On Monday, September 6, 2021 at 2:37:50 AM UTC-5, Richard Hertz wrote:
> On Monday, September 6, 2021 at 4:26:26 AM UTC-3, prokaryotic.c...@gmail.com wrote:
> > On Monday, September 6, 2021 at 1:39:52 AM UTC-5, Richard Hertz wrote:
> >
> > > Do you remember old electric wall clocks from the '60s and '70s, clocked by AC line frequency? It was so
> > > inaccurate by then, losing seconds in a day. Today, line frequencies at the electric grid are locked with local
> > > rubidium clocks which even have a GPS receiver incorporated (if you pay for it), so I bet that its accuracy now
> > > is better than any battery powered alarm watch that you use to wake up.
> > What third-world country did you grow up in?
> >
> > Even in the 50's, although the mains frequency in the US might deviate
> > as much as 1% from the nominal 60 Hz under conditions of exceptionally
> > heavy load, the power was regulated so that over the long term, clocks
> > would always show the correct time to within a few seconds.
> >
> > I learned that in elementary school in an educational film. I think that
> > Don Herbert also mentioned that fact in Watch Mr. Wizard. Unfortunately,
> > I couldn't locate the episode that I was thinking about on YouTube.
> You didn't understand what I wrote. A difference of 1% 50 years ago vs. 1 part/trillion parts is
> what happened since the '70s. The power grid frequency is now locked to atomic clock frequencies.

You don't understand what *** YOU *** wrote. Your language clearly
implied that in the 60's and 70's, that the inaccuracies were cumulative:
"Do you remember old electric wall clocks from the '60s and '70s ,
clocked by AC line frequency? It was so inaccurate by then , losing
seconds in a day ."

On the other hand, even today, the power grid is *** NOT *** locked
to atomic clock frequencies. "Today, AC-power network operators
regulate the daily average frequency so that clocks stay within a few
seconds of correct time."
https://en.wikipedia.org/wiki/Utility_frequency

Den 06.09.2021 01:15, skrev Richard Hertz:
> On Sunday, September 5, 2021 at 5:47:02 PM UTC-3, Paul B. Andersen wrote:
>
> <snip>
>
>> So I was right. It is a "similar system" in the Galileo
>> satellites that make it possible to tune the frequency after launch.
>
> Yes, and it's done periodically on per-satellite basis, in order to sync Earth systems
> with the Galileo's constellation.
>
> > And the satellite clock frequency is adjusted
>> by the factor -4.7219E-10 to align it to the GST (Galileo System Time).
>
> NO. Read the point "3.2. Satellite Clock Corrections" from the document (year 2021)
> "Galileo L10 Satellites: Orbit, Clock and Signal-in-Space Performance Analysis"
> that is at the link I provided in my post.
>
> <snip>
>
>> Galileo L10 Satellites: Orbit, Clock and Signal-in-Space Performance Analysis
>> https://www.mdpi.com/1424-8220/21/5/1695/pdf, see page 6, 2.2.2 equation (3)

Galileo Interface Specification:
https://www.gsc-europa.eu/sites/default/files/sites/all/files/Galileo_OS_SIS_ICD_v2.0.pdf
page 47, equation (13)

>>
>> Compare it to GPS Interface Specification:
>> https://www.gps.gov/technical/icwg/IS-GPS-200M.pdf
>> see page 97, 20.3.3.3.3.1 equation (2)
>>
>> You will see that there are two identical equations.
>> So what are they?
>
> Both documents are from 2021. Even the old spec (1993) IS-GPS-200C has the same
> formula, and I'm almost sure that older release A and B have the same (can't get them).

Yes, of course.
This equation has always been the same, and it is the same
for GPS and Galileo because the SV clock time is corrected
in the receiver in exactly the same way.

>
>> Both GPS and Galileo satellite clocks in orbit are corrected
>> for the relativistic effect by the factors -4.4647E-10 and
>> -4.7219E-10 respectively. But due to the finite precision of
>> clocks, they will inevitably drift off sync with time.
>
> NO, Paul. GPS does on pre-launch. Galileo doesn't. They pass the
> "correction" problem, with a relativistic part, to receiver manufacturers.
>
> <snip>

You are missing the point.
The point is that a SV clock, whether its frequency is adjusted
before or after launch, or not at all, is never exactly correct,
it will be offset from system time System Time.
This offset must be corrected in the receiver.

