Precession of Equinoxes and
Sun's Transit in the Vṛddha-Gārgīya Jyotiṣa


Sunder Chakravarty, Research Associate
R.N. Iyengar, Distinguished Professor

CAHC, IKS Centre of MoE
Jain University, Bangalore, India


5-Nov-2022, BIHS Mumbai

ज्योति:शास्त्रम् (Astral Science)

  • Starts with observations of - sun, moon and the planets- in the background of stars
  • Progresses - from broad observations to finer observations of positions and movements
  • Further progresses towards a computational model

वृद्धगार्गीयज्योतिषम् (VGJ)

  • Big text ~5000 verses and some prose, 24 aṅga-s, 40 upaṅga-s
  • CAHC has published a critical edition of 7 chapters from the 1st and 2nd aṅga

Focus of this talk - two Sun Transit chapters of VGJ

1. आदित्यचारः 11th section
2. ऋतुस्वभावः 59th section, chapters 1-6

Sun's Annual Swing

  • An observer watching every sun rise through the year will see this swing
    img right:60%
uttarāyaṇa start
(winter solstice)		 vernal equinox dakṣiṇāyana
(summer solstice)		 autumn equinox
sun's
longitude		 270° 0° 90° 180°
  • In one year, the Sun makes
    • one uttarāyaṇa (south-to-north) and one dakṣiṇāyana (north-to-south) swing
    • the extreme points are solstices, winter and summer respectively
    • equinox is the mid point of these swings - vernal and autumn equinoxes

Nakṣatra-s

  • Nakṣatra-s are zones/stars on the ecliptic belt in the sky through which Moon, Sun and planets travel. They contain one or constituent stars
  • Using clock analogy
    • Nakṣatra-s are the dial markings - 27(28)in all
    • The quicker hand is the Moon - one round a sidereal month
    • The slower hand is the Sun - one round a sidereal year .
  • Stars of some nakṣatra-s are unambiguously identified
    • कृत्तिका, रोहिणी, मघा, हस्ता, चित्रा,स्वाति, विशाखे, ज्येष्ठा, मूला
  • Others have some ambiguity
    • आर्द्रा, श्रविष्ठा/धनिष्ठा, रेवती
  • These sources help identify stars of nakṣatra-s
    • Gondalekhar(2013), Abhyankar(1991), Saha and Lahiri(1955), PT, VGJ, ...

Precession of the equinoxes

  • Precession has the following effects
    • The nakṣatra marking the seasons/equinoxes move by 1 nakṣatra every ~1000 years
    • The pole star has drifted from abhayadhruva (thuban) around 3000 BCE to around dhruva (polaris) now
  • It is caused by wobble of the earth's axis much like wobble of a spinning top.
  • In the clock analogy precession is rotation of the season dial
    • In direction opposite to Sun/Moon hand
    • And takes ~26000 years to complete a round
  • Is an important phenomena to date astronomical observations
    • In our approach we precess mutiple stars to date observations to minimize errors

Nakṣatra Listings

  • The table shows 83 constituent stars of the nakṣatra-s per VGJ

  • Vedic, Jaina & Baudha texts have astrograph and count information

  • Proxy stars for each nakṣatra, help model the ādi, ardha, anta ( begin, mid, end ) in the text

  • A few astrographs
    img width

आदित्यचारः (Sun's transit)

Verse From To Ṛtu Span
श्रविष्ठादीनि चत्वारि पौष्णार्धञ्च दिवाकरः ।
वर्धयन् सरसस्तिक्तं मासौ तपति शैशिरे ॥ 47		 श्रविष्ठा begin रेवती mid शिशिर 270°-330°
रोहिण्यन्तानि विचरन् पौष्णार्धाद्याच्च भानुमान् ।
मासौ तपति वासन्तौ कषायं वर्धयन् रसम्॥ 48		 रेवती mid रोहिणी end वसन्त 330°-30°
सार्पार्धान्तानि विचरन् सौम्याद्यानि तु भानुमान् ।
ग्रैष्मिकौ तपते मासौ कटुकं वर्धयन् रसम्॥ 52		 मृगशिरा begin आश्लेषा mid ग्रीष्म 30°-90°
सावित्रान्तानि विचरन् सार्पार्धाद्यानि भास्करः ।
वार्षिकौ तपते मासौ रसमम्लं विवर्धयन्॥ 53		 आश्लेषा mid हस्ता end वर्षा 90°-150°
चित्रादीन्यथ चत्वारि ज्येष्ठार्धञ्च दिवाकरः।
शारदौ लवणाख्यं च तपत्याप्याययन् रसम्॥ 54		 चित्रा begin ज्येष्ठा mid शरद् 150°-210°
ज्येष्ठार्धादीनि चत्वारि वैष्णवान्तानि भास्करः ।
हेमन्ते तपते मासौ मधुरं वर्धयन् रसम् ॥ 55		 ज्येष्ठा mid श्रवण end हेमन्त 210°-270°
  • Similar information is found in the PT as prose
    • Maps each of 6 ṛtu to a span 4½ nakṣatra ( of 61 days)
    • PT book dates 6 bright stars(⭐) to 1350-1130 BCE, based on visibility in their stated seasons
  • An improved dating fits below for their stated seasons
    • 9 circled seasonals(🟢) nakṣatra-s
      27 proxy stars
      83 constituent stars
    • This yields 50 years around 1250 BCE - a finer window

