Avinash Research

Dr M L Raja

Month: May 2020

Year of 0 Degree Precession (Oscillation) of Equinox

In order to locate a celestial body in the sky, we are using co-ordinate systems. They are of four types. 1. Ecliptic system, 2. Equatorial System, 3. Horizontal system and 4. Meridian system. In the ecliptic system, the reference circle is the ecliptic at which the Earth revolves round the Sun. Here by using the values of Celestial Longitude and Celestial Latitude, the location of any celestial body with reference to the ecliptic circle can be derived. (Here the ecliptic belt of 360 degrees circle is the belt of ecliptic with 30 degrees of latitude above and below the ecliptic pathway of the Sun. It is divided into 12 zodiac signs and based on the Prominent Stars situated in conjunction within this ecliptic belt, it is divided into 27 Nakshatra (Star) divisions). In the equatorial system, the reference circle is Earth’s equator which is extended to the sky where it is called as celestial equator. Here by using the values of right ascension and declination, we can locate the position of the celestial bodies in the sky with reference to celestial equator which is nothing but the extension of equator of the Earth. Thus, there are two important circles, i.e. 1. ecliptic and 2. equator. These two circles are not in the same plane, but they are tilted at 23 degrees and 27 minutes. This is due to the tilt of the axis of the Earth at 23 degrees and 27 minutes. Thus, these two important circles are not in the same plane but at the angle of 23 degrees and 27 minutes. Because of this tilt, these two circles cut each other at two points. They are called as equinoctial points. They are vernal equinox and autumnal equinox. These two points are not constant as they either revolve backwards or as per Surya Siddhanta they oscillate. The revolving backwards for all 360 degrees of a circle is known as Precession of Equinox. The present rate of precession is 50.28 seconds per year and thus it will complete one revolution of 360 degrees in 25,772 years approximately. The ancient astronomical texts of our Nation (Bharat) call this as Ayanamsa or Ayanacalana or Krantipatagati.
These two cutting points, i.e. vernal and autumnal equinoxes (0 and 180 degrees degree of ecliptic) are not constant and varies with reference to celestial equator. Hindu Astronomy adopts two methods in this aspect. One is Nirayana and other is Sayana. In Nirayana method the variation in the position of vernal and autumnal equinoxes is not added to the longitudes of the celestial bodies and it calculates 0 degree Mesha (Meena Mesha junction) as fixed. In Sayana method the variation in the position of vernal and autumnal equinoxes in degrees of arc are added to the longitudes of celestial bodies and thus 0 degree Mesha is always changing. The difference in degrees of arc between the Nirayana and Sayana longitudes of celestial bodies is known as Ayanamsa or ayanacalana or kranthipatagati in Hindu astronomy or as the degrees of precession in western astronomy. The Nirayana method calculates the zodiac signs and Nakshatra divisions as fixed starting from Mesha 0 degree, as it considers that this is only a to and fro oscillation and is not a constant backward revolution. This is as per Surya Siddhanta, a very ancient astronomical text of our Nation, whose initial date is at the end of Kruta yuga, (Satya yuga) as per the internal evidences found in the text itself. Now we analyse what Surya Siddhanta says about this oscillation of equinoxes.

Sûrya Siddhānta: in the 9th and 10th śloka of the 3rd adhyāya (Tripraśnādhikāra:) mentioned that the equinox oscillates between 3° Mīna to 27° Mesha i.e. on either side of 0° (Mīna and Mesha junction), 27° forwards in Mesha and 27° backwards in Mīna.
Trimśat Krityo Yuge Bhānām Cakram Prāk Parilambate,
Tad GuNād Bhūdinair Bhaktād DyugaNād Yad Avāpyate .9.
Taddos trighnā Daśāptāmśā Vijñeyā Ayanābhidhā:
Tat Samskritād Grahāt Krānticchāyā Caradalādikam .10.
Meaning – 1. Trimśat – Thirty, 2. Kritya: (Krtyo) – Twenty (Kriti – Twenty, plural of Kriti is Kritaya:, like Mati śabda: of Strīlińga:, here it is ‘Kritya:’, 3. Yuge – in one Yuga of 43,20,000 years, 4. Bhānām – of twenty seven (Bha: – number 27, Masculine, 6th case), 5. Cakram – Circle,i.e. twenty seven degrees as stated in the commentary of Parameśvara (1380 C.E.) 6. Prāk – East and as stated by
Parameśvara in his commentary, the meaning is, “from the east movement mentioned here, the west movement is obtainable by UpalakshaNam, which in turn means ‘implying something that has been actually not expressed, implication of something in addition of any similar object, where only one is mentioned” ( hence it means East and West), 7. Parilambate the east and west oscillatory movement up to twenty seven degrees 8. Tad – That, 9. GuNād – in multiplication, 5th case, 10. Bhūdinair – the total number of days (Bhū dina – Earth days) in a yuga, 11. Bhaktād – in division, 5th case, 12. DyugaNād – the number of days so for passed in the yuga, 13. Yad – which, 14. Avāpyate –obtainable, 14. Taddos (Tad + dos – part of an arc defining its sine) – That part of an arc defining its sine i.e. Rsine, 15. Trighnā – multiplied (ghnā) by three (tri), 16. Daśāptāmśā – Daśa -Ten, Amśa – part (divided), {360° x [3÷10] =108°, per each oscillation – explained latter} Âpta – obtained, 17. Vijñeyā – To be perceived or known, 18. Ayana – Oscillation of Equinox, 19. Abhidhā: – Name or appellation.
Thus, the meaning is, in a  Yuga of 43,20,000 years, the ayana oscillates 600 times up to 27 degrees in eastward as well as westward movement (from 0 degree ayanamśa i.e. the junction of Mesha and Mīna Rāśi). This 600 is multiplied by the number of days passed so for in this yuga and divided by the total number of days of the yuga, gives the total number of oscillations happened so far from the beginning of the yuga. The whole number will show the completed oscillations and the fraction shows the present progressing oscillation from 0 degree. Multiply the Rsine (of incomplete oscillations expressed in degrees, minute and seconds) with three and divide it by ten, to obtain the degrees of Ayana. From the longitude of the Graha, as corrected by this, the declination, the shadow and the ascension difference (caradala) are to be calculated.

