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Seasonal Variation of Earth Rotation

Bulletin Horaire was the regular publication of the Bureau International de l'Heure (BIH, International Time Bureau). By the 1950s quartz clocks were beginning to agree with each other better than they agreed with the rotation of the earth. Using the quartz clocks it became clear that the rotation of the earth varied seasonally during the year.

Engineers for radio broadcasts of time signals wanted to provide stable frequency as well as time of day. They began to regulate their broadcast time signals in a way that smoothed out the seasonal variations rather than tracking the rotation of the earth exactly.

By the year 1955 different time services were using different expressions for seasonal corrections to radio broadcast signals. Over the previous 3 decades in the forum of the international commission on time (and also the next several decades after this) any differences in procedure and values of time signals were deemed to be cause for action to create new recommendations.

In 1955 at the IAU General Assembly it was agreed that starting in 1956 all radio broadcast time signals should try to smooth out the seasonal variations and that the expression for calculating the corrections should be published in advance by the BIH. In the original announcement of the expression and subsequent issues of Bulletin Horaire this seasonally smoothed time was called UT2, or Provisional Uniform Universal Time.

The BIH published several expressions for the seasonal variation of the rotation of the earth. Plots showing those expressions are below.

UT2-UT1 (originally tabulated as ΔTS)

H.M. Smith indicated that the Greenwich time service had begun to correct their time for polar motion before 1950. BIH Bulletin Horaire gives the formulae for seasonal variations in rotation that were used by several different time services in the early 1950s. Nicolas Stoyko indicated that by 1955 at least 4 different systems of earth rotation corrections were being used by various time services. Those differences triggered the 1955 IAU meeting to dictate that every time service should use the same scheme and that BIH should formulate and publish those corrections in advance.

UT2 seasonal variation
PDF file SVG file

The change between new and old forms of UT2 during 1962 deserves a closer look.

UT2-UT1 before, during, and after 1962

BIH based the initial (1956/1961) formulation for the UT2 corrections on time service data from 1950/1955. BIH based the new (1962 onwards) formulation for the UT2 corrections on re-reductions of data from 1955-07 to 1961 using the 1958 IAU scheme for polar motion.

BIH corrected the new UT2 formula for the systematic differences between the old FK3 catalog and new FK4 catalog which came into use at the beginning of 1962. Systematic changes in a star catalog necessarily cause a step in the observed time or a shift in the longitudes of the observatories, or both. As part of the change from FK3 to FK4 the IAU directed BIH to compute improved, more self-consistent, values of the longitudes of all the observatories. The resulting solution of celestial and terrestrial coordinates caused the computed value of UT to step by 0.0016 s at 1962-01-01.

Looking at the formulae for old UT2 and new UT2 it is apparent that changing from one to the other on January 1 would cause another step of 0.006 s in the value of UT2. Rather than create an even bigger step in UT2 at 1962-01-01, Anna and Nicolas Stoyko of BIH decided that the UT2 corrections for 1962 would start using the old expression, and smoothly switch to the new expression when those intersected near the end of March. As seen in the plot below the UT2-UT1 corrections for 1962 are different than for any other year.

UT2 during 1962
PDF file SVG file

In practice this 1962 change of expression for UT2 was irrelevant. The 1960 URSI meeting recommended that all time services should follow the lead of the UK and US and broadcast coordinated time using a frequency offset from cesium aimed to match the predicted progression of UT2 with occasional steps as needed. The BIH complied and published a frequency offset from cesium for use in coordinated time broadcasts beginning with 1961. The 1961 IAU meeting concurred with URSI and formally directed the BIH to formulate and publish the frequency offset and steps for coordinated time broadcasts.

Beginning with 1961 Bulletin Horaire tabulated measurements of the offset between the broadcasts of WWV and UT2. The text of all of the recommendations and directives indicated that UT2 was the goal in a bureaucratic sense, but UT2 was not available in a practical sense. By 1962 most broadcast time signals were coordinated, so the time that was available was coordinated time, not UT2. The unusual form of UT2-UT1 during 1962, and the new expression for calculating UT2 after that, were moot except as the underlying basis of the time that was in use.

d/dt(UT2-UT1), the seasonal variation in Length of Day (LOD)

The original impetus for UT2 was in order to allow the broadcasts to maintain a uniform frequency througout the year. The following plots show the derivative of UT2-UT1, and that gives the size of the seasonal frequency deviations.

UT2 LOD variation
PDF file SVG file

Equation of the equinoxes, the Draconic cycle

At the 1925 IAU General Assembly observatories had aquired Shortt free pendulum clocks. These were stable enough to show subsecond variations over the course of a year. In response the IAU resolved that measurements of UT should be referenced to the mean equinox rather than the apparent equinox.

At the 1952 IAU General Assembly the IAU resolved that tabulated planetary Right Ascensions in almanacs should be expressed with respect to the mean equinox rather than the apparent equinox.

The equation of the equinoxes principally shows the 18.6 year Draconic cycle of the regression of the lunar nodes along with smaller semi-monthly variations.

Equation of the Equinoxes
Steve Allen <sla@ucolick.org>
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