Western astrology, as well as astronomical ephemeris, use the tropical zodiac. This kind of calculation sets the point 0 Aries (vernal point) to the position of the Sun at the time of spring equinox.
This kind of zodiac is called tropical or in sanskrit sayana. Tropical zodiac plays only a small role in Vedic astrology; 99% of calculations depend on the sidereal zodiac. This kind of zodiac has the reference point in the stars. The point 0 Aries is interpreted as the beginning of the sign Aries (or the Nakshatra Aswini) in the sky.
Ayanamsa is the difference between tropical and sidereal zodiac. The actual value is about 23:56, i.e. this value must be deducted from the tropical longitude of each planet to get the sidereal longitude.
There is a movement of the vernal point compared with the stars. The speed of the movement (called precession) is given by Jet Propulsion Laboratoy (Nasa) as
5028.83 (+- 0.04) arcsec/century i.e. 1:23:48.83 deg/century
Assumed that the precession is always constant, we get a total period of 25771.4021 years. The tolerance of +-0.04 arcsec/cty implies that the correct value must be between 25771.197 and 25771.716 years.
But we may get a different period if the precession is not constant and has long term fluctuations.
Assumed that the precession given by astronomical ephemeris is correct, the key question for Ayanamsa calculation is to determine the correct Ayanamsa value for a given date (reference date).
Reference date (called t0) can be any date, most Ayanamsas refer to Jan 1 1900. Reference Ayanamsa (called ayan_t0) is the Ayanamsa value at the reference date (e.g. 22:27:37.76 degrees for Lahiri Ayanamsa and Jan 1 1900).
Differences between standard Ayanamsas can be measured in t0 and ayan_t0. The following table gives these values for some standard Ayanamsas. The values are taken from swiss ephemeris. These values for Lahiri, Raman and Krishnamurti are also the built-in defaults of Maitreya.
|Name||t0 (JD)||t0 (Date)||ayan_t0||ayan_t0 (Deg)||Reference|
|Lahiri (Chitra Paksha)||2415020.0||1900 Jan 0.5||22.46047||22:27:37.7||Spica (Chitra) at 0 Libra|
|De Luce||2415020.0||1900 Jan 0.5||26.41305||26:24:46.98||Zeta Piscium (Revati)|
|Raman||2415020.0||1900 Jan 0.5||21.01444||21:00:52||Calculation of B.V. Raman|
|Ushashashi||2415020.0||1900 Jan 0.5||18.66096||18:39:39.46||Unknown|
|Krishnamurti||2415020.0||1900 Jan 0.5||22.363889||22:21:50||Calculation of Krishnamurti|
|Djwhal Khool||2415020.0||1900 Jan 0.5||26.9630976||26:57:47.15||Ingress of vernal point into Aquarius in 2117 AD|
|Sri Yukteswar||2415020.0||1900 Jan 0.5||21.082222||21:04:56||The Holy Science (see below)|
|JN Bhasin||2415020.0||1900 Jan 0.5||21.365556||21:21:56||Unknown|
|Fagan-Bradley||2433282.5||1950 Jan 1||24.04204||24:02:31.36||Spica (Chitra) at 29:06:05 Virgo|