Re: I Owe Einstein an Apology. Sorry Albert!

From: jahn (susysewnshow_at_yahoo.com.au)
Date: 12/13/04 

Date: Mon, 13 Dec 2004 09:49:46 -0500

"Paul B. Andersen" <paul.b.andersen@deletethishia.no> wrote in message news:cpk8u2$9l5$1@dolly.uninett.no...
> Excuse me for butting in, but I find so much
> confusion about the GPS in this thread that I
> feel the need for clearing up a few misconceptions.
>
>
> jahn wrote:
> > "The Ghost In The Machine" wrote:
> >>jahn wrote:
> >>>"The Ghost In The Machine" wrote:
> >>>> jahn wrote:
> >>>>>"The Ghost In The Machine" wrote:
> >>>>>>If the clocks are moving then SR predicts they will not remain
> >>>>>>synchronized.
>
> Clocks moving in a frame of reference will not
> generally stay synchronous in that frame,
> but they may do so in special cases.
> For example, clocks moving in a circle with
> the same speed will stay synchronous to each
> other in the "stationary frame". They will
> run slow compared to stationary clocks,
> but they will stay in sync.
> This is the case in the GPS.
> All the GPS satellite clocks stay in sync
> to each other in the ECI frame because
> they all move in circular orbits with the
> same speed and at the same gravitational potential.
>
> >>>>>SR predicts moving clocks can't keep good time?
> >>>>>I have two garden hoses an egg timer and a bag
> >>>>>of marbles that says they must be broken.
> >>>>>http://www.boulder.nist.gov/timefreq/time/commonviewgps.htm
> >>>>
> >>>>The SR correction is t' = (t-vx/c^2) * gamma .
> >>>
> >>>>The vx/c^2 is merely a reflection that the two clocks are
> >>>>communicating through speed-of-light (e.g., radio), but
> >>>>the gamma is the killer; gamma = 1/sqrt(1-v^2/c^2).
>
> The vx/c^2 is a reflection of the simultaneity of relativity.
> It has nothing to do with "communication through speed of light".
>
> >>>>It's a very slow killer, of course; the typical speed
> >>>>of a spacecraft is on the order of 9 km/s = 3 * 10^-5 c, which
> >>>>results in a gamma of about 4.5 * 10^-10. The GPS delta is
> >>>>almost exactly this: 4.46 * 10^-10. However, this is at
> >>>>best a very very rough estimate, just to give one the feel.
> >>>>It's also the wrong sign. :-)
>
> Which should tell you something. :-)
>
> It is actually quite simple to make a first order
> calculation of the rate of the GPS satellites.
>
> The relative difference in the rate of a clock in circular orbit
> compared to a clock on the surface of the Earth is according to GR
> to a first order approximation:
> (Approximation of the Schwarzchild solution)
>
> (f2 - f1)/f1 =
> (G*M/(c^2*r1) - G*M/(c^2*r2)) - (0.5*v2^2/c^2 - 0.5*v1^2/c^2)
>
> Where G = gravitational constant, M = mass of the Earth,
> r1 = radius of the Earth, r2 = radius of the orbiting clock's orbit,
> v1 = speed of the Earth clock in ECI frame,
> v2 = speed of the orbiting clock in ECI frame
>
> Since we have G*M/r1^2 = g, acceleration at Earth's surface, we have:
> (G*M/(c^2*r1) - G*M/(c^2*r2)) = (g/c^2)*r1*(1-r1/r2)
>
> Altitude of GPS satellites = 20200 km
> Orbital period = half sidereal day
> Radius of the Earth r1 = 6.37*10^6 m
> Radius of GPS orbit r2 = 26.57*10^6 m
> g = 9.81 m/s^2
>
> Inserting these numbers, we find that the rate difference
> due to gravitation is: 5.28*10^-10 (+45.6 us/day)
>
> So to the speed part:
> v1 = 40000km/(23h 56m) = 4*10^7/86160 = 464 m/s
> v2 = 2*pi*r2/(11h 28m)= 3.87*10^3 m/s (-7.1 us/day)
>
> 0.5*v2^2/c^2 = 0.83*10^-10
> 0.5*v1^2/c^2 = 1.2*10^-12
> Thus the rate difference due to the speed will be: -0.82*10^-10
>
> The combined rate difference: (5.28-0.82)*10^-10 = 4.46*10^-10
> Note that the orbiting clock runs _fast_.
>
> During one day, the difference in proper times will amount to:
> 4.46*10^-10*86400 s = 38.5*10^-6 s = 38.5 us
>
> According to:
> http://vishnu.nirvana.phys.psu.edu/mog/mog9/node9.html