And I have explained below how this is done:

unsnip central point:
Monitoring stations on the ground measure the clock errors,
and upload correction parameters to the satellites, which will
transmit them to the receivers. The receivers can then correct
the time when the signal was transmitted with these parameters.

>
>> The equation is: (SV = space vehicle - satellite)
>>
>> δt_SV = a_f0 + a_f1(t-t_oc) + a_f2(t-t_oc)² + δt_rel
>>
>> where t_OC is the time when the parameters were measured,
>> and t is the time when they were transmitted.
>>
>> The correctional parameters received from the SV are:
>> a_f0 - the clock offset (error) at the time t_oc
>> a_f1 - the rate (frequency) error at the time t_oc
>> a_f2 - the rate of change of the frequency at the time t_oc
>>
>> The fourth parameter δt_rel is a relativistic correction which probably normally will be negligible.
>> If the orbit of the satellite is circular then δt_rel = 0.
>> But due to perturbations from the Sun and Moon, the orbit will tend to be elliptical with time (eccentricity > 0),
>> which means that the speed of the satellite will vary during the orbit, and the frequency of the satellite
>> clock (as observed from the ground) will also change during the orbit.
>
>> δt_rel = const⋅sin(E) where E is the phase of the orbit.

Note this:
>>
>> Note that if the satellite frequency was not corrected, then a_f0 would grow by ≈ 38 μS/day, and since this
>> parameter is coded with a limited number of bits, it would inevitably overflow after some time.
>> So the relativistic correction of the SV clock frequencyis necessary.
>>
>> Note how similar GPS and Galileo are.
>> It is no coincident that the time correction equation and the time correction parameters are equal, and even
>> have the same names!
>
> NO, they are not! This is european technology against US technology.
> Both would prefer death before they reach agreement. No part want this.
> I've seen it hundred of times in decades (telecom networks, TV standards, military standards, etc.).
>
> GPS and Galileo are on their own class. Compatible? YES, through complex adaptations.
> The war goes to the extent that the use of Galileo system is forbidden within the US, as well as GLONASS.

Nonsense!

--
Paul

https://paulba.no/

Den 05.09.2021 23:01, skrev Prokaryotic Capase Homolog:
> On Sunday, September 5, 2021 at 3:47:02 PM UTC-5, Paul B. Andersen wrote:
>> Den 05.09.2021 08:50, skrev Richard Hertz:
>>>
>>> https://link.springer.com/content/pdf/10.1007%2FBF03404697.pdf
>>
>> Thanks for a very interesting paper!
>>> uses 6 pages to talk about the impact of SR/GR with formulae that
>>> can be found on almost any paper or book dealing this topic, being
>>> all of them based on theoretical developments from a theory, with
>>> some numbers fed into to produce the same results written all over
>>> for decades, WONDERING WHY Galileo GNSS satellites don't include
>>> such corrections.
>> And this paper answers the question we have been wondering about:
>> "Is the satellite clock corrected for relativistic effects?"
>>
>> Let's quote from the paper:
>> "At the time of writing, the frequency of the Galileo
>> satellite clocks is not corrected to compensate
>> the relativistic shift, unlike GPS. Nevertheless,
>> the capability to adjust the satellite clock frequency,
>> e.g. in order to align it to GST, is available. Galileo
>> onboard clocks will be periodically aligned to GST both
>> and phase and frequency to maintain these parameters
>> within the limits acceptable from the system operations
>> point of view. Furthermore, as an experiment, the relativistic
>> frequency shift of GSAT0102 (PRN E12) was corrected in orbit,
>> after launch."
>
> Well, this is INTERESTING. I suppose that I'll have to take back
> some of what I just posted a few seconds ago... :-)
>

Open this link:
https://www.mdpi.com/1424-8220/21/5/1695/pdf
see fig.8 page 11.

The clock offset (a_f1) will be the dominating factor
in the clock correction.

The GSAT0222/E13 clock correction has been almost constant
≈ -500 μS since April 2019 to January 2021,
The clock has been ≈500 μS ahead of System time all the time.

