Equinoxes — How they precess and sync with the phases of Moon, i.e., the Lunar Tithīs in Vedāṅga Jyotiṣa
Vedāṅga Jyotiṣa is a one of the six limbs of Vedas. The Brāhamaṇas, which are primarily prose, contain in-depth accounts of sacrificial rituals and the ways in which they are to be performed, as well as they contain commentaries on their meanings and related subjects. For yajnādi-sacrifices and righteous rituals the knowledge of appropriate time was sought and for which the Vedāṅga Jyotiṣa comes as an aid. Among all the times/seasons (chāturmāsa) of the year the new year, i.e., Saṃvatsara was the most important event for which many ritualistic actions were sought with the help of Brāhamaṇas. The methods of calculations of Saṃvatsara comes readily from Vedāṅga Jyotiṣa.
I would like to make it clear that if Vedāṅga Jyotiṣa is a one of the six limbs of Vedas, its calculations should not differ from the injunctions of Brāhamaṇas. Know that Mimāṃsā Paribhāṣā says — “tatra vedo dvividhaḥ — mantra rūpo brāhmaṇa rupaśceti.” Therefore, if the saṃvatsara beginning in Vedas and Brāhmaṇas are from Vasanta / Spring season, then the same has to be in Vedāṅga Jyotiṣa too.
The year in Vedic and Saiddhāntic times followed the solar year calendar which apparently seemed to be Luni-Solar since it incorporated many systems of measurements of time to understand how these used to vary from the solar year. In doing so they observed and recorded fantastic informations of the past from deep antiquity, like the Saṃvatsara happening in certain Nakṣatra.
Equinoxes are measured by Solar/Saura (degree — Rāśi based) / Savana (sunrise) / Season’s year. While the full (Pūrnimānta)or the new moon (mānta)— Lunar year, syncing it with vernal equinox, the five year yuga system of Vedāṅga Jyotiṣa was also followed until recently during Chandragupta Maurya’s times.
It is a Pure Astronomy Science of Solar calendar only, and Luni Solar just act as an attaché to Solar year which requires Lunar Tithīs to wait upon the Equinox day.
Understanding directions from previous short articles/notes
In one of the previous few articles I had explained the evolutionary phase of sense of direction with the help of Atharva Vedic illustrations on direct and intermediate directions giving us 8 specific directions to be dealt during the errection of a dwelling*. This gave us a clear idea that by the time of Atharva Veda we were able to see these intermediate directions as well as the intermediate of Zenith and Nadir which is nothing but the near ecliptic on horizon from where the declination of the stars are observed which differs a little from our places as per our latitudes.
It would mean that by the Atharva-vedic times we were able to use Gnomon very properly, precisely and accurately. By the time of Sūryasiddhānta, when we had accurate sine tables, we were measuring the shadows of the gnomon on specific directions also precisely. These readings were very precise and accurate to the minutes and seconds. The sense of direction is as old as Ṛg-Veda. And this sense of direction comes from citing the true east, which could had been sought only on the days on equinoxes, twice a year. To cite the exact equinoxes our anscestors found a way to sync Solar seasons with Lunar months. To sync more with preciseness, they found the way of computation of lunar days syncing with coming lunar day of consecutive equinox. The subsequent Tithī would never be the same in the five years of Yuga, though equinoxes divided the year accurately. To understand this phenomena I give an example below.
Lets take an example of five years yuga system mentioned in Vedāṅga and elaborate upon the conditions of Viṣuva, i.e., Equinox, w.r.t Lunar tithīs.
Vedāṅga verses on tithīs on Vedic Ayana
प्रथमं सप्तमं चाहुरयनाद्यं त्रयोदशम्। चतुर्थम् दशम् चैव द्विर्युग्मं बहुले त्वृतौ॥९॥
prathamaṃ saptamaṃ cāhurayanādyaṃ trayodaśam। caturtham daśam caiva dviryugmaṃ bahule tvṛtau॥9॥ Vedāṅga Y Jyotiṣam
Now lets study five years in contemporary times.