It is further mentioned in the 11th and 12th śloka of the same 3rd adhyāya: of Sûrya Siddhānta: as,
SphuTam drik tulyatām gacchedayane Vishuvad Dvaye,
Prāk Cakram calitam hīne chāyārkāt karaNāgate .11.
Antarāmśairathāvritya Paścāccheshaistatha adhike ,12,
The meaning is that the ayana calanam (at the two equinoxes Dvaye – two, Vernal and Autumnal equinoxes), as calculated, is in motion from
the beginning of Mesha of 0° and Tulā Rāśi of 180° respectively. The ayana calanam is eastward (Prāk) when the longitude of the Sun (Arka) calculated is less (hīne) than that derived from the shadow (chāyā – the shadow). When it is more (adhike), then it is on westward motion.

Thus, this clearly shows that there is only oscillation of equinoxes and not precession, as per Sûrya Siddhānta:. Thus the vernal equinox
moves in oscillatory pattern from the beginning of Mesha of 0°, first eastward up to 27° in Mesha Rāśi i.e. +27° and then it turns back westward by 27° again to reach 0° Mesha i.e.–27°. Then it again proceeds westward by 27° to reach 3° Mīna Rāśi i.e. again –27°. After this it again turns back eastward and moves by 27° to reach 0° Mesha i.e. +27°. Thus, a total of 108° (27° X 4) {360° x [3÷10] =108°, as per 9 and 10th śloka} makes one full oscillation. In a yuga of 43,20,000 years, this ayana calana completes 600 oscillations i.e. 600 X 108° (600 X 108 X 60 X 60″). Thus in one year, the ayana calana is 600 X 108 X 60 X 60″ ÷ 43,20,000 that is 54″. The modern estimation is 50.28″. Thus, for one full oscillation it takes 7200 years (43,20,000 ÷ 600). Thus as per Surya Siddhanta, the 0 degree Ayanamasa was at the beginning of this Mahayuga of 43,20,000 years. Now we can assume that after every 3600 years, there will be 0 degree Ayanamsa.

However there are be minute variations over a period of time. For example, Maha Aryabhatta Siddhanta of Aryabhatta mentioned a different value. This text was written by Aryabhatta at the very early years of Kaliyuga, as mentioned in the 2nd śloka of the 2nd adhyāya: (Pārāśaryamatāntarādhikāra:) of this text as,
Etat Siddhāntadvayam ēshadyāte Kalauyuge jātam
Svasthāne dRktulyā anena kheTā: sphuTā: kāryā:
Meaning :- Etat – This (singular), Siddhāntadvayam – The Siddhānta in dvayam – in pair form (MahāryabhaTTa Siddhānta: contains one Pûrvārdha Rûpa: known as GrahagaNitādhyāya: and the second one Uttarārdha Rûpa: known as Golādhyāya:), ēshat – a very little, slight, yāte – was elapsed, Kalauyuge – in Kaliyugam, jātam – was brought into existence.
Thus, ÂryabhaTTa mentioned it clearly that his MahāryabhaTTa Siddhānta: which is in pair form (Pûrvārdha Rûpa: – GrahagaNitādhyāya: and the Uttarārdha Rûpa: – Golādhyāya:) was brought into existence (written), at the very early years of Kaliyugaya.
In this text at 7th, 11th and 12th sloka of Madhyagati Adhyaya (1st Chapter) Aryabhatta mentioned as,
This means that Ayanagraha (Ayanamsa or Ayanachalana or oscillation of equinoxes) oscillates at the rate of 5,78,159 oscillations in one Kalpa of 432 crore years (432,00,00,000). As per the coding of numerals in Maha Aryabhatta Siddhanta as described in 2nd sloka of 1st Adhyaya, ma is 5, sa (si) is 7, ha is 8 Ta is 1, ma (mu) is 5 and dha is 9 and hence masihaTamudhā: is 5,78,159. Thus, Ayanacalana completes one oscillation in 7472 years (432,00,00,000 ÷ 5,78,159). This value is slightly different from the value of Surya Siddhanta which mentions that in 7,200 years, Ayanacalana completes one oscillation of 108 degrees. (600 oscillations in 43,20,000 years of one Mahayuga and hence 6,00,000 oscillations in 432 crore years of one Kalpa). This variation is because the rate of Ayanacalana varies with time. The picture shows Ayanamsa (oscillation mentioned as precession in the picture) varies much during various periods of time.