The GSAT0220/E33 clock correction has been almost constant
≈ +380 μS since February 2019 to January 2021,
The clock has been ≈380 μS behind System time all the time.

The GSAT0221/E15 clock correction has decreased from
≈ +900 μS in February 2019 to ≈ 820 μS in January 2021.
That's an average rate error of the clock ≈ 0.1 μS/day

The GSAT0219/E36 clock correction has decreased from
≈ +750 μS in February 2019 to ≈ 420 μS in January 2021.
That's an average rate error of the clock ≈ 0.5 μS/day

So the clock frequencies must have been corrected by
the factor -4.7219E-10.

Or am I missing something?

--
Paul

https://paulba.no/

On Monday, September 6, 2021 at 5:23:34 AM UTC-5, Paul B. Andersen wrote:
> Den 05.09.2021 23:01, skrev Prokaryotic Capase Homolog:
> > On Sunday, September 5, 2021 at 3:47:02 PM UTC-5, Paul B. Andersen wrote:
> >> Den 05.09.2021 08:50, skrev Richard Hertz:
> >>>
> >>> https://link.springer.com/content/pdf/10.1007%2FBF03404697.pdf
> >>
> >> Thanks for a very interesting paper!
> >>> uses 6 pages to talk about the impact of SR/GR with formulae that
> >>> can be found on almost any paper or book dealing this topic, being
> >>> all of them based on theoretical developments from a theory, with
> >>> some numbers fed into to produce the same results written all over
> >>> for decades, WONDERING WHY Galileo GNSS satellites don't include
> >>> such corrections.
> >> And this paper answers the question we have been wondering about:
> >> "Is the satellite clock corrected for relativistic effects?"
> >>
> >> Let's quote from the paper:
> >> "At the time of writing, the frequency of the Galileo
> >> satellite clocks is not corrected to compensate
> >> the relativistic shift, unlike GPS. Nevertheless,
> >> the capability to adjust the satellite clock frequency,
> >> e.g. in order to align it to GST, is available. Galileo
> >> onboard clocks will be periodically aligned to GST both
> >> and phase and frequency to maintain these parameters
> >> within the limits acceptable from the system operations
> >> point of view. Furthermore, as an experiment, the relativistic
> >> frequency shift of GSAT0102 (PRN E12) was corrected in orbit,
> >> after launch."
> >
> > Well, this is INTERESTING. I suppose that I'll have to take back
> > some of what I just posted a few seconds ago... :-)
> >
> Open this link:
> https://www.mdpi.com/1424-8220/21/5/1695/pdf
> see fig.8 page 11.
>
> The clock offset (a_f1) will be the dominating factor
> in the clock correction.
>
> The GSAT0222/E13 clock correction has been almost constant
> ≈ -500 μS since April 2019 to January 2021,
> The clock has been ≈500 μS ahead of System time all the time..
>
> The GSAT0220/E33 clock correction has been almost constant
> ≈ +380 μS since February 2019 to January 2021,
> The clock has been ≈380 μS behind System time all the time.
>
> The GSAT0221/E15 clock correction has decreased from
> ≈ +900 μS in February 2019 to ≈ 820 μS in January 2021.
> That's an average rate error of the clock ≈ 0.1 μS/day
>
> The GSAT0219/E36 clock correction has decreased from
> ≈ +750 μS in February 2019 to ≈ 420 μS in January 2021.
> That's an average rate error of the clock ≈ 0.5 μS/day
>
> So the clock frequencies must have been corrected by
> the factor -4.7219E-10.
>
> Or am I missing something?

There's *nothing* like looking at the real data!!!
*** YOU WIN!!! *** :-)

....and thanks for sending me a copy of the paper! With the
Labor Day holiday here in the United States, the university
library is closed for the weekend, and I would have to wait
until next weekend to have a chance to access it!

On Monday, 6 September 2021 at 12:23:34 UTC+2, Paul B. Andersen wrote:

> So the clock frequencies must have been corrected by
> the factor -4.7219E-10.

Instead keeping "proper time" idiocy we're allegedly
FORCED to.