Study of past five year and few forth-coming years of Venal Equinox
Surya/05° Meen 55′ 46″/U Bhadrapada/1/time 4:31/dt.20.03.16/335.93º, Chandra/29° Kark 26′ 02″/Ashlesha/4/119.43º/tithī-dwadashi
Surya/05° Meen 40′ 06″/U Bhadrapada/1/time 10:29/dt.20.03.17/335.67º, Chandra/00° Dhan 39′ 13″/Mula/1/240.65º/tithī-saptami
Surya/05° Meen 39′ 13″/U Bhadrapada/1/time16:15/dt 20.03.18/335.65º, Chandra/11° Mesh 20′ 35″/Ashwini/4/11.34º-tithī-tritiya
Surya/05°Meen 38′24″/UBhadrapada/1/time 21:58/20.03.19/335.64º, Chandra/00° Kany 13′ 49″/U Phalguni/2nd pada/ 150.23º -tithī PUrNimaa (2nd pada would mean the junction of U.Phal and P. Phal are still away by 3º20' to be diametrically opposite to sun to fulfill the Uttaraphalguni and Purvaphalguni junction epoch on vernal equinox day,i.e., it is yet to arrive)
Surya /05° Meen 37′ 36″/UBhadrapada/1/ time 3:50/dt 20.03.20/335.63º, Chandra/16° Maka 37′ 35″/Shravana/2nd pada/Chandra/286.63º-tithī dwadashi( 62:35:03 hrs krishna paksha)- a trayodashi assimilated.
Surya / 05° Meen 36′ 45″/ UBhadrapada/1/ time 9:37/ dt 20.03.21/335.61º Chandra/19° Vibh 47′ 38″/Rohini/3rd pada/49.79-tithī Saptami (remains for more than 30 hrs, Shukla paksha)
Surya / 05° Meen 35′ 55″/ UBhadrapada/1/ time 15:33/ dt 20.03.22/335.60º Chandra/22° Vibh 43′ 53″/Chitra/3rd pada/53.79-tithī tritiya (Krishnapaksha)
Surya / 05° Meen 35′ 06″/ UBhadrapada/1/ time 15:33/ dt 20.03.22/335.59º Chandra/21° Kumb 05′ 02″/P Bhadrapada/1st pada/321.08-tithi Chaturdashi upto 47:06:03 (Krishnapaksha) Amavasya and pratipada assimilated ( if 24 hrs accounted) tithī Pratipada in Uttarabhadrapada on 21st March
Thus, we find that next day after the Amāvasyā, the pratipadā tithī has moon exactly where the Sun was on the Equinox day, a day earlier, from the above observations. Remember that the Sun will be in the same Rāśi for the whole month but it will cross the same Nakṣatra, once or twice in the whole month in the Kriśna or Śukla Pakṣa.
Surya was at 05° Meen 35′ 06″/ UBhadrapada/1/ time 15:33/ dt 20.03.22/335.59º Chandra/21° Kumb 05′ 02″/P Bhadrapada/1st pada/321.08-tithī Chaturdashi upto 47:06:03 , Krishnapaksha, [Amavasya and pratipada assimilated ( if 24 hrs accounted)] next day Pratipada in Uttarabhadrapada is found on 21st March.
This above evaluation of our times is the replication of the case given in Vedāṅga Jyotiṣa.
So, one can note the “precessing of equinox point” from 2016–2023, for five years from 05° Meen 55′ 46″~05°< Meen 40′ 06″~05°< Meen 39′ 13″~05°< Meen 38′24″~05°< Meen 37′ 36″~05°< Meen 36′ 45~05°< Meen 35′ 55″~05° <Meen 35′ 06″( this day is Amavasya which means Sun and Moon is in the same nakṣatra.)
Vedāṅga Jyotiṣa doesn’t advocate pūrṇimā to be the new year beginning but Shukla pakṣa prathama is the first where it starts from Vasus, we will see below how.
In this precessing the Lunar tithīs change and it wobbles from prathama, saptami, tritiya-Chaturthi, dvādaśi, pūrṇimā, saptamī-ashtamī likewise.
Note that Vedāṅga Jyotiṣa has not yet started with nomenclatures like pratipada, saptamī but simply says prathama-saptama-chaturtham-daśam etc.
Now Vedāṅga Jyotiṣa says it begins with śraviṣṭhā.
वसुस् त्वष्टा भवोऽजश् च मित्रः सर्पाश्विनौ जलम् ।धाता कश् चायनाद्याश् चार्थपञ्चमभस् त्व् ऋतुः ॥ ९॥
The nakṣatras at the beginning of the ayanas are śraviṣṭhā, chitra, ārdra, pūrvaproṣṭhapadā, ānurādhā, āśleṣa, āśvinī, pūrvāśāḍha, ūttaraphalgunī and Rohinī.
[Vasus~ deity of Śraviṣthā]
prapadyete śraviṣṭhādau ṣurya-acandramasāvudak। sārpārdhe dakṣiṇārkastu māghaṣrāvaṇyoḥ sadā ..6..RVJ..7..YVJ..
