Article by Pidaparty Purna Satya Hariprasad

Ayana-amsa’ – ‘Ayana’ in Sanskrit means movement or change in position however infinitesimally small it is; ‘Amsa’ means a part or a small part however infinitesimally small it is. ‘Ayana-amsa’ is used traditionally and conventionally in Indian Astronomy to represent ‘movement of ‘Vishuvaths’. Vishuvath in Sanskrit is ‘Equinox’. Therefore ‘Ayana-amsa’ in Sanskrit is ‘Precession of Equinoxes’ in English.

Vishuvaths are points of intersection of Celestial Equator and Ecliptic. Equator (Bhu-madhya Rekha), when extended indefinitely, is known as Celestial Equator. Ecliptic is ‘Kranthi Vrutha’ i.e. Orbit of Sun. These points of intersection are therefore imaginary but assumed great significance in Indian Astronomy.

There are two Vishuvaths – Points of intersection – one in the North and the other in the South. One in the North is known as ‘Vasantha Vishuvath’ or ‘Vernal Equinox’ and the other in the South is known as ‘Sarath Vishuvath’ or ‘Autumnal Equinox’.

These Vishuvaths or Equinoxes keep moving. This movement is known as ‘Precession’. This topic became a centre of controversy for a variety of reasons and it is still a hot topic for discussion among those who are concerned about the subject. Eight questions that rattle their minds may be as follows:

Was the concept of ‘Precession of Equinoxes’ known to ancient Indian Astronomers? If yes, since when it was known?
Is the precession due to movement/trepidation of ‘Equator’ or ‘Ecliptic’? What are the contributory factors for the trepidation?
What were the different rates of precession as estimated or known to Indian Astronomers?
What is/was the effect of precession on the duration of a year or vice-versa?
Is the rate of precession per year constant? What were the different rates of precession as are known to the community?
Is the precession or movement of equinoxes circular or pendular?
When was the ‘zero’ point (of Ayanaamsa) for precession of equinoxes?
What is the current status? Is it possible to verify the accuracy of current status?

A serious attempt is made to collect and place, in this paper, all the material known to the author of this paper and known to the author to be available.

Let us deal with each question in the same serial order.

WAS THE CONCEPT OF PRECESSION OF EQUINOXES KNOWN TO ANCIENT INDIAN ASTRONOMERS? IF YES, SINCE WHEN IT WAS KNOWN?

There is enough evidence to show in ancient Indian scriptures that the concept was known to Indian Astronomers since Vedic times and that Ecliptic is fixed resulting in no movement. In reality it is the trepidation of Equator which results in ‘Precession of Equinoxes’. Gravitational forces acting on the earth’s rotation cause trepidation of Earth’s axis and therefore Equator.

“Iyanah krishne dasabhih sahasraih avathamindrah”

Rigveda

Meaning: Indra (Vishuvath) moves 15 x 10 x 1000 = 150,000 times in one ‘Kalpa’ (4,320,000,000 years). i.e. in one Mahayuga (4,320,000 years) vishuvath revolves 150 times. ‘Kalpa’ is qual to 1000 Mahayugas.

“Thrinsath-kruthyo yuge bhaanam chakram praak parilambathe”

– Sloka 9, Thriprasna-adhikara, (3^rd adhyaya) – Surya Sidhantha

Meaning: There form 30 x 20 = 600 right angles. i.e. Vishuvath makes full circle by moving backwards 150 times in one Mahayuga. The word ‘Praak’ means backwards. This gives us 28,800 years to complete one revolution. Duration of terrestrial year may thus be obtained as 365.2422 mean solar days. Duration of sidereal may be obtained as 365.2564 mean solar days.

In Vedas, accepted and respected interpretations confirm the following synonyms:

‘Vasanta vishuvath’ = ‘Agni’

‘Sarath Vishuvath’ = ‘Indra’

Sun’s entry (Ravi sankramana) into Karkataka (Cancer) = ‘Mitra’,

Sun’s entry into Makara (Capricorn) = ‘Varuna’.

‘Vishuvath chalanam’ = ‘Agastya chara’

In Vishnupurana, it was stated that Dhruva did penance (Tapas). Lord Vishnu was pleased and rewarded his penance stating that ‘Saptarishi Mandalam’ would revolve around Dhruva Nakshatra once every 26,000 years. (Source: ‘Nakshatramulu’ a book by Gobburi Venkata Ananda Raghava Rao).

Age of Vishnupurana is not known. The story confirms that movement of precession of equinoxes is circular and that it takes 26,000 years to complete the cycle. How close is the number to the scientific estimate today! One can safely conclude that the ancient Indian Astronomers are well aware of the concept of ‘Precession of Equinoxes’. Some of the data may be relevant to the period when it was composed and may be considered out of context under the present circumstances.

IS THE PRECESSION OF EQUINOXES DUE TO TREPIDATION OF ‘EQUATOR’ OR ‘ECLIPTIC’?

