[time-nuts] ARRL FMT results

[Magnus Danielson]

From: "Tom Van Baak" <tvb at leapsecond.com>
Subject: Re: [time-nuts] ARRL FMT results
Date: Thu, 4 Jan 2007 10:41:48 -0800
Message-ID: <001201c7302f$ffb50cc0$ba9a8843 at computer>

> > 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?
> > 
> > Warner
> 
> Ah, you may be on to something here. Someone
> else on the list may know for sure, but let me
> think out loud with you.

Sagnac effect is a known relativistic effect which does effect the GPS system.
I have several reference touching on it, but (as usual) Parkinson and Spilker
explains it fairly indepth including its compensation. NIST 1385 is referred to
by Kaplan and Hegarty.

Also, the Sagnac effect is the main driving force for Laser and Fiber-Optical
gyroscopes. My recently bought book on the subject of fiber-optic gyroscopes
has the following chapter and sub-chapter titles (just to make the point):

Chapter 2: Principle of Fiber-Optic Gyroscope

2.1: Sagnac Effect

2.1.1: Sagnac Interferometer

(What I really is trying to do is figuring out what fun I can have with that
100 km fiber stuck under my office table at work, which is just a fraction of
all our fiber rolls in total.)

> Yes, the Sagnac effect is often lumped together
> with relativistic effects, but strictly speaking, it's
> more of a time synchronization problem than a
> feature of SR or GR (time dilation, redshift, etc).
> 
> On the rotating earth, at the equator, it amounts
> to about 200 ns for a round-the-world clock trip
> (40 000 km); or 5 ps/km. It depends on latitude
> and such but it is independent of the speed or
> duration of the trip.

Considering that the GPS satellites has a higher heights above the earth, the
Sagnac effect may manifest itself up to +/- 200 ns.

> Now a frequency shift is phase change over time.
> Unless the receiver and transmitter move during
> the experiment, it seems to me, there's no phase
> change over time and so the Sagnac effect will
> have no impact on a frequency measurement.

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.

However, for most parts it should even out fairly well anyway even if not
properly compensated.

Cheers,
Magnus