On Monday, 6 September 2021 at 13:05:39 UTC+2, Maciej Wozniak wrote:
> On Monday, 6 September 2021 at 12:23:34 UTC+2, Paul B. Andersen wrote:
>
> > So the clock frequencies must have been corrected by
> > the factor -4.7219E-10.
> Instead keeping "proper time" idiocy we're allegedly
> FORCED to.

While looking ingenious on a paper and in gedankens -
it's completely unusable for the real measurements. Too
bad for The Shit.

On Sunday, September 5, 2021 at 5:31:25 PM UTC-7, Python wrote:
> Prokaryotic Capase Homolog wrote:
> > On Sunday, September 5, 2021 at 6:15:26 PM UTC-5, Richard Hertz wrote:
> >
> >> The war goes to the extent that the use of Galileo system is forbidden
> >> within the US, as well as GLONASS.
> >
> > Where in hell did did you get THAT fantasy?
> >
> > Multi-constellation GNSS receivers are widely available in the US.
> > The most common combination that I see is GPS/GLONASS, but if
> > you are willing to pay the money, you can get multi-constellation,
> > multi-wavelength receivers covering ALL of the worldwide/regional
> > systems plus regional SBAS.
> I'm quite astonished by how far some retired (or wannabe) engineers
> are able to spit nonsense when it comes to make up stuff about
> Relativity.

Einstein Derangement Syndrome :-)

--
Jan

On Monday, 6 September 2021 at 14:45:47 UTC+2, JanPB wrote:
> On Sunday, September 5, 2021 at 5:31:25 PM UTC-7, Python wrote:
> > Prokaryotic Capase Homolog wrote:
> > > On Sunday, September 5, 2021 at 6:15:26 PM UTC-5, Richard Hertz wrote:
> > >
> > >> The war goes to the extent that the use of Galileo system is forbidden
> > >> within the US, as well as GLONASS.
> > >
> > > Where in hell did did you get THAT fantasy?
> > >
> > > Multi-constellation GNSS receivers are widely available in the US.
> > > The most common combination that I see is GPS/GLONASS, but if
> > > you are willing to pay the money, you can get multi-constellation,
> > > multi-wavelength receivers covering ALL of the worldwide/regional
> > > systems plus regional SBAS.
> > I'm quite astonished by how far some retired (or wannabe) engineers
> > are able to spit nonsense when it comes to make up stuff about
> > Relativity.
> Einstein Derangement Syndrome :-)

It's not at all that this moronic bullshit violates common sense,
basic definitions and the oldest mathematics existing and
isn't even internallly consistent. Nonononononono! A syndrome
combined with obvious antisemitism.

On 9/5/21 3:53 PM, Prokaryotic Capase Homolog wrote:
> wrote: | The GALILEO system is a European satellite navigation
> system which at | present has two satellites in orbit. Specifications
> for this system call for | all relativistic effects to be the
> responsibility of the receiver. No frequency | offsets will be
> applied in hardware to the orbiting clocks, which will | necessarily
> run faster than TT by a few parts in 10^10. It will be up to |
> software in the receiver to correct the transmitted time ticks for
> this large | time drift. https://tf.nist.gov/general/pdf/2444.pdf

That was 2009. Since then Galileo has applied relativistic corrections
to the clocks in the satellites. Each satellite clock is steered to
Galileo system time; the circular-obit correction is applied in the
satellite, while corrections for orbital eccentricity are left to the
receivers.
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwix_6-ry-ryAhXHZc0KHY-pAQUQFnoECAMQAQ&url=https%3A%2F%2Fwww.opsjournal.org%2FDocumentLibrary%2FUploads%2FMudrak_article_final.pdf&usg=AOvVaw2LnJlILRaQBCzh8wXJasav

Tom Roberts

On 9/5/21 4:01 PM, Prokaryotic Capase Homolog wrote:
> On Sunday, September 5, 2021 at 3:47:02 PM UTC-5, Paul B. Andersen
> wrote:
>> Den 05.09.2021 08:50, skrev Richard Hertz:
>>> https://link.springer.com/content/pdf/10.1007%2FBF03404697.pdf
>>
> Since the paper is behind a paywall, I'll need to pay a trip to the
> university library before I can access it.

