Earth rotation period

Tycho had only very poor clocks. He was thus limited to determine right ascensions by using spherical trig rather than simple clock readings. I chose to emulate his spherical trig approach even though I had good clocks at my disposal, in order to get insight into how he constructed his catalog.

However, because I have decent clocks available, I was able to good timings on solar meridian passages and also stellar meridian passages. The timed solar data allowed me to investigate the Earth's orbit, and the timed stellar data allowed me to measure the Earth's rotation rate. My early attempts to measure stellar transits (the time of meridian passage) were done by simply auto-tracking the altitude of a star as it passed the meridian, and then later fitting a curve to the data to extract the maximum altitude and the time of maximum. I did this because my azimuth encoder readings were not yet reliable, and I was uncertain when an azimuth of 180 degrees had been reached. With this transit technique, I did not need to know my azimuth exactly because maximum altitude occurs only at the time of meridian passage. My timing accuracy was just that of the CPU clock, which was synced to NIST time occasionally. Actual accuracy was probably about a few seconds.

For the Earth rotation estimate, I went back to my meridian data and sorted on the observation type to isolate all the transit events. I found 170 observed transits, of which 67 stars had useful pairs of timings. The difference in the transit timings of the same star is an integer multiple of the earth rotation period. Stars that had a long time interval between transit timings were better suited to estimating the rotation period because of the larger number of rotations that had elapsed. The poorest estimators were those stars that had been timed on successive nights (a single earth rotation). Here are plots of the estimated rotation period as a function of the timespan of the transits.

The left hand plot shows all the 67 transit timing estimates, and the right hand side shows 25 selected data points that eliminated both the outliers and the short timespan baselines. The mean value of the 25 timings gave the best estimate of the Earth rotation period.

The final estimate of 0.99727 days (86164.13s) was close to the accepted value of 86164.09s. I am off by 40 milliseconds. This is not accurate enough to detect the effect of earth precession on the measurement (about 8 milliseconds).

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