[time-nuts] ARRL FMT results

[Magnus Danielson]

From: Hal Murray <hmurray at megapathdsl.net>
Subject: Re: [time-nuts] ARRL FMT results
Date: Thu, 04 Jan 2007 14:19:13 -0800
Message-ID: <20070104221914.05232BE00 at ip-64-139-1-69.sjc.megapath.net>

> 
> > But there's a finite amount of time between when the signal is
> > transmitted and when it is received.  During this time, the earth
> > rotates, thus bringing the receiver either closer to or farther away
> > from the transmitter.  Doesn't that cause a frequency shift?  Isn't
> > this the Sagniac effect?  Small, but measurable as it is a
> > relativistic effect, no? 
> 
> Is that a frequency shift or a phase shift?

After refreshing my memory, I can now report that it is a time difference.

      2*A*Omega
/|t = ---------
         c^2

where
A is the rotational area covered when in transit
Omega is the angular speed of the rotation
c is the speed of light

The area covered may be a bit hard to describe, but if you project the position
of the transmitter and receiver onto a plane of the (effective) equator, then
would the area be that of the triangle from the transmitter into the axis,
the axis to receiver and then the path between the transmitter and receiver.
If using a wave which bends with the surface, the the great circle bow or
whatever best describes it as it projects onto the equatorial plane is what
needs to be used.

> /tvb
> 

So... for the ARRL measurements, they frequency measures would still be safe
from Sagnac, but if they where trying to compare time measures it would be a
different thing. Fortunatly this have not been as important to the radio
amateurs in general as the frequency ability.

However, if say I and Tom would take the timing of a GPS vehicle over the
atlantic we both see, we would experience different Sagnac effects. Infact,
the Parkinson & Spilker book as an excellent example showing the time transfer
in a ring around the world with NBS (now NIST), TAO and PTB with three sats and
how that projected area requires the Sagnac correction.

If Poul-Henning and I would do the same thing, the projected area would be
so small that we hardly notice, and this is because he is mainly south of me
and thus there is less area to project onto.

> The transmitter is moving at the same speed as the receiver.  That motion 
> changes the transit time between the pair, but if the velocity is constant, 
> that makes a time/phase offset rather than a frequency offset.  Do get a 
> frequency offset you want a Doppler where one end is moving relative to the 
> other.

Indeed. So for the ARRL FMT it is irrelevant. For us time-nuts it's a real
effect. That number should be about +/- 100 ns and not +/- 200 ns. Ah well.

Cheers,
Magnus