Ayanamsa - A Scientific Calculation
Data used is from scientific community and not from Vedic text books. But Vedic Seers have to be credited for noting this great scientific data namely Ayanamsa or Precession of Equinox, astronomically long back. This is the greatest Achievement of Vedic Sidereal Astrology and Astronomical observations in India from time immemorial.
Calculation of Ayanamsa using Modern Astronomical Data
Polaris (Alpha UMi) or Urs Major or Dhrurva nakshatra or the Pole star is the present reference star for measuring the precession of Earth or Ayanamsa.
North Ecliptic Pole (NEP) is 90 degree of center of Equator of Earth.
The Earth tilt is about 23 degrees 26 min 11.8 seconds (23.43661 degrees). Again this changes slightly due to Earth nutations, but more or less constant. So, North Celestial Pole (NCP) of Earth is in a tilt of 23.43661 degree with NEP of Earth.
Also the Polaris star is tilted from NCP (NCP-Polaris tilt) by 0.736 degrees away. This value will change according to Earths nutation and Polaris own motion.
Scientifically according to mathematical calculation, NCP will point and will be closet to Polaris in 2140 AD.
The full precession circle of Dhurva or Polaris nakshatra, scientifically is 25,771.58 Julian years. In Hindu terminology it is 25,770 years.
The scientific accumulated precession formula for 2000 as the epoch Julian year is
AP = 5,028.796195 + 2.2108696 × T in ArcSeconds, T being the Julian centuries.
So to use this above formula, we need to know when the tropical and sidereal zodiac coincided.
25771.58 minus 2140 years will take us back in time, when Polaris was in same position as it will be in 2140, meaning NCP will be exactly pointing to Polaris with zero tilt with NCP, that is (25771.58 - 2140) = 23631.58 julian years back.
So the total Julian years expended from that NCP-Polaris-Zero year, is used to calculate the total accumulated precession.
23631.58 plus 2000 = 25631.58, will enable us to use above formula for Epoch 2000 which is the scientific formula for Accumulated precession.
Accumulated Precession (AP) in ArcSeconds AP = 5,028.796195 + 2.2108696 * ( 23631.58 minus 2000) / 365.25) dividing with 365.25 is done to convert normal number of years to Julian years.
The values got from above has to be added to the actual tilt of Earth w.r.t to Dhurva nakshatra on that day, i.e. Epoch 2000.
Why add, one may ask, it is because the Earth arrives later (Or Sun arrives earlier) to same point on celestial plane around Sun, due to this precession.
Adding 23.43661 tilt degree (between NCP and NEP) will give Ayanamsa for Epoch 2000.
So, Ayanamsa = 23.43661 + (AP / 3600). AP is divided by 3600 to convert Arcseconds to degrees for Epoch 2000.
So the perfect scientific Ayanamsa formula for 2000 AD year is
- For birth year before 2000 Epoch
Ay = 23.43661 + (5,028.796195 + 2.2108696 * ( 23631.58 + (2000 - Birth Year) / 365.25)) / 3600
- For birth year after 2000 Epoch
Ay = 23.43661 + (5,028.796195 + 2.2108696 * ( 23631.58 + ((2000 - Birth Year) + (Birth Year - 2000)) / 365.25)) / 3600
The slight changes in Earth tilt (Axial Tilt) changes between 22.1 and 24.5 degrees on a scale of 41000 years.
and Polaris actual degree away from NCP now (40 arcminute or 0.736 degree away), again changes in few arcseconds, needs to be taken into consideration, which would be another calculation for another day for me.
If these two (Axial Tilt and NCP-Polaris Tilt) changes are taken into account, according to that Birth Year, it will make the aynamasa accurate in seconds. For that I need astronomical data, funds and my energy and time. Already I am too old.