Chinese Calendrics Software 16.  Delta T

Both the astronomical and the chronological Julian dates reflect Delta T, the difference between GMT and TDT (terrestrial dynamic time, a.k.a. ephemeris time). TDT is atomic time, and thus, unlike GMT, is independent of the rotation of the Earth. Thus the times displayed for astronomical phenomena such as full moons should be close to the times observed (or, for past events, would have been observed).

Unless great accuracy is required, Delta T is important only for dates in the moderately distant past or future. Currently it is about one minute. It reaches five minutes in the 15th C, and one hour in the 8th C. As regards the distant future, reliable estimates of Delta T cannot be made because we do not know how the Earth's rate of rotation will change.

Delta T for years past has been calculated in two ways: (i) By reference to eclipse records. (ii) By mathematical formulae. The first method gives an estimate of Delta T at specific dates which is as reliable as the historical records. The second method is needed when Delta T must be calculated for any given year (as in this software) but this method is not as accurate as the first.

Delta T is calculated by this program as follows: For years 1915 and later the formula of Espenak, as given on Robert van Gent's informative web page Delta T: Approximate algorithms for historical periods is used (since this gives the best results of all formulas from the mid-20th C. to the present). For years prior to 1915 Delta T is calculated as the average of all non-extreme values obtained from all formulas given on that web page except for the IAU (1952) and the Borkowski (1988) formulas (where a value is non-extreme if it does not exceed three standard deviations from the mean).

This method may not produce values for Delta T as accurate as that based on historical eclipse records, but it does come close. For example, the software calculates Delta T for 33-1-1 JC as as 2 hours and 49 minutes, whereas the true value (based on historical eclipse records — see the tables given in Robert van Gent's web page) is probably 2 hours and 51 minutes.

For times in the distant past there is considerable uncertainty about the value of Delta T. The uncertainty in the value of Delta T outside the range -1000 CE through 2500 CE is too large for lunar phase dates to be computed with any reasonable degree of accuracy. Since the month-to-month structure of the Chinese Calendar depends on the exact times of dark moons, and these times are UT not TDT (with Delta T needed to convert TDT to UT), conversions to and from Chinese calendar dates in the distant past and distant future are not 100% reliable. Thus the software does not accept any input date after 3000-01-01 CE. But since dates in the Chinese Calendar go back almost to -3000 CE the software accepts dates back to the epoch for the Chinese Calendar (-2696 CE or -2636 CE), with the proviso that the structure of the calendar prior to 0 CE is subject to some uncertainty.