As I approach my 90th trip around the sun on this spaceship called Earth, I reflect that life has been so good to me. I AM BLESSED WITH A PRECIOUS FAMILY, FRIENDS, COLLEAUGES, AND THE FULLNESS OF THE GOSPEL OF JESUS CHRIST. I know the Lord loves me and I know He loves you.
The Equinox
This Monday will be the autumnal equinox at 1819 UTC (2:19 p.m. MDT). At that moment, the spin axis of the Earth is exactly at right angles to the direction to the sun (equal day and equal night). The Earth’s spin axis determines the occurrences of the equinoxes and solstices. The sun follows the equation of time–the analemma–as the Earth makes its precise journey each year around the sun. That trip around the sun determines the Sidereal year, which is different than a solar year. Our calendars use the solar year–365 days for the sun to cross the sky except for leap year. The astronomer’s recipe for leap year is unusual: if a year is divisible by four then it is a leap year, unless it is divisible by 100 then it is not, unless it is divisible by 400 then it is. This keeps our calendar almost in sync with the Sidereal year.
The Tropical year is determined by the time between the vernal equinoxes and is 20 minutes and 24 seconds shorter than the sidereal year which is, as mentioned, the time it takes for the Earth to orbit the sun. This because of the precession of the poles. The Earth is like a top spinning in space.
One Second Accuracy
For fun, our son Nate and I annualized 200 years with one-second accuracy of the Tropical year data. This accuracy is documented in Figure 12, p. 35 of the Application Note, THE SCIENCE OF TIMEKEEPING (Allan, Ashby, and Hodge, 1997). When I was consulting for Hewlett Packard (1993-1997) they asked me to write this 88 page booklet with a lot of fascinating timing information. It is now available on line as well.
Official time for the Earth is Universal Time Coordinated (UTC) and is labeled Earth Spin in Figure 12 . One will note that the instabilities in UTC over 200 years amount to hundreds of seconds–much worse than Tropical time or Ephemeris time. Ephemeris time is the same as Sidereal time (labeled as Earth Orbit) and has instabilities better than one second over the 200 years of interest, as shown in Figure 12.
We Found some Surprises
Applying Total Allan Variance (Total ADEV) and Total Time Deviation (Total TDEV) techniques to the Tropical year data along with standard spectral analysis, we uncovered periodicities of 2.8 years, 4.2 years, 6.4 years, 8.3 years, 12.2 years, and 19.5 to 20 years, 36 years, 55.6 years, 72 years, and 92 years with varying amplitudes.
Total TDEV Analysis
Total TDEV analysis revealed periodicities in the tropical year data of 20 years, 36 years, and 55.6 years, with amplitudes of 332 seconds, 113 seconds, and 68 seconds, respectively. Total ADEV has longer averaging times and reveals two more periodicities with periods of 72 years and 92 years. The estimated amplitudes of these two periodicities are 200 seconds and 195 seconds, respectively.
Celebration
I am sure you wanted to know all of that as we celebrate this autumnal equinox, and my 89th birthday on the 25th next Thursday. We live on a flying and unstable Earth. The only constant thing is change. That is why these three variances (ADEV, MDEV, and TDEV) are so useful. They are optimum in measuring change! FUN!!!!!!!!!!
David W. Allan
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