Here is a link without paywall:

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwix_6-ry-ryAhXHZc0KHY-pAQUQFnoECAMQAQ&url=https%3A%2F%2Fwww.opsjournal.org%2FDocumentLibrary%2FUploads%2FMudrak_article_final.pdf&usg=AOvVaw2LnJlILRaQBCzh8wXJasav

Galileo has indeed changed to applying SOME relativistic corrections to
the satellite clocks.

Tom Roberts

On 2021-09-06 00:31:36 +0000, Python said:

> Prokaryotic Capase Homolog wrote:
>> On Sunday, September 5, 2021 at 6:15:26 PM UTC-5, Richard Hertz wrote:
>>
>>> The war goes to the extent that the use of Galileo system is forbidden
>>> within the US, as well as GLONASS.
>>
>> Where in hell did did you get THAT fantasy?
>>
>> Multi-constellation GNSS receivers are widely available in the US.
>> The most common combination that I see is GPS/GLONASS, but if
>> you are willing to pay the money, you can get multi-constellation,
>> multi-wavelength receivers covering ALL of the worldwide/regional
>> systems plus regional SBAS.
>
> I'm quite astonished by how far some retired (or wannabe) engineers
> are able to spit nonsense when it comes to make up stuff about
> Relativity.

You'll find that they (or maybe different engineers) are just as able
to spit nonsense about natural selection.

--
Athel -- French and British, living mainly in England until 1987.

On 9/6/21 3:03 AM, Prokaryotic Capase Homolog wrote:
> [... U.S. power grid]

Certainly by the mid 1960s the grid operators would deliberately vary
the frequency just before midnight to have the correct total number of
cycles each day. So clocks would not accumulate errors. I believe this
is much older than that.

Tom Roberts

On 2021-09-06 15:11:55 +0000, Tom Roberts said:

> On 9/6/21 3:03 AM, Prokaryotic Capase Homolog wrote:
>> [... U.S. power grid]
>
> Certainly by the mid 1960s the grid operators would deliberately vary
> the frequency just before midnight to have the correct total number of
> cycles each day. So clocks would not accumulate errors. I believe this
> is much older than that.

In the 1970s, during a period of serious labour unrest in the UK the
authorities lowered the voltage by slowing down the generators. The
change in voltage was hardly noticeable but the change in frequency
caused problems with clocks.

--
Athel -- French and British, living mainly in England until 1987.

On Monday, September 6, 2021 at 9:54:10 AM UTC-5, tjrob137 wrote:
> On 9/5/21 3:53 PM, Prokaryotic Capase Homolog wrote:
> > wrote: | The GALILEO system is a European satellite navigation
> > system which at | present has two satellites in orbit. Specifications
> > for this system call for | all relativistic effects to be the
> > responsibility of the receiver. No frequency | offsets will be
> > applied in hardware to the orbiting clocks, which will | necessarily
> > run faster than TT by a few parts in 10^10. It will be up to |
> > software in the receiver to correct the transmitted time ticks for
> > this large | time drift. https://tf.nist.gov/general/pdf/2444.pdf
> That was 2009. Since then Galileo has applied relativistic corrections
> to the clocks in the satellites. Each satellite clock is steered to
> Galileo system time; the circular-obit correction is applied in the
> satellite, while corrections for orbital eccentricity are left to the
> receivers.
> https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwix_6-ry-ryAhXHZc0KHY-pAQUQFnoECAMQAQ&url=https%3A%2F%2Fwww.opsjournal.org%2FDocumentLibrary%2FUploads%2FMudrak_article_final.pdf&usg=AOvVaw2LnJlILRaQBCzh8wXJasav
Thanks! That makes a lot more sense than me.

Alternatively, I would have been OK had the architects of the Galileo
system allocated an extra four bits to the clock bias correction
coefficient (35 versus 31 bits, twos complement, scale factor 2^-34 s),
because then the time between forced clock resets would have been
longer than any reasonable expected lifetime of an individual satellite.

Forced resets are a fact of life in computer systems, but one does
not *design* for them to have to happen.