आदित्यचारः - date estimation

  • From the text
    • nakṣatra-s are equally spaced at 13.33° - given seasons are of equal of 4½ nakṣatra-s
    • शिशिर start is sun with श्रविष्ठादि taken as 270°
    • Given the nakṣatra-s sequence and above, span of each nakṣatra is obtained
  • The best fit method finds the epoch where most stars of nakṣatra-s are in their prescribed span
    • Get longitude of 83 stars from -2500 to 500 in 50 year epoch steps
    • For each epoch compute this error metric
    • The epoch with lowest error metric is the best fit

ननतनतननतनतनतनतन

ऋतुस्वभावः

  • Describes Sun's path through

    • 12 vaidika and equivalent laukika months and 12 nakṣatra-s for each of these months - ~30° apart
    • 6 seasons and their months

  • This is different from आदित्यचारः

    • Ṛtu sequence begins with वसन्त not शिशिर
    • Ṛtu are related to months, not nakṣatra span & boundaries
    • श्रविष्ठा is past its time when शिशिर starts, not heralding शिशिर
    • A 12 month solar zodiac, obviating intercalation, emerges

In closing

  • 2 Ayana/6 Ṛtu based sun transit conceptualized earlier - ~ 1700 BCE
  • VGJ/आदित्यचारः observations date to ~1250 BCE with 4½ nakṣatra-s span per season
  • VGJ/ऋतुस्वभावः observations date to ~500 BCE with 12 solar months
  • VGJ is layered and contains information across generations of observations and inferences
  • Solar zodiac is certainly part of original Indian knowledge - that has been recorded and evolved over time

From Observations to Computations
Vedic अथर्ववेद परिशिष्ट Atharvaveda-pariśiṣṭa (AVP)
Vedāṅga पराशरतन्त्रम् Parāśara Tantram(PT)
व्रद्धगार्गीय ज्योतिषम् Vṛddhagārgīyā Jyotiṣam (VGJ)
लागधीय वेदाङ्गज्योतिषम् Lagadhiyā Vedāṅga Jyotiṣam (LVJ)
Jain सूर्य चन्द्र प्रज्ञप्ति Sūrya-candra-prajñapti (SCP)
Baudha शार्दूलकर्णावदान Śardūlakarṇāvadāna (SKA)
Siddhānta आर्यभटीयम् Āyrabhaṭīyam(AB)

Transition from 28 to 27 nakṣatra-s
(अभिजित् , श्रवण, धनिष्ठा/श्रविष्ठा)

  • Winter solstice drift can be seen
    • श्रविष्ठार्धा in Maitrayani Aranyaka Upanishad to
    • श्रविष्ठादि in PT/VGJ
  • At some point in the transition period
    • धनिष्ठा is named the winter solstice nakṣatra
    • अभिजित् is eliminated to pack 6 ṛtu of 4½ nakṣatra-s
    • 27 nakṣatra-s equal regime takes hold for the sun
    • 28 nakṣatra-s unequal regime stays for the moon
  • Validating the transition period with
    • श्रविष्ठा as β Aqr, श्रवण as β Del(श्रवण/धनिष्ठा post transition) per Abhyankar
    • the 9 seasonal nakṣatra-s remain in bound from 1700-1350bce
  • The 6 solar ṛtu system
    • started ~1700 BCE with day counts and per ṛtu
    • stabilized ~1300 BCE with 4½ nakṣatra-s per ṛtu

KYV Samhita

4.4.10 अनुवाक 10 नक्षत्रेष्टकाः

कृत्तिका नक्षत्रमग्निर्देवताऽग्ने रुचः स्थ प्रजापतेर्धातुः सोमस्यर्चे त्वा रुचे त्वा द्युते त्वा भासे त्वा ज्योतिषे त्वा
रोहिणी नक्षत्रम् प्रजापतिर्देवता मृगशीर्षं नक्षत्रं सोमो देवताऽऽर्द्रा नक्षत्रं रुद्रो देवता पुनर्वसू नक्षत्रमदितिर्देवता तिष्यो नक्षत्रम् बृहस्पतिर्देवताऽऽश्रेषा नक्षत्रं सर्पा देवता मघा नक्षत्रम् पितरो देवता फल्गुनी नक्षत्रम्