Once again, there is enough evidence to show in ancient Indian scriptures that Ecliptic is fixed resulting in no movement. In reality it is the trepidation of Equator which results in ‘Precession of Equinoxes’. Gravitational forces acting on the earth’s rotation cause wobbling of Earth’s axis and therefore trepidation of Equator.

Sathapatha Brahmana (2.1.2) confirms that there is no movement in the group of stars called Krithika from the East. This implies Ecliptic is not moving and is static. It is the trepidation in Equator.

Nakshatreshti (an ancient book) confirms that Krithika star is the first star and Bharani star is the last star.

In Vayupurana and Matsyapurana it was mentioned that Vishuvath Punyakala occurred when Ravi (Sun) was in Krithika star and Moon was in Visakha star.

There are other sources such as Mahabharatha referring to Bheeshma’s choice of date for his death, Garga Mahamuni’s statements, Varahamihira in Brihatsamhitha (in III-1) etc.

It is the trepidation in the Equator but not in the Ecliptic, which is responsible for Ayana-amsa or Precession of Equinoxes.

Then the next question is what are the factors contributing to the trepidation? Some of the factors attributed to trepidation are:

Earth is not round.

Inclination of axis of the Earth

Gravitational forces acting on the Earth, the Sun and the Moon

WHAT WERE THE DIFFERENT RATES OF PRECESSION OF EQUINOXES ESTIMATED BY VARIOUS INDIAN ASTRONOMERS FROM TIME TO TIME?

Annual precession of Equinoxes was estimated/calculated by different ancient Indian Astronomers differently at different times. Following are some selected figures with brief explanations:

60”.0 per year

Ganesh Daivajna in Graha Laghava 1520 A. D.

Satananda in Bhaswathi 1099 A.D.

Though Ganesha’s estimate was 60”, it was actually 58”.10 based on

365.25856 days estimated duration of a year.

59”.9 per year

Bhaskaracharya II 1108 A. D.

Munjala 932 A.D.

Though Bhaskaracharya II, estimated 59”.9 as given by Munjala,

actually arrived at 57”.55 using duration of a year as 365.25843 days.

57”.615 per year

Chandrasekhar Singh

54”.00 per year

Surya Sidhantha at least 21,65,111 years old (500 A.D. according to Western Astronomers). Though it is known to be 54”.00 per year, it works out to be 58”.68 per year using duration of a year as 365.25875 days.

50”.0 per year

Varahamihira 505 A.D.

50”.2388 per year

Newcomb 1687 A.D.

46”.5 per year

Parasara

46”.3 per year

Aryabhata 476 A.D.

50”.27 per year

Calendar Reform Committee 1955 A.D.

(It may be noted that Calendar Reforms Committee’s recommendations are close to Varahamihira and Newcomb.)

WHAT IS/WAS THE EFFECT OF PRECESSION OF EQUINOXES ON THE DURATION OF A YEAR OR VICE-VERSA?

Let us look at the duration of a year as estimated by various ancient Hindu Astronomers or in respected texts:

Text Days Hours Minutes

Vedanga Jyotisha 365 —– ——

Romaka Sidhantha* 365 5 55.2

Pulisa Sidhantha* 365 6 12.0

Brahmagupta Sidhantha* 365 6 12.148

Brahmasphuta Sidhantha* 365 6 12.148

Aryabhateeyam 365 6 12.50

Dwiteeya Arya Sidhantha 365 6 12.508

Prathama Arya Sidhantha 365 6 12.56

Surya Sidhantha 365 6 12.6

Pitamaha Sidhantha 365 8 34.28

V B Ketkar’s Jyotirganitham 365 6 9.16

Calendar Reform Committee 365 5 48.768

Vedanga Jyotisha whose author is unknown was transmitted for the benefit of mankind through Lagadha Mahamuni. (There is a view that it was authored by Lagadha Mahamuni. But a close reading “Lagadhasya Mahatmanah” does not give that interpretation) This is the oldest Hindu Astronomical Text (full text not available – only some portions are available).

Surya Sidhantha is the second oldest text after Vedanga Jyotisha. Author is unknown. It was gifted for the benefit of mankind through Mayasura by Surya Bhagwan towards the end of Krita Yuga i.e. at least 2,165,110 years ago – if it was in this Mahayuga. It is not known in which Mahayuga it was gifted. We are currently passing through 28^th Mahayuga. Duration of Mahayuga is 4,320,000 years. Westerns Astronomers dated it as not > 1500 years.

*Varahamihira’s Panchasidhanthika is dated 505 A.D.

V B Ketkar’s Jyotirganitham is dated 1937 A.D. Calendar Reform Committee is dated 1955 A.D.

What is this ‘duration of the year’? This is the time taken by the Sun to travel from the time it leaves one Vishuvath, say Vasantha Vishuvath or Vernal Equinox, to the time it reaches the same Vishuvath or Equinox. This is known as ‘Tropical year’ or ‘Savana year’. Presently it is estimated at 365.242199 days or 365 days, 5 hours, 48 minutes 45.9936 seconds.

Rate of annual precession of equinoxes and the duration of the year are therefore inter-related.