On 9/6/2021 2:39 AM, Richard Hertz wrote:

>
> Do you remember old electric wall clocks from the '60s and '70s, clocked by AC line frequency? It was so
> inaccurate by then, losing seconds in a day. Today, line frequencies at the electric grid are locked with local
> rubidium clocks which even have a GPS receiver incorporated (if you pay for it), so I bet that its accuracy now
> is better than any battery powered alarm watch that you use to wake up.
>

No, I don't remember that. Starting rather early on the electric
company consortiums who controlled the grids in the US (3 of them) would
keep a running count of 60 Hz cycles during a 24 hour day and speed
things up or slow things down specifically to get as close to 86,400*60
cycles in 24 hours as possible. Clocks running from the grid were the
most accurate one the typical consumer usually had. Even some early
computer systems (PDP-11) had options to run its internal clock off the
power source it was connected to, or an internal crystal source.

On 9/6/2021 3:37 AM, Richard Hertz wrote:
> On Monday, September 6, 2021 at 4:26:26 AM UTC-3, prokaryotic.c...@gmail.com wrote:
>> On Monday, September 6, 2021 at 1:39:52 AM UTC-5, Richard Hertz wrote:
>>
>>> Do you remember old electric wall clocks from the '60s and '70s, clocked by AC line frequency? It was so
>>> inaccurate by then, losing seconds in a day. Today, line frequencies at the electric grid are locked with local
>>> rubidium clocks which even have a GPS receiver incorporated (if you pay for it), so I bet that its accuracy now
>>> is better than any battery powered alarm watch that you use to wake up.
>> What third-world country did you grow up in?
>>
>> Even in the 50's, although the mains frequency in the US might deviate
>> as much as 1% from the nominal 60 Hz under conditions of exceptionally
>> heavy load, the power was regulated so that over the long term, clocks
>> would always show the correct time to within a few seconds.
>>
>> I learned that in elementary school in an educational film. I think that
>> Don Herbert also mentioned that fact in Watch Mr. Wizard. Unfortunately,
>> I couldn't locate the episode that I was thinking about on YouTube.
>
> You didn't understand what I wrote. A difference of 1% 50 years ago vs. 1 part/trillion parts is
> what happened since the '70s. The power grid frequency is now locked to atomic clock frequencies.
>

No, what he wrote was that the frequency may be up to 1% off during the
day, but they'd adjust the frequency to keep it accurate to what the
state of the art time source was at the time over 24 hours. I remember
what Tom wrote, the adjustment was typically made around midnight.

On Monday, September 6, 2021 at 10:45:52 AM UTC-5, Prokaryotic Capase Homolog wrote:

> Thanks! That makes a lot more sense than me.
>
> Alternatively, I would have been OK had the architects of the Galileo
> system allocated an extra four bits to the clock bias correction
> coefficient (35 versus 31 bits, twos complement, scale factor 2^-34 s),

Three extra bits should be sufficient. 31 bits twos complement would
allow +- 1/16 second adjustment. Divide by 38 microseconds/day
gives 4.5 years between forced resets.

> because then the time between forced clock resets would have been
> longer than any reasonable expected lifetime of an individual satellite.
>
> Forced resets are a fact of life in computer systems, but one does
> not *design* for them to have to happen.

On Monday, September 6, 2021 at 11:57:43 AM UTC-3, tjrob137 wrote:

<snip>

> Here is a link without paywall:
>
> https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwix_6-ry-ryAhXHZc0KHY-pAQUQFnoECAMQAQ&url=https%3A%2F%2Fwww.opsjournal.org%2FDocumentLibrary%2FUploads%2FMudrak_article_final.pdf&usg=AOvVaw2LnJlILRaQBCzh8wXJasav
>
> Galileo has indeed changed to applying SOME relativistic corrections to the satellite clocks.

Roberts, that's not the link to the original 2015 paper from Mudrak (which I downloaded last Saturday), but is
an analysis over Mudrak paper and consequences, probably from the same year 2015.

I've tried to find a free download link, but I wasn't able.

The equations Mudrak used are:

Δf/f = −μ/(c².Rs) + μ/(c².Re) - J2 . μ/(c².Re) , for gravitational shift.