अर्यमा देवता फल्गुनी नक्षत्रम् भगो देवता हस्तो नक्षत्रं सविता देवता चित्रा नक्षत्रमिन्द्रो देवता स्वाती नक्षत्रं वायुर्देवता विशाखे नक्षत्रमिन्द्राग्नी देवता अनूराधा नक्षत्रम् मित्रो देवता रोहिणी नक्षत्रमिन्द्रो देवता विचृतौ नक्षत्रम् पितरो देवताऽषाढा नक्षत्रमापो देवताऽषाढा नक्षत्रं विश्वे देवा देवता श्रोणा नक्षत्त्रं विष्णुर्देवता श्रविष्ठा नक्षत्रं वसवो

देवता शतभिषङ् नक्षत्रमिन्द्रो देवता प्रोष्ठपदा नक्षत्रमज एकपाद् देवता प्रोष्ठपदा नक्षत्रमहिर् बुध्नियो देवता रेवती नक्षत्रम् पूषा देवताऽश्वयुजौ नक्षत्रमश्विनौ देवताऽपभरणीर्नक्षत्रं यमो देवता
पूर्णा पश्चाद्यत्ते देवा अदधुः ॥

4.4.11 अनुवाक 11 ऋतव्या इष्टकाः

मधुश्च माधवश्च वासन्तिकाव् ऋतू
शुक्रश्च शुचिश्च ग्रीष्माव् ऋतू
नभश्च नभस्यश्च वार्षिकाव् ऋतू
इषश्चोर्जश्च शारदाव् ऋतू
सहश्च सहस्यश्च हैमन्तिकाव् ऋतू
तपश्च तपस्यश्च शैशिराव् ऋतू
अग्नेरन्तःश्लेषोऽसि कल्पेतां द्यावापृथिवी कल्पन्तामाप ओषधीः कल्पन्तामग्नयः पृथङ् मम ज्यैष्ठ्याय सव्रताः

References

Diff of Nakṣatra-s list
img

- This is a 11 slide deck, - Based on a paper published last year - Cover Sun's transit info in VGJ - Context info on Ayana, Equinox, Precession, Nakshatra's - Will walk through dating techniques - Trace Evolution of Indian solar zodiac

- VGJ contains observations and portends - Observations are the focus of this talk - Mention pre-sidd PT/VGJ/LVJ/Vedic . - Siddhantic - Aryabhatiyam, , Bhaskaracharya, Madhava, etc

- While Uttarayana is the start, the zero is at the equinox - This is for computation ease as longitutes are available wrt equinox

![bg right:50% w:100%](sun-transit-clock-analogy.png)

- In this pic moon is with Rohini :) - Tropical year is uttyna to uttyna 365.25 days - Sidereal year/month is Naks to Naks ( 20min shorter than 365.25 )/27.3 - Synodic month is amavasya to amavasya 29.5 - Naks sequence has remained stable for a long duration - Starting with कृत्तिका 4.4.10 of KYV, Ashwini is the current memorized sequence - Abhijit continues to be SCP , while VGJ/PT text have dropped

- Eqnx defn is sun at the junction of ecliptic and equator - Sun rise is most due east - Precession causes equinox to drift by 1 day every 72 days - Uttarayana drift is an example

- Try color Invert Top RtMan|Invert Colors - Precession is the reason why the *nakṣatra* marking the seasons/equinoxes move by 1 *nakṣatra* every ~1000 years - It is caused by wobble of the earth's axis much like wobble of a spinning top. - Precession is rotation of the *nakṣatra* dial - In direction opposite to Sun/Moon hand - And takes ~26000 years to complete a round

- Lists by Lahiri, Abhyankar, RNI ( largely overlap) - Nakshatra spans are equal 13.33 deg - 27 nakshatras are 360 deg - Proxy stars/83 stars are unqually spaced - Unequal treatment needs more work - for moon motion

- talk about 9 seasonal , 6 bright PT, 26 proxy and 83 constituent stars - Ensure PT prose is mentioned - Improved dating because it uses multiple actual stars, factoring aadi, ardha, anta and not 1 star and with the assumptions that others are well defined on that basis - With a single star - choice of an alternate star 6 degrees away is a 500 year error margin

- Error measures how far Naks is from its prescribed span. - The span is derived from Shravistadi at 270 and the naks sequence - Stellarium scripts to scrape longitudes - Python to crunch and plot

- The smooth lines are for better visualization ; possible connection to moons wavy path - The Chaitradi month names are used for solar months - like tamil months now - The months names closely map with sun's naks of the opposite season - We can surmise that the month name is derived from full moon naks

--- <style scoped> h2 { margin-bottom:20px;} { background: silver} </style> Fitting Stars to Nakshatras ![bg fit blur](sun-transit-containment-trend.png)