Now we will analyse the later astronomical texts which dealt with Ayanamsa or Ayanacalana or Krantipadagati. The first text is Mahakavi Kalidasa’s Jyotirvidabharanam, an ancient text written during the rule of Vikramaditya of Agnikula vamsa of Ujjaini who had ruled almost all parts of our Nation and thus started his era of Vikrama Samvat in 57 B.C.E. In this text, in the 21st śloka of the 22nd adhyāya:, Kālidāsa mentioned as,
Varshai: Sindhura Darśanāmbara GuNairyāte Kalau Sammite
Māse Mādhava Samjñike Ca Vihito Grantha Kriyopa Krama:
Meaning : 1. Varshai: – Year, 2. Sindhura – Elephant – so the number Eight, 3. Darśana – ShaT darśana – so the number Six, 4. Ambara – Sky – so the number Zero, 5. GuNa – Tri GuNa – so the number Three i.e. 3068 years, 6. Yāte – was elapsed, 7. Kalau – Kaliyuga, 8. Sammite – Measured out, 9. Māse – Month, 10. Mādhava – Vaiśākha Month.
This means that the poet Kālidāsa started writing this text, JyotirvidābharaNam, in the month of Vaiśākha: (and ended in the Month Kārtika:) in the year 3068 (completed) of Kaliyugābdam. Kali 3068 is 33 B.C.E. (3101 – 3068). Therefore, the great poet Kālidāsa lived in first century B.C.E. is the definite conclusion arrived from this śloka.

In the same text JyotirvidābharaNam, in the 10th śloka of 22nd adhyāya:, Kālidāsa mentioned as,
Dhanvantari:  KshapaNakâmarasimha  Śankur  VetālabhaTTa  GhaTakharpara Kālidâsâ:
Khyāto Varāhamihiro NRupate: sabhāyām ratnâni vai Vararucirnava Vikramasya
This means that the nine gems in the court of the King (NRupa) Vikramāditya were Dhanvantari, KshapaNaka, Amarasimha, Śañku, VetālabhaTTa, GhaTakharpara, Kālidāsa, the celebrated (Khyāta: is past passive participle, denotes a little earlier period than others) Varāhamihira and Vararuci.
According to the 21st śloka mentioned before, Kālidāsa lived in first century B.C.E. Therefore, we can conclude that Varāhamihira who along with Kālidāsa was also there, in the court of Vikramāditya and all the three lived in the first century B.C.E.

In the same text Jyotirvidabharanam, Kalidasa mentioned at 18th sloka of 1st Adhyaya as,
Śāka: śarāmbhodhiyugonito hRuto
Mānam khatarkairayanāmśakā: smRutā:
The meaning is to calculate the Ayanamsa for a particular year, we have to deduct 445  from the year in Śāka: era and divide it by 60. Thus, the sloka mentions that  at 445th year of the Sāka, the Ayanamsa was 0 degree and after that the Ayanamsa deviates from 0 degree at the rate one degree in 60 years i.e. 60 Vikala (Seconds of arc) or one kala (minute of arc0 per year.  Thus, at 445th year of the era of the Saka King, the vernal equinox was exactly at 0 degree Mesha and after that every year it deviated by 60 Vikala (Seconds of arc) away from 0 degree of Mesha. Now we have to find out who is this Saka King and when his era was started. Since Juotirvidabharanam was written by Kalidasa in the year 3068 Kali and Salivahana Saka was started at 3179 Kali (78 C.E.), this Saka King’s era can not be Salivahana Era. Then Vikrama Samvat was started in 57 B.C.E. i.e at 3044 Kali and the date of Jyotirvidabharanam is 3068 Kali which is 24th year of Vikrama Samvat and thus 445 Vikrama Samvat will occur 421 years after the year of Jyotirvidabharanam. Hence, it is not Vikrama Samvat of 57 B.C.E. It must be a prior era. Now one has to found out, the starting year of this Śaka Era.
This was clearly mentioned by Varāhamihira in his BRuhat Samhitā in the 3rd śloka of 13th adhyāya: as,
Âsan Maghâsu Munaya: Śâsati PRithvîm YudhishThire NRupatau
ShaT dvika pañca dviyuta: Śakakâlastasya Rajñaśca
Meaning: 1. Âsan – Inhabit – present in, 2. Maghā – The constellation of Magha group of stars, 3. Munaya: – SaptaRishii ManDalam – Seven Sages – group of Stars – Great Bear Constellation, 4. Śāsati – Ruled (or) governed, 5. YudhishThira – YudhishThira Dharma Raja of Pañca PānDava, 6. NRupa – King, 7. ShaT – Six, 8. Dvika – Two, 9. Pañca – Five, 10. Dvi – Two, i.e. 2526 years, 11. Śakakâla – Śaka Era, 12. Tasya Rājña: – Of that monarch (YudhishThira), 13.Ca – and (denoting the stationing of SaptaRishi ManDalam in Magha constellation).
“The Seven Sages (The Great Bear) were stationed in the Asterism Magha, when the King YudhishThira was ruling. The commencement of the Śaka Era took place 2526 years after the period of that Monarch and the stationing of Seven Sages at Magha” is the meaning. YudhishThira of Pañca PānDava won the Mahābhārata war around 3138 B.C.E. and ruled for 36+ years up to 3102 B.C.E. (completed) In 3101 B.C.E., (current) at which year the Kaliyuga started and YudhishThira went for vanavāśa for 25 years up to 3076 B.C.E. and left the world in 3076 B.C.E., until then the Sapta Rishii ManDalam was in Magha constellation, as per the astronomical data. Therefore, 2526 years after this, the Śaka Era started is the statement of Varāhamihira. BhaTTotpala in his commentary to BRuhat Samhitā, on explaining this śloka, interpreted the word ‘Śakakâla’ as Śaka NRupakâla i.e. the era of the Śaka King. Further, on explaining this śloka in his commentary to BRuhat Samhitā, BhaTTotpala quoted the writing of VRuddha Garga (Garga Rishii Senior) as, ‘tatha ca VRuddha Garga:’
“Kalidvâpara sandhau tu sthitâste PitRudaivatam Munayo
Dharmaniratâ: Prajânâm pâlane ratâ:”
Here, Sage Garga clearly told that the Sapta Rishi ManDalam (Muni) was stationed in Magha constellation (PitRudaivatam), at Kali Dvâpara Yuga junction (Sandhi). Thus, the period of reign of YudhishThira and Kali Dvâpara Yuga junction (Sandhi) were contemporary, as at the time of both, the SaptaRishii ManDalam (Muni) was stationed in Magha constellation. Here, the word “tatha ca” has the meaning “and likewise, and so it has been said, accordingly” (‘A Sanskrit – English Dictionary,’ Monier Williams, Oxford Clarendon Press, London 1872, page 359 & ‘A Sanskrit-English Dictionary’, Sir. Monier Monier – Williams, Motilal Banarsidass Publishers, Delhi 2002 page 433). Thus, it definitely proves that these statements of VRuddha Garga and Varāhamihira are denoting the very same event and period. Bhattotpala quoted the writing of VRuddha Garga here, exactly to point out that the reign of YudhishThira and the end of Dvâpara Yuga & the beginning of Kali yuga were one and the same, in terms of time. Besides, in the 2nd śloka of 13th adhyāya: of BRhat Samhitā, Varāhamihira mentioned that he wrote the movements of SaptaRishii ManDalam, according to the doctrine (Matam) of VRuddha Garga. Thus, it proves that the reign of YudhishThira and Kali Dvâpara Yuga junction were contemporary.

