15. RECTIFICATION OF THE KALIYUGA
By some authorities the kaliyuga epoch is said to have begun at Lanka (Ujjain) sunrise on Friday 18 February 3102 B.C. of the Julian calendar, while by others the previous midnight. We shall adopt the midnight convention, JD 588465.2895.
Indian tradition posits an eclipse of the Sun at the start of the kaliyuga epoch. The Low-Precision Formulae For Planetary Positions by T.C. Van Flandern and K.F. Pulkkinen give the time for a new moon (conjunction in longitude) at 2:36 p.m. at Greenwich on Julian day 588465. This corresponds to 7:39 p.m. mean local time at Ujjain (75° 47' E). By this reckoning, the given kaliyuga epoch would be a civil epoch, the first day of a lunar month.
The modern SuryaSiddhanta in the commentary states that at the kaliyuga epoch the mean longitude of the Sun coincides with the fixed initial point of the sidereal sphere and is 54° from the mean vernal equinox. This is sufficient information to calculate the true astronomical kaliyuga epoch.
From the kaliyuga epoch to the next succeeding mean vernal equinox there are
We use Simon Newcomb's expression for the Sun's mean longitude in the Explanatory Supplement to calculate the Julian date of the 1900 mean vernal equinox. Thus,
54° ---- · 365.2421756 = 54.78632634 mean solar days. 360°
Therefore, the mean vernal equinox nearest the kaliyuga epoch will be on mean Greenwich Julian date
360° = 279°.696678 + 0°.9856473354 d d = 81.47267193 mean solar days JD = 2415020.0 + 81.47267193 = 2415101.473.
The astronomical kaliyuga epoch is, therefore, on mean Greenwich Julian date
2415101.473 - (3101 + 1900)365.2421756 = 588525.3525.
The required rectification constant to convert from the midnight civil kaliyuga epoch to the astronomical kaliyuga epoch is
588525.3525 - 54.78632634 = 588470.5662.
588470.5662 - 588465.2895 = 5.2767 mean solar days.