[time-nuts] ARRL FMT results

[Tom Van Baak]

> Tom,
>
> > > For this to be true, you need to have equal tracking for each vehicle
so
> > that
> > > you integrate equal amount of positive and negative shifts from each
> > vehicle.
> > > Better yeat is naturally to compensate each measure for the mainpart
of
> > the
> > > Sagnac effect. If you know it is there, you can compensate for it
since
> > you
> > > fairly well know your position and the satellites orbit well enought
for
> > the
> > > remaining error to be negliglable.
> >
> > I think we're talking two different things here.
> > The FMT guys -- with fixed transmitter and fixed
> > receiver -- don't experience any Sagnac effect.
>
> Yes, we are talking about different things and I changed midflight.
> But no, you are not correct that they don't experience any Sagnac effect.
> They do if their transmission goes east-west direction. Their transmission
path
> will leave a non-zero area when projected onto the equatorial plane.

Magnus,

OK, let me rephrase what I meant - yes, the FMT
transmissions do experience a Sagnac effect (a
time synchronization propagation delay), as would
any other form of EM transmission: RF or optical.

But the key thing here is that since the FMT event
is a *frequency* measurement, any constant path
delays cancel. Because transmitter and receiver
are stationary, the Sagnac effect is constant. Any
fixed phase offset drops out of a frequency calculation.
And so the Sagnac effect has no effect on FMT.

> If you say that it could silently be ignored I would agree, but mostly
because
> there seem to be some discussion about the actual frequency and stability
of
> their transmissions to start with.

It turns out to be rather small, about 200 ns for a
full 40 000 km around-the-earth trip at the equator.
But no matter how great or small the effect is, it
cancels when you do you frequency measurement.

A good analogy is measuring a time/frequency
receiver against your house standard. If you are
measuring time accuracy, then the cable length
makes a big difference and it has to be taken into
account for accurate results.

On the other hand, if you are measuring frequency
accuracy any cable will do, long or short, as long
as you don't change the cable during the test.

> The fiber optic gyro is actually a good explanation here. The transmitter
and
> receiver sits VERY FIXED in the same frame. However, as the optical wave
goes
> through the fiber, any turning of that fiber-roll will be effected by the
> Sagnac effect and much like a coil, the total area (turns x average area
per
> turn) will be a direct measure on how sensitive they are. Direct laser
gyros
> work the same. They sit in commercial airliners, tactical robots and the
space
> shuttles to give a few examples. The more sensitive ones has a constant
shift
> in them since they feel the earth turning and the most sensitive ones also
> measures the resonances in that turning.

Cool. What sort of sensitivity does one get out of
these things? Do you need three of them; one for
each axis?

> So, Sagnac effects even those measurements, but for most practical parts
it can
> be ignored I guess.
>
> > For traveling clock synchronization experiments,
> > yes, one does have to take Sagnac into effect if
> > you're at the sub-microsecond level.
> >
> > The other thing -- please check your books for
> > me -- is that the GPS clocks don't deal with the
> > Sagnac effect at all. It's the receivers that have
> > to apply the correction.
>
> Indeed. The receivers are the only one being able to correct for it, since
it
> is the receivers position (or rather, projection onto the equatioral
plane)
> which will determine the effect. Infact, it will be different between
eached
> tracked vehicle. If say Poul-Henning (which if is fairly south of me) and
I
> would compare clocks, we would have almost the same Sagnac effect between
the
> sats we track, where as if you and I would compare clock (you are mostly
west
> of me) we would experience very different Sagnac effects from a common
vehicle.

Right.

The GPS receiver knows where the SV is but the
SV cannot know where the receiver is. So Sagnac
corrections must be done by the party with all the
information: the GPS receiver.

The SR and GR corrections, on the other hand are
done in the SV since the altitude/velocity information
is known to the SV (by design or even by dynamic
measurement).

The other reason the SR and GR corrections must
be made in the SV is because they affect the GPS
clock frequency; it's a redshift.

> This is how the Sagnac effect works for us. The Kaplan book(s) just
breifly
> touches the subject on the level saying it is there. The Parkinson &
Spilker
> books goes much deeper into it with alot of nice plots and graphics
spending
> about 10 pages or so on the subject. I have read it before, but it was a
few
> years ago.
>
> Cheers,
> Magnus

Thanks, I'll look into the Parkinson & Spilker book.

I re-read my sources on the Sagnac effect also
when I did the Mt Rainier relativity experiment last
year. Since that was a round-trip road experiment,
the net Sagnac effect was zero. But during various
parts of the trip it would (predicted, not measured)
amount to about +/- 100 ps depending on how far
west or east I was from home.

/tvb