ÂryabhaTTa himself mentioned in the 5th śloka of 1st adhyāya: (Gītikapāda:) of ÂryabhaTTīyam that Mahābhārata war took place before the beginning of the Kaliyuga.

Abul-Fazl ibn Mubarak, a vizier in the court of King Akbar, wrote “Ayeen Akberi” (Ain i Akbari) during the reign of Akbar. This book was rendered English from Persian by Francis Gladwin and was published in London in the year 1800 C.E. (printed by G.Auld Greville Street). In the first volume of this book, in third part, at page 263, on detailing “The Æra of the Hindoos,” Abul-Fazl wrote, “In the beginning of the fourth or present jowg [yuga], Rajah Joodishter [YudhishThira] was universal monarch, and the commencement of his reign became an epoch of an æra of which to this time (being the fortieth year of the reign [of Akbar]) there have elapsed 4696 years.” Akbar came to power in 1556 C.E. and his 40th year of reign was 1595 C.E., which was 4696th year of YudhishThira (Dharma Rājā of Pañca PānDava). 4696 years before 1595 C.E. is 3101 B.C.E. (4696 -1595), which was the beginning of Jayabhyudaya YudhishThira Śaka. Thus, Abul-Fazl clearly mentioned that YudhishThira lived around the beginning of Kaliyuga (3102 B.C.E. completed). These writings of Abul-Fazl were quoted and explained by Sir. Alexander Cunningham, in the page 7 of his book, “Book of Indian Eras with Tables for calculating Indian Dates”, (first edition 1883 C.E.).

Henry Thomas Colebrooke, in the page xliii of his book ‘Algebra with Arithmetic and Mensuration from the Sanscrit of Brahmegupta and Bháscara’ published in London in the year 1817, wrote in his notes and illustrations under the heading ‘Age of ÁRYABHATTA’ as (given verbatim), “It is to be observed, that he [ÂryabhaTTa] does not use the Śaca or Sambat of Vicramáditya nor the Śaca era of Śáliváhana: but exclusively employs the epoch of the war of the Bhárata, which is the era of Yudhist’hira and the same with the commencement of Cali Yuga. Hence it is to be argued, that he flourished before this era was superseded by the introduction of the modern ephochas.” Hence, in 1817 itself it was accepted by Henry Thomas Colebrooke himself, that the epoch of the war of the Bhárata, the era of YudhishThira and the commencement of Kali Yuga, were contemporary.

Thus these evidences clearly show that YudhishTira ruled till 3101 B.C.E (Current) and went to Vanavasa till 3076 B.C.E. In 3076 B.C.E he went to Heaven. Then 2526 years after 3076 B.C.E., Saka  NRupa (the era of Saka King) was started. 2526 years after 3076 B.C.E. is 550 B.C.E. (3076 – 2526 = 550). Śaka king Cyrus II (Cyrus the Great) ended Persian vassalage to the Medes by capturing Ecbatana and ousting the Median dynasty at 550 B.C.E. and founded the Achaemenid Empire of 550–330 B.C.E. He defeated his enemies and became the King of Pāraśîkam in 550 B.C.E. He belongs to Paraśaka, a division of Śaka people. Their place was known after their name Paraśaka, as Paraśakam, later known as Pāraśîkam. His era was followed in those days in Kashmir and other nearby places of Bhārat.

Though, King Vikramāditya (57 B.C.E.) and his great grand son King Śālivāhana (78 C.E.) of Ujjayanî, won these Śaka and become Cakravarties of Bhārat, they were not born in Śaka family. Therefore, they cannot be Śaka and Śaka NRupa (Śaka King, NRupa – King). They can only be Śakāri i.e. enemy or conquerors or ruler (so, rarely as Śakendra) of Śaka and are not at all ŚakanRuupa (Śaka King). We are not mentioning King Aśoka as Kalinga King but only as Maurya and Magadha King, though he won Kalinga. Hence, ŚakanRupa Era, Śaka Era, Śaka Kāla or a mere Śāka does not mean either Vikramāditya Era of 57 B.C.E. or the Śālivāhana Era of 78 C.E., but it means only Cyrus Era of 550 B.C.E.

