Equinoxes — How they precess and sync with the phases of Moon, i.e., the Lunar tithīs

Equinoxes — Solar and how the full Moon — Lunar decided the five year yuga system of Vedāṅga Jyotiṣa in the past and how it is a Pure Astronomy Science of solar calendar only and further, just as an attaché, requires lunar tithī to wait upon equinox day.

Understanding directions from previous short articles/notes

In one of the previous few articles I 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 intermediate of Zenith and Nadir which is nothing but the ecliptic-declination of our places/latitudes. It would mean that by the Atharvavedic 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 of specific directions also precisely. These readings were very precise and accurate to the minutes and seconds. The sense of direction is as old as Rgveda. And this sense of direction comes from citing true east, which could had been sought only on the equinoxes. To cite the exact equinoxes our anscestors found a way to sync Solar seasons with Lunar months. To sync more with precession they found the way to compute syncing of lunar days with next coming lunar days of next equinoxes. To understand this phenomena I give an example below.

Lets take an example of five years yuga system mentioned in Vedāṅga and lets elaborate the condition of Viṣuva, i.e., Equinox w.r.t Lunar tithīs.

Vedāṅga verses on tithīs on Equinox

प्रथमं सप्तमं चाहुरयनाद्यं त्रयोदशम्। चतुर्थम् दशम् चैव द्विर्युग्मं बहुले त्वृतौ॥९॥ वेदाङ्ग ज्योतिषम्

prathamaṃ saptamaṃ cāhurayanādyaṃ trayodaśam। caturtham daśam caiva dviryugmaṃ bahule tvṛtau॥9॥ Vedāṅga Jyotiṣam

Now lets study five years in contemporary times.

Study of past five year and few forth-coming years.

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 Amavasya, the pratipada tithī has moon exactly where the Sun was on equinox day, a day earlier, from the above observations. Remember that the Sun will be in the same Rashi for the whole month but it will cross the same Nakṣatra, once or twice in the whole month in Krishna or Shukla Paksha. 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 is the replicated case given in VJ.

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.)

VJ 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 VJ has not yet started with nomenclatures like pratipada, saptamī but simply says prathama-saptama-chaturtham-daśam etc.

Now VJ says it begins with

वसुस् त्वष्टा भवोऽजश् च मित्रः सर्पाश्विनौ जलम् ।धाता कश् चायनाद्याश् चार्थपञ्चमभस् त्व् ऋतुः ॥ ९

vasus tvaṣṭā bhavo’jaś ca mitraḥ sarpāśvinau jalam ।dhātā kaś cāyanādyāś cārthapañcamabhas tv ṛtuḥ ॥ 9

[Vasus~ deity of Śraviṣthā]

So, now can you imagine Vasu-Vāsavaḥ, i.e., means when Dhaniṣtḥā will be experiencing Sun and Moon Together? Yes, now you can…

But wait!, this same phenomena can happen on and around Winter Solstice day also, then how to resolve whether this phenomena belongs to only Vasanta- sampāt, 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 VJ.

Lets understand through śābdabodha prakriyā — understanding of the sentences in Nyāya way.

We now have certain verses in VJ which gives us an account of isolating a date and identifying the exact Viṣuva date with the help of some calculation.

According to Nyāya, the sannikarṣa, i.e., proximity, in the sentence between the pada and padaartha smaraNa-and the vyaapaara will also matter. So this would also mean correct in the continuity of Vaakyas-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 around WS). Now read the three verses of the VJ below.

VJ verse no. 31, 32, and 33

The verses are about the calculations to cite, isolate and identify the parva and so verses 31 and 33 gives a complete idea how to cite the tithī. Now how would you avoid the middle verse on Māghaśuklapravṛtasya…, indeed the Viṣuva 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 VJ.

Now read Shri K V Sharma’s note in VJ book with translation.

Note that the calculations are made for the parvas between two Viṣuvas, i.e., vernal to autumnal and not Winter solstise to summer solstice, infact no such verse is available. 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 which has been unnecessarily being sought for Winter solstice point. Secondly, why would he give verse 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 where both Sun and Moon are present on equinox day. The next day of Viṣuva is pratipadā which marked the new year according to the VJ text then. Not only this that pratipada as a word is absent in VJ, it is completely silent on Agastya visibility which has been one of the most interesting phenomena recorded in some of the other astronomical books. Read here.

I have proved this 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 give that Samvatsara 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.

1. One cannot avoid the verse no. 32 between 31 and 33.
2. Māgha month was experiencing Vasanta and Śraviṣthā was experiencing Vernal equinox. Timing ; around 21500 BCE. During this time Agastya was only visible till south of Kāśī. Lagadha certainly missed Agastya’s visibility from his place.

Next in line, sometime down the lane, as time permits, we will see how Tapas word in one of the verses of VJ is deceptive and created all this confusion among the scholars and finally evaluate how old VJ is with all the evidence.

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Footnote and reference

• *dwelling in Atharva veda
• VJ; Vedāṅga Jyotiṣam
• Viṣuva=Vernal equinox, Viṣuvaan= Autumnal equinox
• Identifying “Udagayana” with Sun’s course in “Northern Hemisphere”; An evidence from Āpastamba-gṛhya-sūtra