we both
understand that, what you are missing is that
only the clock rate at time t1 versus t3 matters.

But time t1 and t3 are with the same clock and you are forgetting that
it is comparison with the model's frequency that makes the anomaly.
George

John P

John C. Polasek wrote:
On Sun, 2 Jul 2006 23:49:28 +0100, "George Dishman"
wrote:


"John C. Polasek" wrote in message
news
On Sun, 2 Jul 2006 19:13:14 +0100, "George Dishman"
wrote:
"John C. Polasek" wrote in message
...
On Sat, 1 Jul 2006 22:35:39 +0100, "George Dishman"
wrote:


"John C. Polasek" wrote in message
om...
On Sat, 1 Jul 2006 20:22:56 +0100, "George Dishman"
wrote:

big snip of background


... The times a

t1: time of transmission
t2: time when the signal is transponded by the craft
t3: time of reception

t3 is as recorded in the data files but since the
propagation time depends on the range, t2 and then t1
have to be calculated using the modelled location at
time t2. The transmit frequency was generally constant
through any contact period but the times are needed to
apply the ephemeris and Earth rotation Doppler effects.

...

Remember back ( in 1983 I think), it was decreed and "it is so
written" that the 133Cs maser delivers 9+ gigacycles in one second
which at once compromised both the frequency and the second. The
station clock will read today the same as 20 years ago, by comparison
with that clock. But that's not to say that it isn't running faster.
There is no way to assess whether the frequency has indeed increased,
certainly not with that method of comparison.

There is a method in theory. One could have sent a
signal in 1983 to a probe 11.5 light years away
which sent it back to Earth at the same frequency.
Neglecting Doppler efefcts, you would then have a
copy of that original frequency to compare with
the present clocks. In fact that is what your paper
assumes happened.

I did not have that in my paper, but let's agree that a transmitted
frequency will retain its same value. In the imaginary experiment you
cite, there would be a frequency difference corresponding to Hf0x23yr
as I see it either by frequency beat or Lissajou figure on a
scope(theoretically).

The curious thing is with the above, there would be a beat even
though we know the original transmitted signal had the frequency f0
(2.292 as painted on the side of the clock), and you just checked with
NIST and they assured you that your station was "dead-on" at 2.292
just like the marking. Yet you get a frequency difference that is not
Doppler. It's the cosmic effect of clocks moving up in a gravity well.
NIST has no way to keep track .

Right, that is the effect you are describing.

The frequency increase, which I put as only a hypothesis, is "proved"
in my theory: ...

No it isn't because in reality the signal was sent to
the craft only a few hours earlier, not in 1987.

As you say above, you "tried to 'make it happen' during
flight time and arrived at the 1/25,000 ratio" which is
the correct conclusion, this sort of simple drift doesn't
work. There is no place for an "f0" in the model and you
cannot just invent it because it suits your goal.

Yes George there has to be a place for f0 in the model. It's the only
way you can get to compare frequencies with the Pioneer. You have just
calculated the number v = 12km/s and now you need to multiply by
-1/lambda and then you need to add in the base frequency f0. You need
that in order to compare against Pioneer's f3.

Nope, they apply the speed to the Tx frequency
at time t1 as recorded in the file in the "ramp"
records.

Could you clarify this mathematically, applying the speed to the TX
frequency?

It's really simple and to me entirely obvious. You
seem to have some sort of blind spot here.

At time t1, a number which I call F_tx is written into
a file. That number is the value fed to a synthesiser
which multiplies the station reference frequency
(f_ref) to produce the transmitted signal. Assuming
they were using the 10MHz reference, the actual
transmitted frequency, which I call f_tx, was:

f_tx = F_tx * f_ref / 1e7

Since all of this happened at time t1, we can write
this in parameterised form as:

f_tx(t1) = F_tx(t1) * f_ref(t1) / 1e7

Note the key part: f_ref is the value at that time, not
what it was in 1987.

If your f0 is the 'true' frequency of the station
reference at time t1 and f87 is the same as it
was in 1987 then another way to look at it is:

f0 / f87 = 1 + H * ( t1 - 1987)

where

f0 = f_ref(t1)
f87 = f_ref(1987)

and H is a clock frequency drift rate equivalent
in some way to the Hubble Constant.

You mean adjusting the model? How specifically? You have a
way to modernize the coefficients in the model?

No, I mean the hardware allows no alternative to
using the CURRENT frequency of the station
reference at any time, not what it was years
earlier. I consider that completely obvious and
you say something similar later.

Those are a comparison of the actual
transmitted frequency with the station clock at
time t1, not what it was in 1987.

Can this actual transmitted frequency be brought into the model as a
numeric factor? Why would it not be the standard 2.292?

The numerical factor stored in the data file is the
ratio of the actual transmitted frequency to the
frequency of the station reference at the time
of transmission. How could it be anything else?

Or is there a
wasy to transfuse it into the model even without knowing its value? If
you had reason to think it might be different, then some new questions
need to be raised.

There is no way to use the frequency as it was
some time earlier which is the unknown quantity.

The chart comes from "whole frequency" comparison.

I know, but the hardware doesn't have any way to
reproduce the clock signal as it was years earlier.
Only the current clock can be used.

Well of course everything is done currently in the station ...

Exactly, that is the obvious point.

... and always
rechecked for conformance to 2.292Ghz. The model must likewise have
that same 2.292 imprimatur. And it must use it some way to produce the
total frequency fmod = f0 - vf0/c,

No, replace your "f0" by "f87(1 +h(t-1987)) because
"of course everything is done currently in the station".

of which the 2d term is
negligible. f0 is added ...

Nope, all the processes are multiplicative (other
than the heterodyne and that factors out by the
associative law).

... to the converted velocity stream in the model
(f87 in my diagram).

But meanwhile the real clock frequencies have theoretically moved on
up by f0Ht with no one able to prove otherwise, right from clocks that
are currently certified as 2.292. NIST nor any one else can decide.

Yes, so you have to use the "moved on" value, in
other words your f0 is defined as:

f0 / f87 = 1 + H * ( t1 - 1987)

The declaration of 133Cs being 9,192,631,770 cycles to equal 1
second, with c *declared* as 299,792,458 m/s merely locks the
wavelength of the Cesium transition to 0.0326xxx m.

Don't bring up that
little Doppler effect; it only confuses the issue. For me, the two
doppler beats deltaf can be identical.

Doppler is a separate issue and I think we both
understand that, what you are missing is that
only the clock rate at time t1 versus t3 matters.

But time t1 and t3 are with the same clock ...

Yes that the point I'm trying to get across, the clock
at t1 is NOT at the frequency f87 which is your mistake.

... and you are forgetting that
it is comparison with the model's frequency that makes the anomaly.

The model's prediction for the frequency received
at time t3 is the numerical value recorded as at
time t1 as F_tx(t1) multiplied by the various
Doppler factors.

George