Further, the Sanskrit word ‘Śaka’ has two distinct meanings. The first one is ‘power and strength.’ The root is ‘Śak.’ From this only the Śaka people who are powerful and strong, got their name. In the legends, it was mentioned that they were produced by the holy cow of VasishTha, Kâmadhenu: from her sweat to destroy the army of Viśvāmitra (Kauśika Rājā). So Śaka Era means the era of these Śaka people only. The second meaning is ‘era or epoch – Kāla’ where the root is Vedic with the meaning ‘to know’ – to know from which event, the years are counted. In that meaning only, it is named as Vikrama Śaka and Śālivāhana Śaka, where Śaka means Era (Kāla –Time). Thus, the word, Śaka has two different meanings. The two meanings for the word ‘Śaka’ can be understood easily through the following two types of titles given to the King Vikramāditya of Ujjainī (57 B.C.E.) First type denotes the people of Śaka as in Śakāri (enemy of Śaka) and in Śakāntaka: (destroyer of Śaka) and the second type denotes era as in Śakakāraka, ŚakakRta and ŚakakartRu (founder of an era). It is important to note that the word Śaka in the title of Vikramāditya is used here with two different meanings. 1. Denotes the people of Śaka, as in Śakāri (ari, enemy) Śakāntaka: (Antaka:, destroyer) of Śaka people and it cannot be enemy or destroyer of era or epoch, 2. Denotes era, as in ŚakakRuta, Śakakāraka or ŚakakartRu (kRuta, karaka and kartRu means founder) i.e. founder of an era and cannot be founder or creator of Śaka people. Hence, one has to be careful in understanding the meaning exactly and correctly, whenever and wherever Śaka and its related words were used.
Besides, if we assume that Śaka Kāla (Śaka Era) mentioned in the text BRuhat Samhitā of Varāhamihira, in the 3rd śloka of 13th adhyāya: is denoting Vikrama Śaka and Śālivāhana Śaka, then the meaning will be Era Era or Kāla Kāla or Śaka Śaka, which doesn’t make any meaning. This is because, in “Vikrama Śaka and Śālivāhana Śaka” the word Śaka already has the meaning of era (Kāla). Hence, what is the necessity of repeating again the word “Kāla,” in “Śaka Kāla?” Thus, in the word ‘Śaka Kāla,’ Śaka means strength, thereby denotes Śaka King Cyrus only and not ‘Era’ as it was denoted already by the word ‘Kāla’ in Śaka Kāla. (Śaka – Śaka King, Kāla – Era). Hence, Śaka Kāla mentioned in the foreseen 3rd śloka of 13th adhyāya of BRUhat Samhitā meant only Cyrus era of 550 B.C.E.

We have already seen that as per Jyotirvidabharanam of Kalidasa in the 10th śloka of 22nd adhyāya: that Varahamihira was senior contemporary to Kalidasa and King Vikramaditya of Ujjaini who started his era at 57 B.C.E. The date of Jyotirvidabharanam is 33 B.C.E. as per its 21st śloka of the 22nd adhyāya:. Thus it proves that Varahamihira lived in the early part of 1st Century B.C.E. Further, Varahamihira clearly mentioned his period in Pañca Siddhāntikā, in the 8th śloka of the 1st adhyāya: as,
Saptāśvi Veda sankhyam Śakakālamapāsya Caitra Śuklādau*
Arddhāstamite Bhānau Yavanapure Saumyadivasādye**
Meaning : 1. Sapta – Seven, 2. Aśvi – Two, 3. Veda – Four, i.e. 427 years, 4. Sankhyam – Reckoning or Counting from, 5. Śakakālam – Śaka Era, 6. Apāsya – Having left – completed, 7. Caitra – Caitra month, 8. Śukla – The bright or light half of a lunar month, 9. Âdi – Beginning, 10. Ardha – Half, 11. Astama – Setting, 12. Bhānau – Sun, 13. Yavanapure – The city Yavanapuri, 14. Saumya: – Budhan – the planet Mercury, Divasa – Day.
The meaning is, deduct the year 427 of Śaka Era elapsed (i.e. deduct 427 from the number of years in Śaka Era for which the ahargaNa is wanted) at the beginning of the bright half of Caitra lunar month, when the Sun has half set at Yavanapuri at the beginning of Wednesday. This means Varāhamihira had compiled Panca Siddhāntikā in the year 427 of Śaka Era. This Śakakālam (Śaka Era) is the era of the Śaka king Cyrus II, (explained in detail already). In the 2nd śloka of the 12th adhyāya: (Paitāmaha Siddhānta) of Pañca Siddhāntikā, this era was mentioned as Śakendra Kālam (the era of Śakendra, the king of Śaka people i.e. King Cyrus II). This also proves that Sāka era of Jyotirvidabharanam is the era of Saka King Cyrus II of 550 B.C.E.

Besides, Bhāskarācārya, in the 28th śloka of Kālamānādhyāya: of Madhyamādhikāra: of GrahagaNitādhyāya: of Siddhānta Śiromanī, mentioned clearly that this ŚakanRupa Era (Cyrus Era of 550 B.C.E.) came to end in 3179 Kali. The śloka is,
“Nanda Adri Indu GuNāstatha ŚakanRupasyânte Kalervatsarâ:
GodrīndvadrikRtāńkadasranagagocandrā: Śakābdānvitā:”
Meaning : 1. Nanda – Nava (nine) Nanda – so Nine, 2. Adri – Seven Hills – so Seven, 3. Indu – Moon – so One, 4. GuNa – TriguNa – so Three i.e. 3179 years, 5. ŚakanRupasya – (Era) of Śaka King (NRupa – King) 6. Anta: – End, (Ante is 7th case [Locative case] of Anta: meaning at the end, limit, boundary), 7. Kaler – in Kaliyugābdam, 8. Vatsarā: – Years, 9. Godrīndvadrik􀃋tāńkadasranagagocandrā: – 197,29,47,179 (Go is 9, Adri is 7, Indu is 1, Adri is 7, KRita is 4, Ańka is 9, Dasra is 2, Naga is 7, Go is 9, Candra is 1), 10. Śakābda – Śaka years, 11. Anvitā: – Gone alongwith, joined, connected with (past passive participle, in past tense). Thus the Śāka era or ŚakanRupa era or Śakakāla or Śakaboopa kāla means the era of the Saka King Cyrus II who started his era at 550 B.C.E. and it was followed in Kashmir and adjacent parts of our Nation and it came to an end in 3179 Kali (78 C.E.) at which year Salivahana Saka was started.

