Thursday, February 18, 2016

JPL HORIZONS 132 Autumnal Equinox

  I checked JPL's HORIZONS online ephemeris for the date and time of the 132 AD autumnal equinox and received the following results from which the time of the equinox can be determined.

      Date__(UT)__HR:MN     R.A._(ICRF/J2000.0)_DEC
      0132-Aug-28 19:00     11 59 46.47 +00 01 17.9
      0132-Aug-28 20:00     11 59 55.46 +00 00 18.7
      0132-Aug-28 21:00     12 00 04.46 -00 00 40.5
      0132-Aug-28 22:00     12 00 13.45 -00 01 39.7


      interpolated equinox date & time
      132 Aug 28 20:19 UT

This is the descending node since the declination is decreasing as it passes through 0° DEC as expected for the autumnal equinox. On p. 168 of Toomer, Ptolemy's Almagest Ptolemy states,

      "Now we have established that, among the first of the equinoxes 
      observed by us, one of the most accurately determined was the 
      autumnal equinox which occurred in the seventeenth year of 
      Hadrian, on Athyr [III] 7 in the egyptian calendar [132 Sept. 25], 
      about 2 equinoctial hours after noon."

JPL's equinox is about a month prior to Ptolemy's. It appears that somehow we got the date wrong. What could be the explanation? On p. 9 Toomer says that Ptolemy used the 365 day Egyptian calendar. The Julian calendar has on average 365.25 days per year so there were about 132/4 = 33 leap days which may account for some of the difference. Each leap day would shift the Egyptian calendar one day forward relative to the Julian calendar. The dates given in HORIZONS are Julian dates and adding 33 days would take us to Sept. 30. The equinox is still a few days off and Ptolemy's datum is probably just an estimate. If Ptolemy didn't take into account the fact that the diffraction of the atmosphere affects apparent positions his pole would be shifted slightly north as well as his equator if he assumed it was 90° south of the pole. Since the Sun descends in declination at the autumnal equinox his estimate of the date and time would be a little early. Ptolemy was concerned about diffraction later in life so he may have become aware of the problem after the Almagest was written. An error in Ptolemy's anomaly could also affect the times of the equinoxes that of perigee.

Supplemental (Feb 18): While researching calendar creep I came across this Amagest Ephemeris Calculator which gives Toomer's Julian calendar date for Hathor 7. The discrepancy in the date of the autumnal equinox is a puzzle.

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