[time-nuts] ARRL FMT results

[Tom Van Baak]

> > It turns out to be rather small, about 200 ns for a
> > full 40 000 km around-the-earth trip at the equator.
> 
> Actually, 207 ns. :-)

Magnus,

Yes, right. Let me take this opportunity to show
where that number comes from. For equatorial
circumnavigation the total Sagnac effect is:

    T = -omega * R^2 * 2*pi / c^2

where omega is the earth rotation rate, which is
2*pi radians over one [sidereal] day, about 86164
seconds (86164.09056 if you're picky).

R is the mean radius of the earth at the equator,
which is about 6378 km (6378.135 if you're picky).

c, of course, is the 300000 km/s speed of light
(299792.458 if you're picky).

Your calculator should then give: T = -207 ns.

See also the equations at:
http://en.wikipedia.org/wiki/Hafele-Keating_experiment
where cos(phi) is 1 and delta_lambda is 2 pi

Note you'll see slightly different values in various
books and papers (any of them correct enough)
depending on the constants they picked for earth
radius or length of day, etc.

I like to use the 200 ns approximation along with
a 40 000 km earth circumference approximation
(well, almost the definition) because they divide
to give the following equator traveling clock Sagnac
effect rule-of-thumb: 5 ps / km .

/tvb
http://www.LeapSecond.com/great2005/