Thus the Śāka mentioned in the text Jyotirvidabahranam of Kalidasa in the 18th soka of Manaprakaranam (1st Adhyaya:) is the era of the Saka King Cyrus II of 550 B.C.E. Then the year of 0 degree Ayanamasa was 550 – 445 = 105 B.C.E.

This is further confirmed by one more ancient astronomical text of our Nation.
BRuhat Samhita, an encyclopedia of various subjects, written by Varahamihira, in its 3rd Adhyaya on Sun’s Transit at 1st and 2nd sloka mentioned as,
Âśleshārddhāt dakshiNam uttaram ayanam raverdhanishThādyam
noonam kadācit āsīd yenoktam pūrva śāstreshu
As per ancient texts that the Sun turned south at the middle of Aslesha Nakshatra (middle of 106 degrees and 40 minutes of arc to 120 degrees, i.e. around 113 degrees and 40 minutes of arc) and turned north at the beginning of Dhanishtha Nakshatra (293 degrees and 20 minutes of arc to 306 degrees and 40 minutes of arc i.e at 293 degrees and 20 minutes of arc).
sāmpratam ayanam savitu: karkaTakādyam mRugāditaścānyat
uktābhāvo vikRuti: pratyaksha parīkshaNairvyakti:
At present the Sun turns southwards at the beginning of Karkataka at 90 degrees (Cancer) and northwards at the beginning of Makara at 270 degrees (Capricorn). This as per the actual observation.
This means that the summer solstice occurred at 90 degrees and winter solstice occurred at 270 degrees at the time of Varahamihira. Thus it states that the vernal equinox was at 0 degrees and autumnal equinox was at 270 degrees. There will be a 90 degrees difference between winter and summer solstice to vernal equinox and in the same way to autumnal equinox. Thus at the time of Varahamihira there was 0 degree ayanamsa i.e. vernal equinox was at 0 degree Nirayana. Jyotirvidabharanam which was written by Kalidasa at 33 B.C.E. and it mentions that Varahamihira was senior contemporary to Kalidasa. Hence it fits with the date of 0 degree ayanamsa at 105 B.C.E.

As Aryabhatta who lived at the very early years of Kaliyuga mentioned in his text Maha Aryabhatta Siddhanta that Ayanacalana completed one oscillation in 7472 years and thus in 3736 years after Kaliyuga beginning, there will be 0 degree ayanamsa, i.e. 3736 – 3101 = 635 C.E. However as per Surya Siddhanta, it is 3600 years after Kaliyuga beginning and hence 0 degree ayanamsa is at 499 C.E. (3600 – 3101 = 499). However, these calculations are based on the assumption that at the beginning of Kaliyuga, there was 0 degree ayanamsa. However we can not find its mention in any of the ancient astronomical texts of our Nation. Since it is only an oscillation movement between 3 degree Meena to 27 degrees of Mesha, centering on 0 degree Mesha (at Meena Mesha junction), there will not be much deviation in seasons except for a maximum of 27 days either this side or that side, but centering on 0 degree ayanamsa. Hence if we fix seasons as per 0 degree ayanamsa at Meena Mesh junction of 0 degree Mesha, there will not be much deviation. Hence in our Nation, this Ayanamsa was not mentioned in all the ancient astronomical texts. These texts used Nirayana positions of Graha for calculations and calendar purposes.

Since Kalidasa and Varahamihira who lived at 1st century B.C.E., wrote their texts in the 1st century B.C.E. and these texts fixed 0 degree ayanamsa year at 105 B.C.E. i.e. is within their period of time, we must give importance to it. Thus we can conclude that 0 degree Ayanamsa was at 105 B.C.E.

Year of birth of Kothai Andal

Year of birth of Kothai Andal
Sreemat Andal is one of the 12 Azhvars who devoted their whole life in the devotion on Sreemath Narayana. These 12 Azhvars also sang devotional songs on Sreemat Narayana which are collectively known as Nalayira Divya Prabhantham. Kothai Andal who is worshiped as Mother Goddess by Hindus especially Vaishnavits, is famous for Her song Tiruppavai which was sung by Her in the holy month of Margasirsa. Sreemat Andal, who is worshiped as the incarnation of Mother Earth, was born in the holy city Srivilliputhur which is in southern part of Tamilnadu state of Bharat, close to the western mountain range. Sree Vishnu chittar who is famously known as Periyazhvar (one of the 12 Azhvars) is Her father. (zha is a special la in our Tamil language)
The time at which these 12 Azhvars lived is not given adequate importance, as the people gave more attention to their teachings and show more interest on the devotional songs sung by them and the devotees are always fond of dipping in the ocean of these songs and immersing in the spiritual enjoyment of the immense feelings in the devotion and realising their identity and oneness with the Almighty. However, there are references either internally in their devotional songs or in the sloka of later Vaishnavits about the time of these Azhvars.