Δf/f = −Vs²/(2.c²) + (a.Ωe)²/(2.c²) , for SR time dilation.

where

μ = G.ME = 3.986004418×10^14 m³/s²
c = 299792458 m/s
Rs = 26936715 m (Galileo satellite orbit radius)
Re = 6378136.55 m (Earth radius)
J2 = 0.0010826267 (Oblate Earth gravity coefficient)
Vs = 3669.6 m/s (Galileo satellite average velocity)
a = 63.83678 m/s (Undisclosed coefficient)
Ωe = 7.2921151467 rad/s (mean angular rotation rate of the Earth)

When applied into the formulae, it gives:

Δf/f(Galileo Total) = 5.3146E-10 -7.37090E-11 , and this produces a daily time drift

Δt(Galileo Total)/day = 47.1982 μsec - 6.3685 μsec = 40.8298 μsec

If GPS coefficients are applied:

Rs = 26936715 m (GPS satellite orbit radius)
Vs = 3669.6 m/s (GPS satellite average velocity)

it gives

Δt(GPS Total)/day = 45.9177 μsec - 7.2141 μsec = 38.7036 μsec

Still, the "a" factor is unexplained on the paper, and I don't understand its origin. If you eliminate the
2nd. order Ωe part, a difference of less than 1.5% occurs in the SR formula, which reduces to a first
degree approximation of Lorentz transform:

Δt/t = −Vs²/(2.c²)

Excerpt from 2015 Mudrak paper:
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4. Relativistic Corrections Implemented in Galileo

The relativistic effects analysed so far would introduce significant errors in the ranging and consequently
positioning accuracies of a GNSS system, unless they are carefully taken into account in the system design
and user algorithms.
In GPS and GLONASS the systematic relativistic net effect (i.e. the combination of the gravitational
frequency shift and the time dilation due to the orbital motion of the satellite) is compensated by adequately
offsetting the onboard clocks before launch, while time-varying effects are corrected at user receiver level.

It is anticipated that THIS IS NOT the approach in the Galileo system. As explained in detail in the following
paragraphs, the correction of relativistic errors is performed at user receiver level, on the basis of information
broadcasted through the navigation message.
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

So, by year 2015, Mudrak, De Simone, and Lisi were writing the paper "Relativistic Corrections in the European
GNSS Galileo" and were critics of the decision about not to implement a solution of pre-tuning like in GPS.

As far as I could find, this critic was ignored and Galileo doesn't use fixed pre-launch corrections, and leave
the compensation to the manufacturers of Galileo receivers (for industrial, scientific or commercial use).

Do the manufacturers implement such corrections? It's what really matter to find out, because in the GPS world
the truth about this is obscured by Terabytes of data since 1985 (and still some data is confidential). It can be
to protect IP or to hide the truth.

I have a question:

Being GR correction the largest value, and due to the alleged fact that time shrinks as elevates from ground, I
wonder what effect gravity causes on hyperfine transitions of rubidium and cesium atoms.

And yet more: How come do you believe that such a profound quantum impact of gravity was anticipated by Einstein
in 1915, with his "theory about how to displace Newton with this non-linear stuff".

Even more, how come the brightest minds in Europe, working on Quantum Mechanics (1913-1930) didn't see it
coming, specially the tortured genius Dirac when introduced relativity into Schrodinger-Born theory?

Is that nobody could think about what happened in QM if one elevated an atom 100m or 10,000m. Were they
blind to the allegation of gravitational time shift, when trying to match QM with spectral lines of H atoms?

If it was true, they would have found the Holy Grail of unification between gravity and the quantum world.

Am I so far from the truth? So confused? I DON'T THINK SO, not even for an instant.

And this is why I firmly believe that relativity applied to the REAL world is just a pile of crap.

Op 06-sep.-2021 om 20:43 schreef Richard Hertz:

[snot]

>
> And this is why I firmly believe that relativity applied to the REAL
> world is just a pile of crap.
>

Yeah right. Next time when you take a plane, ask for one
that uses a special GPS without relativity corrections.

Dirk Vdm

On Monday, September 6, 2021 at 11:43:03 AM UTC-7, Richard Hertz wrote:
>
> The equations Mudrak used are:
>
> Δf/f = −μ/(c².Rs) + μ/(c².Re) - J2 . μ/(c².Re) , for gravitational shift.
>
> Δf/f = −Vs²/(2.c²) + (a.Ωe)²/(2.c²) , for SR time dilation.
>

Both equations are GR, imbecile. There is no "SR". Both fall out from Schwarzschild solution, I have told you that long ago. It flew right over your bald spot.

