[time-nuts] Pendulums & Atomic Clocks & Gravity

Tom Van Baak tvb at LeapSecond.com
Sat May 26 15:02:39 EDT 2007

> Then a pendulum calculator at:
> http://www.ajdesigner.com/phppendulum/simple_pendulum_equation_period.php
> allows solving any of 8 pendulum related equations.

Note that this simplistic l/g formula does not characterize the
period of precision pendulum clocks, as it ignores factors
such as circular error, and a host of other static and dynamic
corrections. But it should be good enough for your SWCC.

> Tom has pointed out that the stability limit on pendulum clocks is in the area
> of 1E-7 because of the complex effect of the Sun and Moon on the value of "g".
> http://www.leapsecond.com/hsn2006/ch1.htm

> Gravity also effects atomic clocks, see: http://www.leapsecond.com/great2005/
> and this puts a limit on what can be done with any atomic clock that's on
> Earth.  "g" will always have minor fluctuations (noise) due to all sorts of
> things like the Sun, Moon, planets, asteroids, earthquakes, etc.  It's still a
> direct "g" effect called red shift like (U2 − U1)/c2, where the Us are
> gravitational potentials, only smaller by c squared.

Mostly Sun (

> I expect that in not too many years the official master clocks will no longer
> be on Earth, but instead in satellites.  There "g" is precisely known to be
> zero.  Since GPS satellites are excellent for time transfer that's where they
> will be.  The ensemble will be the full constellation.
> In "Time Too Good to Be True" Kleppner
> http://www.physicstoday.org/vol-59/iss-3/p10.html
> says "...a primary standard in space would not overcome the problem of
> comparing time or frequency at different locations on Earth."
> I don't understand why that would be the case with a standard in a GPS
> satellite.  Granted E-18 can not now be done using the current GPS system, but
> when atomic clocks get into the E-16 or better area and are in satellites, I
> think the quality of time transfer will keep up.
> Just an idea & Have Fun,
> Brooke Clarke
> http://www.PRC68.com
> http://www.precisionclock.com
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