In this article, let us analyse the year of birth of Kothai Andal. If we search internet or any text about the period of Sreemat Andal or of any other Alvar, it is said that they belong to 7th or 8th century C.E. Actually speaking, there is no research or study have been conducted on the dates of Alvars and even Nayanmars, the great Saiva Bhakta Jnanies. It is commonly said that 7th and 8th century can be considered as the period of Bhakti movement in Tamilnadu and hence these Alvars and Nayanmars were belong to this period. Then if we ask the question why 7th and 8th century C.E. is considered as the period of Bhakti movement, the answer told was that this is because the Alvars and Nayanmars lived in this period and they spread Vaishnava and Saiva Bhakti among the people during this period. Thus it is clearly a circular argument, where one proves the other and the proof of the first theory is the second theory which is totally based on the first theory. Except this, there is no other proof. Hence it is essential to derive the date of Sreemat Andal independently, not based on any type of circular argument.
Sreemat Andal’s birth year is given in the text of Pinbazhakiya Perumal Jeeyar who was a disciple of Nampillai who in turn is a strong Vaishnavit and lived during the time of Sreemat Ramanujar. Since this text was composed during the period of Sree Ramanujar, it is 1000 years ancient. This text was published by Se.Krishnamacaryar and printed at Noble Printing Press, Tiruvallikeni, Chennai in 1927. In his “Araayirappadi Guru Parampara Prabhavam” Pinbazhakiya Perumal Jeeyar wrote as,
“siddhaanaam Saradaam Kalaavapagame Varshe Nalaakhye Ravaau
yate karkkatakam vidhaavupacite shashti ahni Sreemati
nakshatra aryamadaivate Kshitabhuvo vaare caturthyaam tithau
Godaa pradurabhooda cintyamahimaa Sreevishnucittaatmajaa”
(S is pronounced as in Sankara, s is pronounced as sarasvati, sh is pronounced as shanmukha, aa is long vowel, a is short vowel.
Thus, it means that Sreemat Andal, the daughter of Sree Vishnucitta, was born in 97 years of Kaliyuga (‘siddha” in Katapayati sankhya and by Angaanaam vaamato gati denotes the number 97, s is 7 and dha is 9 and we have to reverse it and thus it is 97), in Nala year, in Ashadha month (Sun in Karkkataka), Poorva Phalguni (Poora) Nakshatra, 6th day, Sukla Paksha 4th thithi, Tuesday.

In the same way the year of birth of Periyazhvar, father of Sreemat Andal is mentioned in the same text as,
“tatvaabdaapagame Kalau yugavare samvatsare krodhane
canDaamSau mithunangata ahni navame pakshe valarksha api ca
svaatyaam Bhaaskaravaasare SubhatithavekaadaSeenaamani
Sreemaanaavirabhooda cintyamahimaa Sreevishnucitta Anagha:”
(ta, tha, da and dha are of “tha” series and Ta, THa, Da and Dha are of “Ta” series)
Thus, it means Sree Vishnucitta (Periyazhvar) was born in 46th year of Kaliyuga (‘tatva” in katapayati sankhya and anganaam vaamatogati denotes 46 as ta is 6 and va is 4 and we have to reverse it and thus it is 46), in Krodhana year, in Jyeshtha month (Sun in Mithuna), 9th day, Sukla paksha Ekadasi thithi, Sunday, Svati Nakshatra.
Thus Periyazhvar (Vishnucittar) was born in 46th year of Kaliyuga in Krodhana year i.e. 3101 – 46 = 3055 B.C.E. and Sreemat Andal was born in 97th year of Kaliyuga in Nala year i.e. 3101 – 97 = 3004 B.C.E. The difference between the birth year of Periyazhvar and Sreemat Andal is 51 years and Periyazvar actually found out the child in a flower garden and took the child to his home and brought Her up and that child is Sreemat Andal. That is why the age difference is 51 years. The difference between the 60 years cyclic year Krodhana to Nala is also 51 years i.e. from Krodhana to Nala and thus it also fits within correctly.

Now we are going to analyse the internal evidence for the birth time of Sreemat Andal.
Sreemat Andal’s highly devotional poem is Tiruppavai (Tamil). It has 30 songs. Here one song is for each day and thus 30 songs are for 30 days of Margasirsa month and first song was sung on the first day and second song on the second day and like that up to 30 days of the month. These songs were sung to wake up the young girls in the early morning before Sun rise and to motivate them in Sree Krishna Bhakti. In Tiruppavai in 1st song, which was sung on the first day of Margasirsa month, Sreemat Andal mentioned two things.
The first line is,
“Maargazhi thingal Mati niraintha nannaalaal”
This means that on the first day of Margasirsa month (Maargazhi Thingal), the Moon was either Full Moon or near Full Moon (Mathi is Moon in Tamil and Niraintha means with fully filled in). In Candramana calendar, based on Moon’s revolution around Earth, there are two types, one is Paurnamanta where the Candramana month begins on the next day of Full Moon (Pratama thithi after Paurnamai Krishna Paksha) and ends on the day of Full Moon and Amanta type where the Candramana month begins on the next day of New Moon (Pratama thithi after Amavasya Sukla Paksha) and ends on the day of New Moon. Since here the Month began with Full or near Full Moon, it is Paurnamanta type of Candramana month of Margasirsa.