IS THE RATE OF PRECESSION PER YEAR CONSTANT? WHAT WERE THE RATES OF PRECESSION KNOWN TO THE COMMUNITY?

Annual Rate of Precession is not constant year after year. Changes noticed by modern scientists are as given below:

50”.279 per year in 2000 A.D.

50”.256 per year in 1900 A.D.

49”.835 per year in 0000 A.D.

49”.391 per year in 2000 B.C.

Source: Report of the Calendar Reform Committee

IS THE PRECESSION OR MOVEMENT OF EQUINOXES CIRCULAR OR PENDULAR?

There is a belief that the movement is pendular. The movement is believed to be within a range of 54⁰ i.e. 27⁰ on either side. This is based on four verses 9, 10, 11 and 12 in Triprasna Adhikara in Suryasidhantha reproduced below:

Verse 9: Trimsath kruthyo yugo bhanam chakrath prak parilambathe,

Thatgunath bhudenairbhakthath dyuganath yadavapyathe

Verse 10: Thaddostrighnadasasthamsaa vijne ayanabhidhah,

Thathsanskruthath grahath kranthi chayacharadaladikam

Verse 11: Sphutam driktulyatham gacheth ayane vishuvathdwaye

Prak chakram chlritham heene chayarkath karanagathe

Verse 12: Antharaamsairadhavruthya paschath seshaih thathadhike

Evam vishuvathee chaya swadeshi ya dinardhaja

Dakshinothara rekhayam sa thatra vishuvath prabha

Asiatic Society, Calcutta (Kolkata) published a book “Suryasidhantha” in English by A. K. Chakravarty. It is supposed to be a Research Publication. In pages 113, 114 and 115 he commented on this topic as follows:

“…. The language is cryptic, the principle is contradictory to the text itself and the results obtained are erroneous. These errors could be easily detected by gnomon shadow. It is now believed that these verses were interpolated in the text in a later period. Such interpolations are not uncommon…….”

Sathapatha Brahmanam (2.1.2) quoted earlier in response to Question 2 also supports the contention that movement is circular and not pendular. “Group of stars under the title “Krithika” are always on the East and are close to the Ecliptic. In times of Sathapatha Brahmana this group of stars was close to 0⁰ Latitude. Principal star in the Krithika group is 36⁰ away from the beginning of Ashwini group of stars. If the movement is pendular, this cannot happen.” Says Dr S Madhavan, Astronomer from Thiruvananthapuram, Kerala, India.

The difference between the durations of Driksidha ‘Nirayana’ sidereal year and sidhanteeya ‘Nirayana’ solar year gives us a difference of 8”.5. This difference gets added to annual precession every year. (Please see the comment below 54”.0 annual precession). That means 50”.27 + 8”.5 = 58”.77 which is not in conformity with visible reality.

Surya Sidhantha contains ‘Bhaganas’ . These Bhaganas give us the annual precession at 54”. Therefore these Bhaganas are incorrect and validity of 54” is questionable.

WHEN WAS THE ZERO POINT (OF AYANAAMSA) FOR PRECESSION OF EQUINOXES?

Some of the guestimates are given below:

388 B.C. – Cheiro

317 B.C. – D Davidson

255 B.C. – G Massey

125 B.C. – Thierens

213 A.D. – C Fagan

285 A.D. – N. C. Lahiri/Calendar Reform Committee

291 A.D. – K P Krishnamurty

490 A.D. – Bhaskaracharya II

498 A.D. – Sepharial

499 A.D. Suryasidhantha, Brahmasidhantha, Somasidhantha, Laghu Vasisthasidhantha, Vridha vasisthasidhantha, Ganakananda, Thatvaviveka

505 A.D. – Varahamihira

There is no basis to confirm that anyone of them is correct or wrong. They are based on the estimate of annual precession of equinoxes by respective Astronomer. They can at best be their best guess because annual precession of equinoxes is not constant in the past and therefore in the future also. It is futile to dwell on this issue. It is not much of consequence.

WHAT IS THE CURRENT STATUS? IS IT POSSIBLE TO VERIFY THE ACCURACY OF CURRENT STATUS?

As on 1^st April 2012, cumulative Precession of Equinoxes is 24⁰ 01’ 57” is as given by Positional Astronomy Centre at Kolkata. The Centre is now continuing the traditions established by Calendar Reform Committee. Annual Precession, as determined by this Institution is 50”.27.

I believe it is possible to verify and establish the accuracy through the Satellites and NASA.

Conclusions

Ancient Indian Astronomers are well aware of the Precession of Equinoxes.
Precession is caused by trepidation of Equator and not of Ecliptic. The trepidation is mainly due to gravitational forces acting on the Earth.
Annual rate of precession is not constant. Therefore it is possible only to guess, not accurately determine, date of ‘Zero’ AYANA-AMSA.
Precession of Equinoxes is CIRCULAR and only CIRCULAR.
Until it is proved otherwise, cumulative precession as on 1^st April 2012 is 24⁰ 01’ 57” and annual rate of precession is 50”.27. They are in conformity with Newcomb, Varahamihira and Calendar Reform Committee.