132 AD Orbital Elements

  I computed the Sun's "orbital elements" for the 132 AD HORIZONS data and got the following results:

The HORIZONS' osculating elements for 132 Jan 1 gives an eccentricity of about 0.018 which is a slightly better match to the 0.020 value obtained from Ptolemy's anomaly. It would have been interesting to see what Ptolemy's values for the lengths of the seasons were. The obliquity of the Ecliptic, ι, is close to the "observed" differences in the solstice meridian altitudes. Using the equation for the secular changes in the obliquity found on p. 114 of USNO Explanatory Supplement to the Astronomical Almanac I got a value of 23° 40' 43.77".

Supplemental (Mar 7): I checked some of the elements using Newcomb's formulas for the secular variations and got the following results for the eccentricity, angle of perigee and obliquity of the ecliptic:

     e = 0.01745
     π = 250° 56' 58.33"
     ι = 23° 40' 44.62"

The angle of perigee, λ_p or π, indicates that it is in Sagittarius at ♐10.9° which is not far from Ptolemy's ♐5½°. I don't know how accurate Newcomb's formulas are since he doesn't specify a range for their accuracy. Nutation might account for some of the differences.