> Do the manufacturers implement such corrections?

Of course, odious crank.

> It's what really matter to find out, because in the GPS world
> the truth about this is obscured by Terabytes of data since 1985 (and still some data is confidential). It can be
> to protect IP or to hide the truth.
>

You are full of shit, all the info is im many documents. You need to stop lying.

> I have a question:
>
> Being GR correction the largest value, and due to the alleged fact that time shrinks as elevates from ground, I
> wonder what effect gravity causes on hyperfine transitions of rubidium and cesium atoms.
>

It is called "gravitational time dilation", it falls out of the Schwarzschild solution and it is verified by hundreds of experiments, look up Pound-Rebka class of experiments, crass ignoramus.

> Am I so far from the truth? So confused?

Nah, you are just a crank piece of shit.

On Monday, September 6, 2021 at 4:34:25 PM UTC-3, Dono. wrote:
> On Monday, September 6, 2021 at 11:43:03 AM UTC-7, Richard Hertz wrote:
> >
> > The equations Mudrak used are:
> >
> > Δf/f = −μ/(c².Rs) + μ/(c².Re) - J2 . μ/(c².Re) , for gravitational shift.
> >
> > Δf/f = −Vs²/(2.c²) + (a.Ωe)²/(2.c²) , for SR time dilation.
> >
> Both equations are GR, imbecile. There is no "SR". Both fall out from Schwarzschild solution, I have told you that long ago. It flew right over your bald spot.
> > Do the manufacturers implement such corrections?
> Of course, odious crank.
> > It's what really matter to find out, because in the GPS world
> > the truth about this is obscured by Terabytes of data since 1985 (and still some data is confidential). It can be
> > to protect IP or to hide the truth.
> >
> You are full of shit, all the info is im many documents. You need to stop lying.
> > I have a question:
> >
> > Being GR correction the largest value, and due to the alleged fact that time shrinks as elevates from ground, I
> > wonder what effect gravity causes on hyperfine transitions of rubidium and cesium atoms.
> >
> It is called "gravitational time dilation", it falls out of the Schwarzschild solution and it is verified by hundreds of experiments, look up Pound-Rebka class of experiments, crass ignoramus.
> > Am I so far from the truth? So confused?
> Nah, you are just a crank piece of shit.

Read the Mudrak 2015 paper, if you can afford the 14.99 USD it cost. Miserable rat.
I didn't derived anything. I just used Mudrak et all. equations being there.. Also, the
paper is a critic to a decision about to not pre-tune clocks prior lunch in Galileo.

Read the paper and shut the fuck up, cretin!

On Monday, September 6, 2021 at 12:43:37 PM UTC-7, Richard Hertz wrote:

> I didn't derived anything.

Of course you didn't, you are just a sad sack imbecile who cannot read.

Dirk Van de moortel wrote:
> Op 06-sep.-2021 om 20:43 schreef Richard Hertz:
>
> [snot]
>
>>
>> And this is why I firmly believe that relativity applied to the REAL
>> world is just a pile of crap.
>>
>
> Yeah right. Next time when you take a plane, ask for one
> that uses a special GPS without relativity corrections.
>
> Dirk Vdm

Good one!

On Monday, 6 September 2021 at 17:12:02 UTC+2, tjrob137 wrote:
> On 9/6/21 3:03 AM, Prokaryotic Capase Homolog wrote:
> > [... U.S. power grid]
>
> Certainly by the mid 1960s the grid operators

were FORCED!!! To THE BEST WAY!!!

On Tuesday, 7 September 2021 at 01:27:40 UTC+2, Python wrote:
> Dirk Van de moortel wrote:
> > Op 06-sep.-2021 om 20:43 schreef Richard Hertz:
> >
> > [snot]
> >
> >>
> >> And this is why I firmly believe that relativity applied to the REAL
> >> world is just a pile of crap.
> >>
> >
> > Yeah right. Next time when you take a plane, ask for one
> > that uses a special GPS without relativity corrections.
> >
> > Dirk Vdm
> Good one!

Next time when you take a plane, poor halfbrain, ask for
one that uses "elapsed proper time" instead TAI.