When situated at the beginning of the śraviṣṭhā segment, the Sun and the Moon begin to move north. When they reach the mid point of Aśleṣā segment they begin moving south. In the case of Sun this happens always in the month of Māgha and śravaṇa. 6..RVJ..7..YVJ.. (Traslation by TS Kuppanna Shastry)
Note 2 (by TS Kuppanna Shastry) — Prapadyete here means ‘move’, not simply ‘reach’ and ayanam means ‘movement’, primarily. The secondary meaning is ‘period of movement’.
So, now can you imagine Vasu-Vāsavaḥ, i.e., when Dhaniṣtḥā will be experiencing Sun and Moon together. To understand the Vedic Ayana coinciding with Vasanta and Vishuva of Vasanta lets look into the verses from Māitrayāṇi Araṇyaka Upaniśad.
अग्निर्गायत्रं त्रिवृद्रथन्तरं वसन्तः प्राणो नक्षत्राणि वसवः पुरस्तादुद्यन्ति तपन्ति वर्षन्ति स्तुवन्ति पुनर्विशन्ति अन्तर्विवरेणेक्षन्ति…॥ ७.१॥
Māitrayāṇi āraṇyaka upaniśad 7.1 says that, “Agni, the Gāyatrī meter, the Trivṛt stoma, the rathanthara sāman, the spring, the vital air that goes upward (prāṇa), the lunar mansions, the vasus, — they rise to the east of (of the sun).”
This statement clearly states that Agni is synonym of spring season and as the prāṇa goes upward the Sun traverses in Northern hemisphere upward from equator, and this points to Vernal equinox which points to insulation of northern hemisphere due to greater day light factor.
विश्वे देवा अनुष्टुबेकविंशो वैराजः शरत्समानो वरुणः साध्या उत्तरत उद्यन्ति तपन्ति वर्षन्ति स्तुवन्ति पुनर्विशन्ति अन्तर्विवरेणेक्षन्ति अन्तःशुद्धः पूतः शून्यः शान्तोऽप्राणो निरात्मानन्तः ॥ ७.४॥
Māitrayāṇi āraṇyaka upaniśad 7.4 says that, “The viśve devāḥ, anuśtubh meter, the ekaviṃśa stoma, the vairāja sāman, the autumn, the vital air that equalizes, the Varuṇa, the sādhyas, — they rise to the North (of the sun).
It clearly states that, the Varuṇa is synonym of autumn season and apparently Autumnal equinox.
But wait!
Sun and moon on the horizon hopping towards northern hemisphere on the day of equinox can be measured, this same phenomena can happen on and around Winter Solstice day also, in this case also sun starts coursing north ( but by remaining, rising and setting in Southern hemisphere) then how to resolve whether this phenomena belongs to only at Vishuva, i.e., Vernal Equinox and not on Uttarāyaṇa , i.e., Winter Solstice.
For that matter one needs to find what Ayana actually means. We have messed up two words namely, Udagayana and Uttarāyaṇa, and for this reason every eastern or western authors and researchers have started to think that both are similar phenomenas. How to reconcile on this matter for Vedāṅga Jyotiṣa.
First of all lets see how Saṃvatsara in Vedic texts are been recollected.
Lets understand through śābdabodha prakriyā — understanding of the sentences in Nyāya way.
From the above introcution we know Vedāṅga Jyotiṣa as one of the six limbs of Vedas. The Brāhamaṇas clearly mention
madhuśca mādhavaśca vāsantikāv ṛtu। śukraśca śuciśca graiśmāva ṛtu। nabhaśca nabhasyaśca vārṣikāv ṛtu, iśasca ūrjaśca śāradāv ṛtū, sahaśca sahasyaśca haimantāv ṛtu, tapaśca tapasyaśca śaiśirāv ṛtu।
This gives a clarity that the Brāhmaṇa and Araṇyaka text which are the inseperable part of Veda saṃhitās has first solar ṛtu as one of the vasanta’s month.
अग्निरसि वैश्वानरोऽसि । संवत्सरोऽसि परिवत्सरोऽसि । इदावत्सरोऽसीदुवत्सरोऽसि । इद्वत्सरोऽसि वत्सरोऽसि । तस्य ते वसन्तः शिरः । ग्रीष्मो दक्षिणः पक्षः । वर्षाः पुच्छम् । शरदुत्तरः पक्षः । हेमन्तो मध्यम् । पूर्वपक्षाश्चितयः । अपरपक्षाः पुरीषम् । अहोरात्राणीष्टकाः । तस्य ते मासाश्चार्धमासाश्च कल्पन्ताम् । ऋतवस्ते कल्पन्ताम् । संवत्सरस्ते कल्पन्ताम् । अहोरात्राणि ते कल्पन्ताम् । एति प्रेति वीति समित्युदिति । प्रजापतिस्त्वा सादयतु । तया देवतयाऽङ्गिरस्वद्ध्रुवः सीद १ — तैत्तिरीयारण्यकम् , प्रपाठकः ४ , अनुवाक १९
Here Taittirīya Araṇyaka clearly says Agni — Saṃvatsara — Vasanta — Head — Ahorātra — Prajāpati are related.