*****MORE BS ******
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> the factor used in the GPS satellites is 4.4647*10^-10.
>
> >>>>An accurate clock left running for a year in a GPS orbit
> >>>>will gain about a hundredth of a second.
>
> You mean a "normal clock" not slowed down
> by the factor 4.4647*10^-10?
> Yes. It would gain ca. 14 ms a year.
>
> [..]
> >>>>(SR predicts loss
> >>>>of time, but then SR requires straight-line freespace
> >>>>travel. :-) ). Therefore, GPS clocks are "broken" by
> >>>>design, coding in this adjustment factor -- and even
> >>>>then, they have to be steered from the ground using
> >>>>synchronization signals from the TAI.
>
> 1. "GPS time" is a coordinated time where the coordinate
> system in question is stationary in the ECI-frame.
> The coordinate time is per definition such that
> clocks on the geoid will stay in sync (run at the same
> rate) with this coordinate time.
> "GPS time" is a theoretical time, derived from
> all the clocks in the system, that is all the satellite
> clocks and all the ground station clocks.
>
> 2. This "GPS time" is steered so that it (but for a number
> of whole seconds) is equal to UTC. The spec says it should
> be within 1 us, but in actual practice, it differs but
> few ns. This difference is known by the system, and each
> satellite will transmit the difference GPS-time - UTC
> so that a receiver can calculate the correct UTC.
> ftp://tycho.usno.navy.mil/pub/gps/utcgps30.dat
>
> 3. The GPS satellite clock are built to run slow
> (compared to a clock using the SI definition of a second)
> by the factor 4.4647*10^-10 prior to launch.
> In orbit, they will thus run synchronously to GPS-time.
>
> 4. The precision of the clocks is in the order of 10^-13.
> That means that they during one day may drift off sync
> by several ns - or even tens of ns. The most that can
> be tolerated is a few tens of ns.
> (Less than 100ns at the very most)
>
> 5. To correct for the latter, ground stations are monitoring
> the satellite clocks, and are uploading correctional data
> typically once a day. The "clock offset" is simply how
> much the clock is off sync. For some satellites, this may
> be up to milliseconds. The satelite clocks are not corrected,
> but the "clock offset" is transmitted together with the
> "clock time", and the receiver calculates the corrected time.
>
> >>>Indeed:
> >>><< GPS TIME STEERING
> >>>=================
> >>>GPS time is automatically steered to UTC(USNO) on a daily basis to keep
> >>>system time within one microsecond of UTC(USNO), but during the last
> >>>several years has been within 50 nanoseconds. The rate of steer being
> >>>applied is +/-1.0E-19 seconds per second squared.
> >>>ftp://tycho.usno.navy.mil/pub/gps/gpstt.txt
>
> Right.
> But note that as stated above. this is steering of
> the GPS-time, not of the individual satellites.
> You have two different coordinated time systems,
> each "living its own life" which should be made
> to run equal. The +/- 1.0E-19 seconds per second squared
> is the maximun "speed" with which the GPS time is changed.
>
>
> >>>It must take a REAL good mathematician to get 7 microseconds
> >>>per day out of that. ;-)
>
> .. and a real bad physicist to try. :-)
>
> >>I get 38.53 microseconds per day out of the 4.46*10^-10 corrective factor.
> >>It's a simple enough multiplication:
> >>
> >>4.46*10^-10 sec/sec * 86400 sec/day
>
> Right.
>
> > The altitude effect isn't cumulative.
>
> Utter nonsense.
>
> > That is, you can move
> > from Honolulu to Tibet and make one adjustment to the
> > length of a pendulum. You don't have to do it every day.
>
> But the error is still cumulative, isn't it? :-)
>
> > The 7 ns per day is for transverse doppler effect (less
> > frequently called the SR correction )
>
> 3 orders of magnitude wrong.
> (But we will call this a typo.)
>
> > It was included in
> > the preset because it does save the receiver some calculating
> > (there may have been some political reason to have all
> > the "relativistic" effects in one synthezer too [shrug] )
> > Anyway the 7ns error would accumulate if it represented
> > a clock rather than a propagtaion effect.
>
> Of course a rate error of 7 us/day would accumulate 7 us a day.
>
> > I think you can tell at a glance that +/-1.0E-19 steering
> > and +/- 50 ns / daily won't on the worst day add up to
> > the 7ns necessary to atrribute to an SR clock anomaly.
>
> This confusion is too gigantic to try to remedy. :-)
> You really have no clue whatsoever, have you jahn Sue?
>
> > It's all public information.
> > http://tycho.usno.navy.mil/gps_datafiles.html
> > http://tycho.usno.navy.mil/systime.html
>
> But you have no idea of what they mean?
>
> Paul