JPL HORIZONS AD 132 Phenomena (Corrected)

When fatigue starts setting in your error rate goes up and that may account for some of the calendar creep. One of my settings for HORIZONS was J2000.0 which doesn't use the reference frame for the dates calculated. There is also a switch for the Julian date and decimal RA and DEC make it easier to check the time of the equinoxes and solstices. I also used apparent solar time and got a better fit to Ptolemy's data.

     Date__(UT)__HR:MN   JDUT     R.A._(a-appar)_DEC.

      0132-Mar-19 00:00 1769348.5  357.63697  -1.03602
      0132-Mar-20 00:00 1769349.5  358.53070  -0.64442
      0132-Mar-21 00:00 1769350.5  359.42378  -0.25287
      0132-Mar-22 00:00 1769351.5    0.31632   0.13854
      0132-Mar-23 00:00 1769352.5    1.20843   0.52971

      0132-Jun-21 00:00 1769442.5   87.33879  23.65461
      0132-Jun-22 00:00 1769443.5   88.37944  23.66893
      0132-Jun-23 00:00 1769444.5   89.42051  23.67628
      0132-Jun-24 00:00 1769445.5   90.46193  23.67666
      0132-Jun-25 00:00 1769446.5   91.50360  23.67006
      0132-Jun-26 00:00 1769447.5   92.54542  23.65648

      0132-Sep-22 00:00 1769535.5  178.07833   0.84227
      0132-Sep-23 00:00 1769536.5  178.99124   0.44213
      0132-Sep-24 00:00 1769537.5  179.90462   0.04163
      0132-Sep-25 00:00 1769538.5  180.81856  -0.35911
      0132-Sep-26 00:00 1769539.5  181.73312  -0.75999
      0132-Sep-27 00:00 1769540.5  182.64839  -1.16091

      0132-Dec-19 00:00 1769623.5  266.83065 -23.64465
      0132-Dec-20 00:00 1769624.5  267.94346 -23.66328
      0132-Dec-21 00:00 1769625.5  269.05640 -23.67395
      0132-Dec-22 00:00 1769626.5  270.16930 -23.67667
      0132-Dec-23 00:00 1769627.5  271.28202 -23.67144
      0132-Dec-24 00:00 1769628.5  272.39439 -23.65827

Using cubic splines gives the following estimates for the equinoxes. The solstices were found by estimating the zero for the differences.

      Mar 21 15:30   Vernal Equinox
      Jun 23   01:18   Summer Solstice
      Sep 24  02:30   Autumnal Equinox
      Dec 21  08:13   Winter Solstice

The astronomical day starts at noon so the morning hours would be on one day and the afternoon hours on the next. If the dates indicated are ordinary Julian calendar dates then Sept 25 12:00 would be Julian date 1769539.0 as previously determined. There is still seems to be a little bit of discrepancy between HORIZONS' and Ptolemy's dates and times.

It might help if we could develop a "personal equation" for Ptolemy as an observer. It might help to characterize the Alexandrians of his time and the members of the Museum.

edit (Feb 28): corrected the time of the summer solstice to 01:18 which is what my saved data indicates.