> 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 You'll enjoy ch2 and ch3 too; when they're ready... > 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. I think 99.999% the Moon and Sun. You can ignore all other objects. True, mathematically, any object of any mass has a non-zero effect on g, but if you do the tide calculations even something as massive and as "close" as Jupiter is so far down in the noise (a few millionths the effect of the moon) that we don't worry about it for delta g calculations. > 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. No, g isn't zero at all. Remember g is inverse square to the distance from Earth. The other way to think about it is that satellites wouldn't be (free-fall orbiting) satellites if g were zero, eh? > 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. I believe the point he is making is that time/frequency on earth is dependent on altitude. Altitude is both a function of place and of time (e.g., time of day, time of month, as in tides). And since altitude is wiggling up and down by fractions of a meter (due to earth tides) you have a real time transfer problem down in the 18th decimal place. By analogy, how do you ultra-precisely measure the elevation of a lake when there are winds, waves, or ripples? Now think about ripples on the space-time pond. If you want more references on tides, let me know. Also, related, here's a humbling four-part paper on: What Does Height Really Mean? http://www.aagsmo.org/resources.htm /tvb _______________________________________________ time-nuts mailing list time-nuts@febo.com https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
