Zero point of various ayanamshas

Ayanamsha (ayanāṃṡa) is defined as an offset from the tropical coordinates (longitudes) of spatial objects. Though it is extensively used in astrology, it is quite useful in astronomy too. In fact, sidereal coordinates is what you’d observe in the night-sky. This ayanamsa changes its value all the time due to precession of equinoxes. Well, what goes around comes around. So, at some point of time in history, the coordinates of tropial and sidereal longitudes were aligned perfectly. People disagree when this might’ve happened. Each one proposed his own ayanamsha. Oh, yeah, a reminder that astrology is pseudo-science!

The following table lists the dates of when the 0° Aries sidereal and tropical zodiacs is imagined to have coincided. These are called roots or zero points or zero values or zero ayanamsha year (ZAY). It is generated using the Swiss Ephemeris v2.08. All dates are in UT (Universal Time) in the form YYYY/MM/DD, HH:MM:SS. The years (YYYY) are in proleptic Gregorian (negative years are such that year 0 = 1 BCE, year –1 is 2 BCE etc.). The table is sorted in chronological order of dates. The last column gives the annual precession rate in year 2000 CE (measured in angle-seconds/year). The period of precession of earth’s axis is 25,771.5 years, i.e. the expected value is 50.28796195 sec per year (360 degrees/25771.57534 years). Other models put it at 25,676 yrs at the average rate of 50.475"/yr (see wikipedia). Note that this rate is always increasing over time (centuries), so the cycle could be slightly longer than 25676 too.

Python code can be downloaded here. Basically, the code does a bisection/binary search for x such that get_ayanamsha_ut(x) == 0 (i.e. root-finding algorithm). Other tables found on the internet may give slightly different values depending upon the options used (e.g. nutation, atmospheric refraction etc.)