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From: "Paul.B.Andersen" <relativity@paulba.no>
Newsgroups: sci.physics.relativity
Subject: Re: Electron size, shape and spin.Confusion and conflicts with
 Einstein's 1905 SR.
Date: Thu, 20 Mar 2025 22:24:30 +0100
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Den 19.03.2025 22:38, skrev rhertz:
> On Wed, 19 Mar 2025 19:53:36 +0000, Paul.B.Andersen wrote:
> 
> <snip all the repeated crap. I left this part as a sample of your
> idiocy>
> 
>> You claim to be an engineer.
>> When an engineer by practical measurement finds that the SV clock
>> runs too fast by Δf/f = 4.425e-10, wouldn't he correct the problem
>> by adjusting the clock down by  Δf/f = - 4.425e-10 ?
>>
>> What would the engineer Richard Hertz do?
>> Claim that the measurements must be wrong because he did't
>> get the expected result, and give up the GPS project?
> 
> <snip>
> 
> You are an engineer too.
> 
> The other imbecile wrote that BOTH Cs clocks are locally running at
> 10,230,000.000000 Hz. But THIS IS NOT WHAT RELATIVISTS CLAIM.

No, that was what YOU said.
I was responding to your scenario:

Richard Hertz wrote:
|- Suppose that the time of the onboard Cs clock is measured
|   by accumulating  counts of cycles of the 10.23 Mhz master
|   TCXO clock. This, to accumulate  pulses with a period of
|   97.7517 nsec during 86,400 sec, requires an  onboard
|   digital counter displaying 883,872,000,000 counts (12 digits).
|   Such  data,  at the end of the 24 hours period MUST be sent
|   down to Earth station,  where  a twin Cs clock is also counting
|   pulses in sync with the onboard Cs clock.
|   Will a comparison differ in 389 LOST PULSES (38 usec)?

You say that the reference frequency is 10.23 Mhz, but in
a GPS SV clock the reference frequency is: 10.2299999954326 MHz

So the clock you describe is an ordinary clock running
at the rate defined by SI.
After 86,400 seconds the clock will show 86,400 seconds,
and your counter would have counted 86400*10.23e6 = 883872000000 cycles,
just as you correctly states.

An ordinary SI-clock will obviously always show 86400 seconds
when it has been running for 86400 seconds.
It doesn't matter if the clock is in a satellite, on the ground
or on the moon.

--------------------------

But let us see if we can find your missing pulses.
A "solar day" is defined as the time between each time the sun
passes the same meridian. Let us suppose that we are at one
of the two times of the year when a solar day by a clock
at Earth's geoid is measured to be 86400 seconds.

A normal clock with rate as defined by SI which is in GPS orbit
will according to GR measure a solar day to be
   86400*(1+4.4647e-10) s = 86400s + 38.575μs

Note that this means that the SV clock will be 38.575μs
more ahead of the ground clock every day.

The number of pulses from the oscillator counted by your counter
will then be  86400*(1+4.4647e-10)*10.23e6 = 883872000394 pulses.

The counter on the ground will count 86400*10.23e6 = 883872000000
pulses from the local oscillator.
So the counter in the SV will count 394 pulses more.

There are your missing counts.

-------------------------

Your blunder was that you didn't realise that a "day" measured
by the clock in the SV is 38.575μs longer that a day measured by
a clock on the ground. This is THE central point.

So when you specified that the counter should count the pulses
during 86400 seconds, you missed the pulses sent during the 38.575μs.

That's why I wrote:

"If the satellite counter is counting the cycles from the 10.23 MHz
  oscillator for 86,400 sec measured in the satellite, then:
  the satellite counter counts 883872000000 cycles"


> 
> They claim that the onboard TCXO master clock was tuned to
> 10,229,999.995430 Hz,
> with a difference of 0.00457 Hz wrt the Earth'c clock.

Right. But in your scenario you specified an uncorrected clock.

In a real GPS satellite the reference oscillator is adjusted down
by the factor (1-4.4647e-10) so it will measure the number of second
during a solar day to be (86400s + 38.575μs)*(1-4.4647e-10) = 86400s

So it will stay in sync with the ground clock.

> 
> Clock on Earth station: accumulates 883,872,000,000 pulses in 86400 sec
> (1 day).

Right.

> 
> Clock on GPS SV: accumulates 883,871,999,605 pulses in 86400 sec (1
> day).

It accumulates 883872000000 pulses in (86400s + 38.575μs) (1 day)

> 
> 
> The STUPID CLAIM OF RELATIVISTS is that the frequency L1 (1575.42 Mhz),
> which is GENERATED BY MULTIPLYING THE MASTER FREQUENCY OF 10.23 Mhz by
> EXACTLY 154 is what ALLOWS THAT SUCH CARRIER REACHES EARTH AS IF IT WAS
> GENERATED BY THE ONBOARD Cs CLOCK WORKING AT 10,229,999.995430 Hz,
> creating an L1 carrier at the GPS SV of 1,575,419,999.29622 Hz.

What are you talking about?
All the frequencies in the SV are derived from the reference
frequency 10.2299999954326 MHz.
There is no "MASTER FREQUENCY OF 10.23 Mhz" in the SV.

 From the Interface Specification Document.
------------------------------------------
The carrier frequencies for the L1 and L2 signals shall be coherently
derived from a common frequency source within the SV. The nominal
frequency of this source -- as it appears to an observer on the ground 
-- is 10.23 MHz. The SV carrier frequency and clock rates -- as they
would appear to an observer located in the SV -- are offset to
compensate for relativistic effects. The clock rates are offset by
Δf/f = -4.4647E-10, equivalent to a change in the P-code chipping
rate of 10.23 MHz offset by a Δf = -4.5674E-3 Hz. This is equal to 
10.2299999954326 MHz.

The "common frequency source within the SV" is 10.2299999954326 MHz.

The main reason for the GR correction is to make the SV clock
run synchronously to UTC.
(Or to the GPS coordinated time which is the same as UTC but for
a known offset)

> 
> When that GPS carrier reaches Earth, it has been shifted (by the
> mathemagics of relativity) to EXACTLY 1,575,412 Hz = 10,230,000 Hz x
> 154.

When the carrier reaches the receiver it is Doppler shifted
up to  Δf/f = ± 1e-7  , up to 200 times the GR correction.

The frequency of the carrier is irrelevant, the receiver
must have bandwidth enough to receive the carriers from
up to 12 satellites. The carriers are all Doppler shifted
differently.

The satellites are not separated by their frequency, but
by their PRN sequence.

The frequency that is important is the shipping rate,
since this frequency is used by the receiver to calculate
the time when the signal was transmitted.
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