In Tiruppavai, at the 4th line of 13th song (which was sung on the 13th day early morning before Sun rise) it was mentioned as,
“Velli ezhunthu Viyazham urangitru”
which means that on the 13th day early morning before Sunrise, Venus rose (in the East, Velli is Venus and ezhunthu means rose) and Jupiter set (in the west, Viyazham is Jupiter and urangitru means set). Thus on the 13th day early morning i.e on the near completion of 12th day of Margasirsa month, Venus rose in the east before Sun and Jupiter set in the west. Since the rise of Venus and setting of Jupiter especially the rise of Venus must be before Sun rise, because if the Venus rises after Sun rise, one cannot see the rise of Venus, as it will be obscured by the bright Sun light. Venus is always close to Sun because it revolves around the Sun within the elliptical orbit of the Earth. The maximum elongation of Venus i.e. the difference between the longitude of Sun and Venus is 45 to 47 degrees only. The songs were sung in the early morning before Sun rise. Hence it means that Venus rose in the east just before Sun rise in the east on this day. Then Jupiter is revolving the Sun external to the elliptical orbit of Earth. Hence it always rises in the east and sets in the west, as the Earth rotates on its axis from west to east. Thus on the 13th day early morning Jupiter set in the west at Sunrise. This means that Jupiter was opposite to Sun and Venus in the zodiac circle i.e. around 180 degrees away from Sun and Venus.

Since this Margasirsa month began on the first day of pratama thithi of Krishna Paksha, then on the end of 12th day, the difference between the longitude of Sun and Moon will be 24 to 42 degrees, depending on the time of occurrence of Paurnamai and Amavasya, as Amavasya occurs after 14th to 16th day from Paurnami. Hence the longitude of Moon is 24 to 42 degrees less than that of Sun, on the completion of 12th day in Krishna Paksha. Since this is Margasirsa month in Candramana Paurnamanta calendar, Sun and Venus will be at Dhanus or in Vrischika zodiac sign. There is a difference between Candramana and Sauramana Calendar. Sauramana Calendar is based on the Earth’s revolution around the Sun. In Sauramana Calendar only, at the beginning of Margasirsa month, Sun will be at 240 degrees. In Candramana Calendar it will be less than 240 degrees, up to a maximum of 27 degrees less and when the difference touches 30 degrees, it will be calculated as excess (Adhika) month, as in 30 days, the Earth will revolve 30 degrees around the Sun making it as a month. (Earth’s revolution around the Sun is counted as Sun’s revolution and hence Sun’s revolution for 30 degrees in 30 days is counted as a month). Thus the longitude of Sun can be less than 240 degrees and hence Sun can be in Vrischika zodiac sign. Then Moon will be in Vrischika or Tula zodiac sign, Venus in Vrischika and Jupiter is in Mithuna or Vrishibha zodiac sign, in the year of Tiruppavai, i.e. when Sreemat Andal had grown up as a young girl.

Now since Jupiter revolves around the Sun in 11.8609631541 years for one full revolution. Thus once in (almost) 12 years only Jupiter will be at Vrishibha or Mithuna zodiac sign. Based on this, we can calculate in which year Jupiter was at Mithuna or just before Mithuna. After that we can fix Sun and then Moon. Finally the longitude of Venus is calculated and it must be just 5 to 10 degrees less than the longitude of Sun, as Venus rose just before Sun rise. The year which satisfies all these 4 conditions, will be the year of Tiruppavai.

The Graha Laghava is an astronomical text wrote by Sri Ganesa Daivajna in 1442nd year of Salivahana Saka i.e. 1520 C.E. (500 years before present). He lived in the area of Maharashtra. In that text he wrote the mean (Madhya) positions of Graha and Sighrakendra of Venus and Mercury, at Sun rise on the Sukla Paksha Pratama thithi of Chaitra month of 1442nd Salivahana Saka year at Ujjaini. From that using the Trigonometric calculations as found in the ancient astronomical texts of our Nation, any one can calculate the mean positions of Graha for any date either past or future or for the present year. From the mean position of Graha, by applying Desantara, Manda, Sighra and Bhujantara corrections, we can get the exact (sphuta) positions of the Graha for any day at any place. First we have to calculate the Ahargana (the number of days elapsed since the epoch i.e. the reference year) and then calculate the Mandoccha and Sighroccha of the Graha for the required year. Based on this we can calculate the exact Graha position. The details of these calculations are fully explained in my book “Astronomical Evidence of the Date of Mahabharata War” which can be read as a Kindle edition in amazon.in, amazon.uk.in and amazon.com.

Now the results are,
On the 108th year of Kaliyuga (2993 B.C.E.) when Sreemat Andal was 11 years old girl, on completion of 12th day, on the early morning of the 13th day of Candramana Paurnamanta Margasirsa month, the exact positions of 4 Graha were,
1. Sun 233 Degrees 36 Minutes, 2. Moon 191 Degrees 43 Minutes, 3. Venus 227 Degrees 35 Minutes and 4. Jupiter 61 Degrees 17 Minutes.
Venus was 6 degrees and 1 minute less than Sun and hence satisfied. Jupiter was 174 degrees and 19 minutes less than Sun and 166 degrees and 18 minutes less than Venus and hence it is at the opposite of the zodiac sign to Sun and Venus. Hence it is satisfied. Moon was 41 degrees 53 minutes less than Sun and hence satisfied. Sun was in the end part of Vriscika (210 to 240 degrees) and hence it is acceptable for Candramana Paurnamanta Calender. Venus was in Vriscika, Moon was in Tula and Jupiter was in Mithuna zodiac sign. Thus all are acceptable.
All these satisfy the fore mentioned 4 conditions. Hence the year at which Sreemat Andal sung Tiruppavai is 108 Kali (2993 B.C.E.)and it confirms the birth year of Sreemat Andal at 97 Kali (3004 B.C.E.) as given in the sloka of the text Araayirappadi Guru Parampara Prabhavam written 1000 years ago by Pinbazhakiya Perumal Jeeyar, who was a disciple of Nampillai who in turn lived during the time of Sreemat Ramanujacaryar.

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