We now have certain verses in Vedāṅga Jyotiṣa which gives us an account of isolating a date and identifying the exact Viṣuva date with the help of some calculation. Lets see what Brāhmaṇas have to say for Viṣuva.
विषूवान् दिवाकीर्त्यम् । यथा शालायै पक्षसी । एवम्̐ संवत्सरस्य पक्षसी ।
“The two equinoxes are full of glory. They are similar to the outer wall of a house or the two fortnights of the year.”, Anuvāk 1–2–3–1 (section 6) Taittiriya Brāhmaṇa
विषुवाभ्यां वत्सरः स्यादिति शब्दविदां मतम् ।
According to Nyāya, the sannikarṣa, i.e., proximity, in the sentence between the pada and padārtha smaraṇa and the vyāpāra will also matter. So this would also mean correct in the continuity of Vākyas-sentences which shares the meaningful content of the sentences as well. How silly it would look like when you read two sentences on same subject but the middle third one will be out of context (here for Winter Solstice). Now read the three verses of the Vedāṅga Jyotiṣa below.
The verses are about the calculations to cite, isolate and identify the total number of parvas and the tithī on the day of Viṣuva, so the verse no. 31 and 33 gives a complete idea on how to cite the tithī. Now how would you avoid the middle verse on Māghaśuklapravṛtasya…, Māgha here means the lunar month. With the help of logic of proximity indeed it is talking about the Viṣuva which is happening in Māgha month, which may happen in any part of 2000 years and can flange till 30 degree which can point to atleast 3 nakṣatra and partly the fourth. But we know that its happening in Dhaniṣṭhā nakṣatra from the verse no. 9, where equinox, but not solstice, was happening within Vedāṅga Jyotiṣa.
Now, read Shri K V Sharma’s note in Vedāṅga Jyotiṣa book with translation.
Note that the calculations are made for the parvas between two Viṣuvas, i.e., vernal to autumnal and not from winter solstice to summer solstice, infact no such verse is available for winter solstice. the verses also illuminated upon the tithīs on the viṣuva days. Any wise man can understand now that why on earth would Lagadha miss this important information on nakṣatra at equinoxes when he is able to compute that which parva and tithī will arrive at Viṣuva day. Simply because he is writing Māgha month and Śraviṣthā nakṣatra in his text for vernal equinox which has been unnecessarily being sought for Winter solstice point by the researchers.
Secondly, why would Lagadha give verse no. 32 sandwiched between verse 31 and 33, because that was needed for the record. Of course, since this has pointed to Māgha month, thus this is the pointing to Śraviṣthā star, where both Sun and Moon are present on equinox day. The next day of Viṣuva is the pratipadā which marked the new year according to the Vedāṅga Jyotiṣa text.
Not only pratipadā as a (noun) word is absent in Vedāṅga Jyotiṣa, it is completely silent on Agastya’s visibility which has been one of the most interesting phenomena recorded in almost all the other astronomical texts. Read here.
I have about this issue earlier also in one of my blogs. Read here.
I have tried to read Vedas, Brāhmaṇas and all the astronomy texts by self and have tried to accumulate as many evidence to bring the correct meaning of Saṃvatsara in vedic calendar which never began from Winter Solstice day in any of the Indian Scriptures. The year beginning always had been from Vasanta-Sampāt, i.e., Vernal equinox day.
What is the takeway of this little write-up.
- One cannot avoid the presence of verse no. 32 between 31 and 33.
- Māgha month was experiencing Vasanta and Śraviṣthā was experiencing Vernal equinox. Timing ; around 21500 BCE.
- Vedāṅga Jyotiṣa is consistent with it’s new year from Vasanta-Vishuva.
Next in the line, sometimes down the lane, as time permits, we will see how Tapas word taken as month name in one of the verses of Vedāṅga Jyotiṣa by many commentators is deceptive and created all this confusion among the scholars and finally we will evaluate how old Vedāṅga Jyotiṣa is with all the evidence.
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Footnote and reference
- *dwelling in Atharva veda
- Viṣuva, Viṣuvaan= equinoxes
- Identifying “Udagayana” with Sun’s course in “Northern Hemisphere”; An evidence from Āpastamba-gṛhya-sūtra
